diff options
47 files changed, 31237 insertions, 28986 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 8e651fd6..0a6ffee6 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,12 @@ 2009-02-28 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/nruncomp.boot (genDeltaEntry): Return optimized + implementation after slot allocation. + * share/algebra: Update databases. + * algebra/strap: Update cached Lisp translation. + +2009-02-28 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/define.boot (NRTPARSE): Remove. (mkCategoryPackage): Remove dead code. (compDefineFunctor1): Tidy. diff --git a/src/algebra/strap/ABELGRP-.lsp b/src/algebra/strap/ABELGRP-.lsp index dc10e8f6..b25c65a5 100644 --- a/src/algebra/strap/ABELGRP-.lsp +++ b/src/algebra/strap/ABELGRP-.lsp @@ -26,11 +26,11 @@ (DEFUN |ABELGRP-;*;I2S;4| (|n| |x| $) (COND - ((ZEROP |n|) (|spadConstant| $ 17)) - ((< 0 |n|) (SPADCALL |n| |x| (|getShellEntry| $ 20))) + ((ZEROP |n|) (|spadConstant| $ 19)) + ((< 0 |n|) (SPADCALL |n| |x| (|getShellEntry| $ 24))) ('T (SPADCALL (- |n|) (SPADCALL |x| (|getShellEntry| $ 7)) - (|getShellEntry| $ 20))))) + (|getShellEntry| $ 24))))) (DEFUN |AbelianGroup&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -38,7 +38,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|AbelianGroup&|)) (LETT |dv$| (LIST '|AbelianGroup&| |dv$1|) . #0#) - (LETT $ (|newShell| 22) . #0#) + (LETT $ (|newShell| 27) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -47,7 +47,7 @@ (COND ((|HasCategory| |#1| '(|Ring|))) ('T - (|setShellEntry| $ 21 + (|setShellEntry| $ 26 (CONS (|dispatchFunction| |ABELGRP-;*;I2S;4|) $)))) $)))) @@ -55,16 +55,19 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . -) (5 . +) |ABELGRP-;-;3S;1| (11 . -) (|Union| $ '"failed") |ABELGRP-;subtractIfCan;2SU;2| (|Integer|) (17 . *) - (|NonNegativeInteger|) |ABELGRP-;*;Nni2S;3| (23 . |Zero|) - (|PositiveInteger|) (|RepeatedDoubling| 6) (27 . |double|) - (33 . *)) - '#(|subtractIfCan| 39 - 45 * 51) 'NIL + (|NonNegativeInteger|) |ABELGRP-;*;Nni2S;3| (|Boolean|) + (23 . |zero?|) (28 . |Zero|) (32 . |Zero|) (36 . <) + (|PositiveInteger|) (|RepeatedDoubling| 6) (42 . |double|) + (48 . -) (53 . *)) + '#(|subtractIfCan| 59 - 65 * 71) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 21 + (|makeByteWordVec2| 26 '(1 6 0 0 7 2 6 0 0 0 8 2 6 0 0 0 10 2 - 6 0 13 0 14 0 6 0 17 2 19 6 18 6 20 2 - 0 0 13 0 21 2 0 11 0 0 12 2 0 0 0 0 9 - 2 0 0 13 0 21 2 0 0 15 0 16))))) + 6 0 13 0 14 1 13 17 0 18 0 6 0 19 0 + 13 0 20 2 13 17 0 0 21 2 23 6 22 6 24 + 1 13 0 0 25 2 0 0 13 0 26 2 0 11 0 0 + 12 2 0 0 0 0 9 2 0 0 13 0 26 2 0 0 15 + 0 16))))) '|lookupComplete|)) diff --git a/src/algebra/strap/ABELMON-.lsp b/src/algebra/strap/ABELMON-.lsp index bfdc7eee..c0a9b85f 100644 --- a/src/algebra/strap/ABELMON-.lsp +++ b/src/algebra/strap/ABELMON-.lsp @@ -25,7 +25,7 @@ (DEFUN |ABELMON-;*;Nni2S;4| (|n| |x| $) (COND ((ZEROP |n|) (|spadConstant| $ 7)) - ('T (SPADCALL |n| |x| (|getShellEntry| $ 17))))) + ('T (SPADCALL |n| |x| (|getShellEntry| $ 18))))) (DEFUN |AbelianMonoid&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -33,7 +33,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|AbelianMonoid&|)) (LETT |dv$| (LIST '|AbelianMonoid&| |dv$1|) . #0#) - (LETT $ (|newShell| 19) . #0#) + (LETT $ (|newShell| 20) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -42,7 +42,7 @@ (COND ((|HasCategory| |#1| '(|Ring|))) ('T - (|setShellEntry| $ 18 + (|setShellEntry| $ 19 (CONS (|dispatchFunction| |ABELMON-;*;Nni2S;4|) $)))) $)))) @@ -50,14 +50,15 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |Zero|) (|Boolean|) (4 . =) |ABELMON-;zero?;SB;1| (|NonNegativeInteger|) (10 . *) (|PositiveInteger|) - |ABELMON-;*;Pi2S;2| |ABELMON-;sample;S;3| - (|RepeatedDoubling| 6) (16 . |double|) (22 . *)) - '#(|zero?| 28 |sample| 33 * 37) 'NIL + |ABELMON-;*;Pi2S;2| |ABELMON-;sample;S;3| (16 . |zero?|) + (|RepeatedDoubling| 6) (21 . |double|) (27 . *)) + '#(|zero?| 33 |sample| 38 * 42) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 18 - '(0 6 0 7 2 6 8 0 0 9 2 6 0 11 0 12 2 - 16 6 13 6 17 2 0 0 11 0 18 1 0 8 0 10 - 0 0 0 15 2 0 0 11 0 18 2 0 0 13 0 14))))) + (|makeByteWordVec2| 19 + '(0 6 0 7 2 6 8 0 0 9 2 6 0 11 0 12 1 + 11 8 0 16 2 17 6 13 6 18 2 0 0 11 0 + 19 1 0 8 0 10 0 0 0 15 2 0 0 11 0 19 + 2 0 0 13 0 14))))) '|lookupComplete|)) diff --git a/src/algebra/strap/BOOLEAN.lsp b/src/algebra/strap/BOOLEAN.lsp index 93546360..9241d5a1 100644 --- a/src/algebra/strap/BOOLEAN.lsp +++ b/src/algebra/strap/BOOLEAN.lsp @@ -143,18 +143,18 @@ (DEFUN |BOOLEAN;size;Nni;18| ($) (DECLARE (IGNORE $)) 2) (DEFUN |BOOLEAN;index;Pi$;19| (|i| $) - (COND ((SPADCALL |i| (|getShellEntry| $ 26)) 'NIL) ('T 'T))) + (COND ((SPADCALL |i| (|getShellEntry| $ 28)) 'NIL) ('T 'T))) (DEFUN |BOOLEAN;lookup;$Pi;20| (|a| $) (COND (|a| 1) ('T 2))) (DEFUN |BOOLEAN;random;$;21| ($) - (COND ((SPADCALL (|random|) (|getShellEntry| $ 26)) 'NIL) ('T 'T))) + (COND ((SPADCALL (|random|) (|getShellEntry| $ 28)) 'NIL) ('T 'T))) (DEFUN |BOOLEAN;convert;$If;22| (|x| $) - (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 33))) + (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 37))) (DEFUN |BOOLEAN;coerce;$Of;23| (|x| $) - (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 36))) + (SPADCALL (COND (|x| '|true|) ('T '|false|)) (|getShellEntry| $ 40))) (DEFUN |Boolean| () (PROG () @@ -178,7 +178,7 @@ (RETURN (PROGN (LETT |dv$| '(|Boolean|) . #0=(|Boolean|)) - (LETT $ (|newShell| 40) . #0#) + (LETT $ (|newShell| 44) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -192,24 +192,25 @@ (FUNCALL (|dispatchFunction| |BOOLEAN;true;$;3|) $)) (CONS IDENTITY (FUNCALL (|dispatchFunction| |BOOLEAN;false;$;4|) $)) - |BOOLEAN;not;2$;5| |BOOLEAN;~;2$;6| |BOOLEAN;and;3$;7| - |BOOLEAN;/\\;3$;8| |BOOLEAN;or;3$;9| |BOOLEAN;\\/;3$;10| - |BOOLEAN;xor;3$;11| |BOOLEAN;nor;3$;12| - |BOOLEAN;nand;3$;13| (|Boolean|) |BOOLEAN;=;3$;14| + |BOOLEAN;not;2$;5| (|Boolean|) (0 . |false|) (4 . |true|) + |BOOLEAN;~;2$;6| |BOOLEAN;and;3$;7| |BOOLEAN;/\\;3$;8| + |BOOLEAN;or;3$;9| |BOOLEAN;\\/;3$;10| |BOOLEAN;xor;3$;11| + |BOOLEAN;nor;3$;12| |BOOLEAN;nand;3$;13| |BOOLEAN;=;3$;14| |BOOLEAN;implies;3$;15| |BOOLEAN;equiv;3$;16| |BOOLEAN;<;3$;17| (|NonNegativeInteger|) - |BOOLEAN;size;Nni;18| (|Integer|) (0 . |even?|) - (|PositiveInteger|) |BOOLEAN;index;Pi$;19| - |BOOLEAN;lookup;$Pi;20| |BOOLEAN;random;$;21| (|Symbol|) - (|InputForm|) (5 . |convert|) |BOOLEAN;convert;$If;22| - (|OutputForm|) (10 . |outputForm|) |BOOLEAN;coerce;$Of;23| - (|String|) (|SingleInteger|)) - '#(~= 15 ~ 21 |xor| 26 |true| 32 |test| 36 |size| 41 |random| - 45 |or| 49 |not| 55 |nor| 60 |nand| 66 |min| 72 |max| 82 - |lookup| 92 |latex| 97 |index| 102 |implies| 107 |hash| - 113 |false| 118 |equiv| 122 |convert| 128 |coerce| 133 - |and| 138 |\\/| 144 >= 150 > 156 = 162 <= 168 < 174 |/\\| - 180) + |BOOLEAN;size;Nni;18| (|Integer|) (8 . |even?|) + (|PositiveInteger|) |BOOLEAN;index;Pi$;19| (13 . |One|) + |BOOLEAN;lookup;$Pi;20| (17 . |random|) + |BOOLEAN;random;$;21| (|Symbol|) (|InputForm|) + (21 . |convert|) |BOOLEAN;convert;$If;22| (|OutputForm|) + (26 . |outputForm|) |BOOLEAN;coerce;$Of;23| (|String|) + (|SingleInteger|)) + '#(~= 31 ~ 37 |xor| 42 |true| 48 |test| 52 |size| 57 |random| + 61 |or| 65 |not| 71 |nor| 76 |nand| 82 |min| 88 |max| 98 + |lookup| 108 |latex| 113 |index| 118 |implies| 123 |hash| + 129 |false| 134 |equiv| 138 |convert| 144 |coerce| 149 + |and| 154 |\\/| 160 >= 166 > 172 = 178 <= 184 < 190 |/\\| + 196) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0)) (CONS '#(NIL |OrderedSet&| NIL NIL |Logic&| @@ -217,21 +218,22 @@ (CONS '#((|OrderedFinite|) (|OrderedSet|) (|PropositionalLogic|) (|Finite|) (|Logic|) (|SetCategory|) - (|ConvertibleTo| 32) (|BasicType|) - (|CoercibleTo| 35)) - (|makeByteWordVec2| 39 - '(1 25 18 0 26 1 32 0 31 33 1 35 0 31 - 36 2 0 18 0 0 1 1 0 0 0 10 2 0 0 0 0 - 15 0 0 0 7 1 0 0 0 6 0 0 23 24 0 0 0 - 30 2 0 0 0 0 13 1 0 0 0 9 2 0 0 0 0 - 16 2 0 0 0 0 17 0 0 0 1 2 0 0 0 0 1 0 - 0 0 1 2 0 0 0 0 1 1 0 27 0 29 1 0 38 - 0 1 1 0 0 27 28 2 0 0 0 0 20 1 0 39 0 - 1 0 0 0 8 2 0 0 0 0 21 1 0 32 0 34 1 - 0 35 0 37 2 0 0 0 0 11 2 0 0 0 0 14 2 - 0 18 0 0 1 2 0 18 0 0 1 2 0 18 0 0 19 - 2 0 18 0 0 1 2 0 18 0 0 22 2 0 0 0 0 - 12))))) + (|ConvertibleTo| 36) (|BasicType|) + (|CoercibleTo| 39)) + (|makeByteWordVec2| 43 + '(0 10 0 11 0 10 0 12 1 27 10 0 28 0 29 + 0 31 0 27 0 33 1 36 0 35 37 1 39 0 35 + 40 2 0 10 0 0 1 1 0 0 0 13 2 0 0 0 0 + 18 0 0 0 7 1 0 0 0 6 0 0 25 26 0 0 0 + 34 2 0 0 0 0 16 1 0 0 0 9 2 0 0 0 0 + 19 2 0 0 0 0 20 0 0 0 1 2 0 0 0 0 1 0 + 0 0 1 2 0 0 0 0 1 1 0 29 0 32 1 0 42 + 0 1 1 0 0 29 30 2 0 0 0 0 22 1 0 43 0 + 1 0 0 0 8 2 0 0 0 0 23 1 0 36 0 38 1 + 0 39 0 41 2 0 0 0 0 14 2 0 0 0 0 17 2 + 0 10 0 0 1 2 0 10 0 0 1 2 0 10 0 0 21 + 2 0 10 0 0 1 2 0 10 0 0 24 2 0 0 0 0 + 15))))) '|lookupComplete|)) (MAKEPROP '|Boolean| 'NILADIC T) diff --git a/src/algebra/strap/CHAR.lsp b/src/algebra/strap/CHAR.lsp index 9fd5e64d..ef10b20b 100644 --- a/src/algebra/strap/CHAR.lsp +++ b/src/algebra/strap/CHAR.lsp @@ -126,22 +126,22 @@ (DEFUN |CHAR;coerce;$Of;12| (|c| $) (DECLARE (IGNORE $)) |c|) (DEFUN |CHAR;digit?;$B;13| (|c| $) - (SPADCALL |c| (|spadConstant| $ 23) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 29) (|getShellEntry| $ 31))) (DEFUN |CHAR;hexDigit?;$B;14| (|c| $) - (SPADCALL |c| (|spadConstant| $ 27) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 33) (|getShellEntry| $ 31))) (DEFUN |CHAR;upperCase?;$B;15| (|c| $) - (SPADCALL |c| (|spadConstant| $ 29) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 35) (|getShellEntry| $ 31))) (DEFUN |CHAR;lowerCase?;$B;16| (|c| $) - (SPADCALL |c| (|spadConstant| $ 31) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 37) (|getShellEntry| $ 31))) (DEFUN |CHAR;alphabetic?;$B;17| (|c| $) - (SPADCALL |c| (|spadConstant| $ 33) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 39) (|getShellEntry| $ 31))) (DEFUN |CHAR;alphanumeric?;$B;18| (|c| $) - (SPADCALL |c| (|spadConstant| $ 35) (|getShellEntry| $ 25))) + (SPADCALL |c| (|spadConstant| $ 41) (|getShellEntry| $ 31))) (DEFUN |CHAR;latex;$S;19| (|c| $) (STRCONC "\\mbox{`" (STRCONC (MAKE-FULL-CVEC 1 |c|) "'}"))) @@ -149,8 +149,8 @@ (DEFUN |CHAR;char;S$;20| (|s| $) (COND ((EQL (QCSIZE |s|) 1) - (SPADCALL |s| (SPADCALL |s| (|getShellEntry| $ 40)) - (|getShellEntry| $ 41))) + (SPADCALL |s| (SPADCALL |s| (|getShellEntry| $ 49)) + (|getShellEntry| $ 50))) ('T (|userError| "String is not a single character")))) (DEFUN |CHAR;upperCase;2$;21| (|c| $) @@ -184,7 +184,7 @@ (RETURN (PROGN (LETT |dv$| '(|Character|) . #0=(|Character|)) - (LETT $ (|newShell| 46) . #0#) + (LETT $ (|newShell| 55) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -195,45 +195,50 @@ (MAKEPROP '|Character| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|Boolean|) |CHAR;=;2$B;1| |CHAR;<;2$B;2| (|NonNegativeInteger|) |CHAR;size;Nni;3| - |CHAR;char;Nni$;6| (|PositiveInteger|) |CHAR;index;Pi$;4| - |CHAR;ord;$Nni;7| |CHAR;lookup;$Pi;5| |CHAR;random;$;8| - |CHAR;space;$;9| |CHAR;quote;$;10| |CHAR;escape;$;11| - (|OutputForm|) |CHAR;coerce;$Of;12| (|CharacterClass|) - (0 . |digit|) (|Character|) (4 . |member?|) - |CHAR;digit?;$B;13| (10 . |hexDigit|) - |CHAR;hexDigit?;$B;14| (14 . |upperCase|) - |CHAR;upperCase?;$B;15| (18 . |lowerCase|) - |CHAR;lowerCase?;$B;16| (22 . |alphabetic|) - |CHAR;alphabetic?;$B;17| (26 . |alphanumeric|) - |CHAR;alphanumeric?;$B;18| (|String|) |CHAR;latex;$S;19| - (|Integer|) (30 . |minIndex|) (35 . |elt|) + (|PositiveInteger|) (0 . |One|) (4 . |One|) (|Integer|) + (8 . -) |CHAR;char;Nni$;6| |CHAR;index;Pi$;4| + |CHAR;ord;$Nni;7| (14 . +) |CHAR;lookup;$Pi;5| + (20 . |random|) |CHAR;random;$;8| |CHAR;space;$;9| + |CHAR;quote;$;10| |CHAR;escape;$;11| (|OutputForm|) + |CHAR;coerce;$Of;12| (|CharacterClass|) (25 . |digit|) + (|Character|) (29 . |member?|) |CHAR;digit?;$B;13| + (35 . |hexDigit|) |CHAR;hexDigit?;$B;14| + (39 . |upperCase|) |CHAR;upperCase?;$B;15| + (43 . |lowerCase|) |CHAR;lowerCase?;$B;16| + (47 . |alphabetic|) |CHAR;alphabetic?;$B;17| + (51 . |alphanumeric|) |CHAR;alphanumeric?;$B;18| + (|String|) (55 . |new|) (61 . |concat|) |CHAR;latex;$S;19| + (67 . |#|) (72 . |one?|) (77 . |minIndex|) (82 . |elt|) |CHAR;char;S$;20| |CHAR;upperCase;2$;21| |CHAR;lowerCase;2$;22| (|SingleInteger|)) - '#(~= 41 |upperCase?| 47 |upperCase| 52 |space| 57 |size| 61 - |random| 65 |quote| 69 |ord| 73 |min| 78 |max| 88 - |lowerCase?| 98 |lowerCase| 103 |lookup| 108 |latex| 113 - |index| 118 |hexDigit?| 123 |hash| 128 |escape| 133 - |digit?| 137 |coerce| 142 |char| 147 |alphanumeric?| 157 - |alphabetic?| 162 >= 167 > 173 = 179 <= 185 < 191) + '#(~= 88 |upperCase?| 94 |upperCase| 99 |space| 104 |size| + 108 |random| 112 |quote| 116 |ord| 120 |min| 125 |max| 135 + |lowerCase?| 145 |lowerCase| 150 |lookup| 155 |latex| 160 + |index| 165 |hexDigit?| 170 |hash| 175 |escape| 180 + |digit?| 184 |coerce| 189 |char| 194 |alphanumeric?| 204 + |alphabetic?| 209 >= 214 > 220 = 226 <= 232 < 238) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0)) (CONS '#(NIL |OrderedSet&| NIL |SetCategory&| |BasicType&| NIL) (CONS '#((|OrderedFinite|) (|OrderedSet|) (|Finite|) (|SetCategory|) (|BasicType|) - (|CoercibleTo| 20)) - (|makeByteWordVec2| 45 - '(0 22 0 23 2 22 6 24 0 25 0 22 0 27 0 - 22 0 29 0 22 0 31 0 22 0 33 0 22 0 35 - 1 37 39 0 40 2 37 24 0 39 41 2 0 6 0 - 0 1 1 0 6 0 30 1 0 0 0 43 0 0 0 17 0 - 0 9 10 0 0 0 16 0 0 0 18 1 0 9 0 14 0 - 0 0 1 2 0 0 0 0 1 0 0 0 1 2 0 0 0 0 1 - 1 0 6 0 32 1 0 0 0 44 1 0 12 0 15 1 0 - 37 0 38 1 0 0 12 13 1 0 6 0 28 1 0 45 - 0 1 0 0 0 19 1 0 6 0 26 1 0 20 0 21 1 - 0 0 9 11 1 0 0 37 42 1 0 6 0 36 1 0 6 - 0 34 2 0 6 0 0 1 2 0 6 0 0 1 2 0 6 0 + (|CoercibleTo| 26)) + (|makeByteWordVec2| 54 + '(0 11 0 12 0 9 0 13 2 14 0 0 0 15 2 9 + 0 0 0 19 1 9 0 0 21 0 28 0 29 2 28 6 + 30 0 31 0 28 0 33 0 28 0 35 0 28 0 37 + 0 28 0 39 0 28 0 41 2 43 0 9 30 44 2 + 43 0 0 0 45 1 43 9 0 47 1 9 6 0 48 1 + 43 14 0 49 2 43 30 0 14 50 2 0 6 0 0 + 1 1 0 6 0 36 1 0 0 0 52 0 0 0 23 0 0 + 9 10 0 0 0 22 0 0 0 24 1 0 9 0 18 0 0 + 0 1 2 0 0 0 0 1 0 0 0 1 2 0 0 0 0 1 1 + 0 6 0 38 1 0 0 0 53 1 0 11 0 20 1 0 + 43 0 46 1 0 0 11 17 1 0 6 0 34 1 0 54 + 0 1 0 0 0 25 1 0 6 0 32 1 0 26 0 27 1 + 0 0 9 16 1 0 0 43 51 1 0 6 0 42 1 0 6 + 0 40 2 0 6 0 0 1 2 0 6 0 0 1 2 0 6 0 0 7 2 0 6 0 0 1 2 0 6 0 0 8))))) '|lookupComplete|)) diff --git a/src/algebra/strap/CLAGG-.lsp b/src/algebra/strap/CLAGG-.lsp index 8af8cab5..6f4a5528 100644 --- a/src/algebra/strap/CLAGG-.lsp +++ b/src/algebra/strap/CLAGG-.lsp @@ -140,43 +140,43 @@ (DEFUN |CLAGG-;find;MAU;5| (|f| |c| $) (SPADCALL |f| (SPADCALL |c| (|getShellEntry| $ 9)) - (|getShellEntry| $ 18))) + (|getShellEntry| $ 24))) (DEFUN |CLAGG-;reduce;MAS;6| (|f| |x| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 21))) + (|getShellEntry| $ 27))) (DEFUN |CLAGG-;reduce;MA2S;7| (|f| |x| |s| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) |s| - (|getShellEntry| $ 23))) + (|getShellEntry| $ 29))) (DEFUN |CLAGG-;remove;M2A;8| (|f| |x| $) (SPADCALL (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 25)) - (|getShellEntry| $ 26))) + (|getShellEntry| $ 31)) + (|getShellEntry| $ 32))) (DEFUN |CLAGG-;select;M2A;9| (|f| |x| $) (SPADCALL (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 28)) - (|getShellEntry| $ 26))) + (|getShellEntry| $ 34)) + (|getShellEntry| $ 32))) (DEFUN |CLAGG-;remove;S2A;10| (|s| |x| $) (SPADCALL (CONS #'|CLAGG-;remove;S2A;10!0| (VECTOR $ |s|)) |x| - (|getShellEntry| $ 31))) + (|getShellEntry| $ 37))) (DEFUN |CLAGG-;remove;S2A;10!0| (|#1| $$) (SPADCALL |#1| (|getShellEntry| $$ 1) - (|getShellEntry| (|getShellEntry| $$ 0) 30))) + (|getShellEntry| (|getShellEntry| $$ 0) 36))) (DEFUN |CLAGG-;reduce;MA3S;11| (|f| |x| |s1| |s2| $) (SPADCALL |f| (SPADCALL |x| (|getShellEntry| $ 9)) |s1| |s2| - (|getShellEntry| $ 33))) + (|getShellEntry| $ 39))) (DEFUN |CLAGG-;removeDuplicates;2A;12| (|x| $) (SPADCALL (SPADCALL (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 35)) - (|getShellEntry| $ 26))) + (|getShellEntry| $ 41)) + (|getShellEntry| $ 32))) (DEFUN |Collection&| (|#1| |#2|) (PROG (|dv$1| |dv$2| |dv$| $ |pv$|) @@ -185,7 +185,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|Collection&|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|Collection&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 37) . #0#) + (LETT $ (|newShell| 43) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -200,35 +200,35 @@ (COND ((|testBitVector| |pv$| 3) (PROGN - (|setShellEntry| $ 11 + (|setShellEntry| $ 12 (CONS (|dispatchFunction| |CLAGG-;#;ANni;1|) $)) - (|setShellEntry| $ 14 + (|setShellEntry| $ 18 (CONS (|dispatchFunction| |CLAGG-;count;MANni;2|) $)) - (|setShellEntry| $ 15 + (|setShellEntry| $ 21 (CONS (|dispatchFunction| |CLAGG-;any?;MAB;3|) $)) - (|setShellEntry| $ 16 + (|setShellEntry| $ 22 (CONS (|dispatchFunction| |CLAGG-;every?;MAB;4|) $)) - (|setShellEntry| $ 19 + (|setShellEntry| $ 25 (CONS (|dispatchFunction| |CLAGG-;find;MAU;5|) $)) - (|setShellEntry| $ 22 + (|setShellEntry| $ 28 (CONS (|dispatchFunction| |CLAGG-;reduce;MAS;6|) $)) - (|setShellEntry| $ 24 + (|setShellEntry| $ 30 (CONS (|dispatchFunction| |CLAGG-;reduce;MA2S;7|) $)) - (|setShellEntry| $ 27 + (|setShellEntry| $ 33 (CONS (|dispatchFunction| |CLAGG-;remove;M2A;8|) $)) - (|setShellEntry| $ 29 + (|setShellEntry| $ 35 (CONS (|dispatchFunction| |CLAGG-;select;M2A;9|) $)) (COND ((|testBitVector| |pv$| 2) (PROGN - (|setShellEntry| $ 32 + (|setShellEntry| $ 38 (CONS (|dispatchFunction| |CLAGG-;remove;S2A;10|) $)) - (|setShellEntry| $ 34 + (|setShellEntry| $ 40 (CONS (|dispatchFunction| |CLAGG-;reduce;MA3S;11|) $)) - (|setShellEntry| $ 36 + (|setShellEntry| $ 42 (CONS (|dispatchFunction| |CLAGG-;removeDuplicates;2A;12|) $)))))))) @@ -237,34 +237,38 @@ (MAKEPROP '|Collection&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|List| 7) (0 . |parts|) (|NonNegativeInteger|) (5 . |#|) - (|Boolean|) (|Mapping| 12 7) (10 . |count|) (16 . |any?|) - (22 . |every?|) (|Union| 7 '"failed") (28 . |find|) - (34 . |find|) (|Mapping| 7 7 7) (40 . |reduce|) - (46 . |reduce|) (52 . |reduce|) (59 . |reduce|) - (66 . |remove|) (72 . |construct|) (77 . |remove|) - (83 . |select|) (89 . |select|) (95 . =) (101 . |remove|) - (107 . |remove|) (113 . |reduce|) (121 . |reduce|) - (129 . |removeDuplicates|) (134 . |removeDuplicates|)) - '#(|select| 139 |removeDuplicates| 145 |remove| 150 |reduce| - 162 |find| 183 |every?| 189 |count| 195 |any?| 201 |#| - 207) + (10 . |#|) (15 . |One|) (19 . +) (25 . |Zero|) (|Boolean|) + (|Mapping| 16 7) (29 . |count|) (35 . |true|) + (39 . |false|) (43 . |any?|) (49 . |every?|) + (|Union| 7 '"failed") (55 . |find|) (61 . |find|) + (|Mapping| 7 7 7) (67 . |reduce|) (73 . |reduce|) + (79 . |reduce|) (86 . |reduce|) (93 . |remove|) + (99 . |construct|) (104 . |remove|) (110 . |select|) + (116 . |select|) (122 . =) (128 . |remove|) + (134 . |remove|) (140 . |reduce|) (148 . |reduce|) + (156 . |removeDuplicates|) (161 . |removeDuplicates|)) + '#(|select| 166 |removeDuplicates| 172 |remove| 177 |reduce| + 189 |find| 210 |every?| 216 |count| 222 |any?| 228 |#| + 234) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 36 - '(1 6 8 0 9 1 0 10 0 11 2 0 10 13 0 14 - 2 0 12 13 0 15 2 0 12 13 0 16 2 8 17 - 13 0 18 2 0 17 13 0 19 2 8 7 20 0 21 - 2 0 7 20 0 22 3 8 7 20 0 7 23 3 0 7 - 20 0 7 24 2 8 0 13 0 25 1 6 0 8 26 2 - 0 0 13 0 27 2 8 0 13 0 28 2 0 0 13 0 - 29 2 7 12 0 0 30 2 6 0 13 0 31 2 0 0 - 7 0 32 4 8 7 20 0 7 7 33 4 0 7 20 0 7 - 7 34 1 8 0 0 35 1 0 0 0 36 2 0 0 13 0 - 29 1 0 0 0 36 2 0 0 7 0 32 2 0 0 13 0 - 27 4 0 7 20 0 7 7 34 3 0 7 20 0 7 24 - 2 0 7 20 0 22 2 0 17 13 0 19 2 0 12 - 13 0 16 2 0 10 13 0 14 2 0 12 13 0 15 - 1 0 10 0 11))))) + (|makeByteWordVec2| 42 + '(1 6 8 0 9 1 8 10 0 11 1 0 10 0 12 0 + 10 0 13 2 10 0 0 0 14 0 10 0 15 2 0 + 10 17 0 18 0 16 0 19 0 16 0 20 2 0 16 + 17 0 21 2 0 16 17 0 22 2 8 23 17 0 24 + 2 0 23 17 0 25 2 8 7 26 0 27 2 0 7 26 + 0 28 3 8 7 26 0 7 29 3 0 7 26 0 7 30 + 2 8 0 17 0 31 1 6 0 8 32 2 0 0 17 0 + 33 2 8 0 17 0 34 2 0 0 17 0 35 2 7 16 + 0 0 36 2 6 0 17 0 37 2 0 0 7 0 38 4 8 + 7 26 0 7 7 39 4 0 7 26 0 7 7 40 1 8 0 + 0 41 1 0 0 0 42 2 0 0 17 0 35 1 0 0 0 + 42 2 0 0 7 0 38 2 0 0 17 0 33 4 0 7 + 26 0 7 7 40 3 0 7 26 0 7 30 2 0 7 26 + 0 28 2 0 23 17 0 25 2 0 16 17 0 22 2 + 0 10 17 0 18 2 0 16 17 0 21 1 0 10 0 + 12))))) '|lookupComplete|)) diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index d3096b93..5e8043f1 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -386,9 +386,9 @@ (|getShellEntry| $ 10)) |DFLOAT;OMwrite;$S;1|) (SPADCALL |dev| (|getShellEntry| $ 12)) - (SPADCALL |dev| |x| (|getShellEntry| $ 14)) - (SPADCALL |dev| (|getShellEntry| $ 15)) + (SPADCALL |dev| |x| (|getShellEntry| $ 15)) (SPADCALL |dev| (|getShellEntry| $ 16)) + (SPADCALL |dev| (|getShellEntry| $ 17)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$S;1|) (EXIT |s|))))) @@ -403,23 +403,23 @@ (|getShellEntry| $ 10)) |DFLOAT;OMwrite;$BS;2|) (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 12)))) - (SPADCALL |dev| |x| (|getShellEntry| $ 14)) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 15)))) - (SPADCALL |dev| (|getShellEntry| $ 16)) + (SPADCALL |dev| |x| (|getShellEntry| $ 15)) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 16)))) + (SPADCALL |dev| (|getShellEntry| $ 17)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$BS;2|) (EXIT |s|))))) (DEFUN |DFLOAT;OMwrite;Omd$V;3| (|dev| |x| $) (SEQ (SPADCALL |dev| (|getShellEntry| $ 12)) - (SPADCALL |dev| |x| (|getShellEntry| $ 14)) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 15))))) + (SPADCALL |dev| |x| (|getShellEntry| $ 15)) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 16))))) (DEFUN |DFLOAT;OMwrite;Omd$BV;4| (|dev| |x| |wholeObj| $) (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 12)))) - (SPADCALL |dev| |x| (|getShellEntry| $ 14)) + (SPADCALL |dev| |x| (|getShellEntry| $ 15)) (EXIT (COND - (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 15))))))) + (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 16))))))) (DEFUN |DFLOAT;checkComplex| (|x| $) (DECLARE (IGNORE $)) @@ -448,7 +448,7 @@ (FLOAT (FLOAT-RADIX 0.0) |$DoubleFloatMaximum|) $) - (|getShellEntry| $ 29))) + (|getShellEntry| $ 35))) |DFLOAT;bits;Pi;10|) (|check-subtype| (AND (COND ((< #0# 0) 'NIL) ('T 'T)) (< 0 #0#)) @@ -480,10 +480,10 @@ (DEFUN |DFLOAT;pi;$;17| ($) (DECLARE (IGNORE $)) PI) (DEFUN |DFLOAT;coerce;$Of;18| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 39))) + (SPADCALL |x| (|getShellEntry| $ 49))) (DEFUN |DFLOAT;convert;$If;19| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 42))) + (SPADCALL |x| (|getShellEntry| $ 52))) (DEFUN |DFLOAT;<;2$B;20| (|x| |y| $) (DECLARE (IGNORE $)) (< |x| |y|)) @@ -595,10 +595,10 @@ (DEFUN |DFLOAT;differentiate;2$;68| (|x| $) (DECLARE (IGNORE $)) 0.0) (DEFUN |DFLOAT;Gamma;2$;69| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 95))) + (SPADCALL |x| (|getShellEntry| $ 104))) (DEFUN |DFLOAT;Beta;3$;70| (|x| |y| $) - (SPADCALL |x| |y| (|getShellEntry| $ 97))) + (SPADCALL |x| |y| (|getShellEntry| $ 106))) (DEFUN |DFLOAT;wholePart;$I;71| (|x| $) (DECLARE (IGNORE $)) @@ -610,7 +610,7 @@ (DEFUN |DFLOAT;convert;2$;73| (|x| $) (DECLARE (IGNORE $)) |x|) (DEFUN |DFLOAT;convert;$F;74| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 103))) + (SPADCALL |x| (|getShellEntry| $ 110))) (DEFUN |DFLOAT;rationalApproximation;$NniF;75| (|x| |d| $) (|DFLOAT;rationalApproximation;$2NniF;84| |x| |d| 10 $)) @@ -716,7 +716,7 @@ (DEFUN |DFLOAT;rationalApproximation;$2NniF;84| (|f| |d| |b| $) (PROG (|#G103| |nu| |ex| BASE #0=#:G1530 |de| |tol| |#G104| |q| |r| - |p2| |q2| #1=#:G1538 |#G105| |#G106| |p0| |p1| |#G107| + |p2| |q2| #1=#:G1539 |#G105| |#G106| |p0| |p1| |#G107| |#G108| |q0| |q1| |#G109| |#G110| |s| |t|) (RETURN (SEQ (EXIT (SEQ (PROGN @@ -788,14 +788,14 @@ (- (* |nu| |q2|) (* |de| |p2|))) (|getShellEntry| $ - 120)) + 141)) (* |de| (ABS |p2|)))) (EXIT (PROGN (LETT #1# (SPADCALL |p2| |q2| (|getShellEntry| $ - 119)) + 139)) |DFLOAT;rationalApproximation;$2NniF;84|) (GO #1#))))) (PROGN @@ -838,34 +838,34 @@ ((< |ex| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |ex|)))) - (|getShellEntry| $ 121))))))) + (|getShellEntry| $ 142))))))) #1# (EXIT #1#))))) (DEFUN |DFLOAT;**;$F$;85| (|x| |r| $) - (PROG (|n| |d| #0=#:G1548) + (PROG (|n| |d| #0=#:G1549) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (COND - ((SPADCALL |r| (|getShellEntry| $ 122)) + ((SPADCALL |r| (|getShellEntry| $ 143)) (|error| "0**0 is undefined")) - ((SPADCALL |r| (|getShellEntry| $ 123)) + ((SPADCALL |r| (|getShellEntry| $ 144)) (|error| "division by 0")) ('T 0.0))) - ((OR (SPADCALL |r| (|getShellEntry| $ 122)) + ((OR (SPADCALL |r| (|getShellEntry| $ 143)) (= |x| 1.0)) 1.0) ('T (COND - ((SPADCALL |r| (|getShellEntry| $ 124)) |x|) + ((SPADCALL |r| (|getShellEntry| $ 145)) |x|) ('T (SEQ (LETT |n| (SPADCALL |r| - (|getShellEntry| $ 125)) + (|getShellEntry| $ 146)) |DFLOAT;**;$F$;85|) (LETT |d| (SPADCALL |r| - (|getShellEntry| $ 126)) + (|getShellEntry| $ 147)) |DFLOAT;**;$F$;85|) (EXIT (COND ((MINUSP |x|) @@ -925,7 +925,7 @@ (RETURN (PROGN (LETT |dv$| '(|DoubleFloat|) . #0=(|DoubleFloat|)) - (LETT $ (|newShell| 140) . #0#) + (LETT $ (|newShell| 161) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -937,26 +937,28 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|OpenMathEncoding|) (0 . |OMencodingXML|) (|String|) (|OpenMathDevice|) (4 . |OMopenString|) (|Void|) (10 . |OMputObject|) - (|DoubleFloat|) (15 . |OMputFloat|) + (|DoubleFloat|) |DFLOAT;convert;2$;73| (15 . |OMputFloat|) (21 . |OMputEndObject|) (26 . |OMclose|) |DFLOAT;OMwrite;$S;1| (|Boolean|) |DFLOAT;OMwrite;$BS;2| |DFLOAT;OMwrite;Omd$V;3| |DFLOAT;OMwrite;Omd$BV;4| - (|PositiveInteger|) |DFLOAT;base;Pi;6| (|Integer|) - |DFLOAT;mantissa;$I;7| |DFLOAT;exponent;$I;8| - |DFLOAT;precision;Pi;9| |DFLOAT;log2;2$;37| (31 . *) - |DFLOAT;bits;Pi;10| |DFLOAT;max;$;11| |DFLOAT;min;$;12| - |DFLOAT;order;$I;13| (CONS IDENTITY (FUNCALL (|dispatchFunction| |DFLOAT;Zero;$;14|) $)) + (|PositiveInteger|) |DFLOAT;base;Pi;6| (|Integer|) + |DFLOAT;mantissa;$I;7| |DFLOAT;exponent;$I;8| + |DFLOAT;precision;Pi;9| (31 . |base|) (35 . =) (41 . *) + (47 . |coerce|) |DFLOAT;log2;2$;37| (52 . *) + |DFLOAT;wholePart;$I;71| |DFLOAT;bits;Pi;10| + |DFLOAT;max;$;11| |DFLOAT;min;$;12| (58 . +) (64 . |One|) + (68 . -) |DFLOAT;order;$I;13| (CONS IDENTITY (FUNCALL (|dispatchFunction| |DFLOAT;One;$;15|) $)) - |DFLOAT;exp1;$;16| |DFLOAT;pi;$;17| (|OutputForm|) - (37 . |outputForm|) |DFLOAT;coerce;$Of;18| (|InputForm|) - (42 . |convert|) |DFLOAT;convert;$If;19| |DFLOAT;<;2$B;20| - |DFLOAT;-;2$;21| |DFLOAT;+;3$;22| |DFLOAT;-;3$;23| - |DFLOAT;*;3$;24| |DFLOAT;*;I2$;25| |DFLOAT;max;3$;26| - |DFLOAT;min;3$;27| |DFLOAT;=;2$B;28| |DFLOAT;/;$I$;29| - |DFLOAT;sqrt;2$;30| |DFLOAT;log10;2$;31| + |DFLOAT;/;3$;62| |DFLOAT;exp1;$;16| |DFLOAT;pi;$;17| + (|OutputForm|) (74 . |outputForm|) |DFLOAT;coerce;$Of;18| + (|InputForm|) (79 . |convert|) |DFLOAT;convert;$If;19| + |DFLOAT;<;2$B;20| |DFLOAT;-;2$;21| |DFLOAT;+;3$;22| + |DFLOAT;-;3$;23| |DFLOAT;*;3$;24| |DFLOAT;*;I2$;25| + |DFLOAT;max;3$;26| |DFLOAT;min;3$;27| |DFLOAT;=;2$B;28| + |DFLOAT;/;$I$;29| |DFLOAT;sqrt;2$;30| |DFLOAT;log10;2$;31| |DFLOAT;**;$I$;32| |DFLOAT;**;3$;33| |DFLOAT;coerce;I$;34| |DFLOAT;exp;2$;35| |DFLOAT;log;2$;36| |DFLOAT;sin;2$;38| |DFLOAT;cos;2$;39| |DFLOAT;tan;2$;40| |DFLOAT;cot;2$;41| @@ -969,62 +971,63 @@ |DFLOAT;sech;2$;55| |DFLOAT;asinh;2$;56| |DFLOAT;acosh;2$;57| |DFLOAT;atanh;2$;58| |DFLOAT;acsch;2$;59| |DFLOAT;acoth;2$;60| - |DFLOAT;asech;2$;61| |DFLOAT;/;3$;62| - |DFLOAT;negative?;$B;63| |DFLOAT;zero?;$B;64| - |DFLOAT;one?;$B;65| (|SingleInteger|) |DFLOAT;hash;$Si;66| - (|Union| $ '"failed") |DFLOAT;recip;$U;67| - |DFLOAT;differentiate;2$;68| - (|DoubleFloatSpecialFunctions|) (47 . |Gamma|) - |DFLOAT;Gamma;2$;69| (52 . |Beta|) |DFLOAT;Beta;3$;70| - |DFLOAT;wholePart;$I;71| |DFLOAT;float;2IPi$;72| - |DFLOAT;convert;2$;73| (|Float|) (58 . |convert|) - |DFLOAT;convert;$F;74| (|Fraction| 24) + |DFLOAT;asech;2$;61| |DFLOAT;negative?;$B;63| + |DFLOAT;zero?;$B;64| |DFLOAT;one?;$B;65| (|SingleInteger|) + |DFLOAT;hash;$Si;66| (|Union| $ '"failed") + |DFLOAT;recip;$U;67| |DFLOAT;differentiate;2$;68| + (|DoubleFloatSpecialFunctions|) (84 . |Gamma|) + |DFLOAT;Gamma;2$;69| (89 . |Beta|) |DFLOAT;Beta;3$;70| + |DFLOAT;float;2IPi$;72| (|Float|) (95 . |convert|) + |DFLOAT;convert;$F;74| (|Fraction| 26) (|NonNegativeInteger|) |DFLOAT;rationalApproximation;$2NniF;84| - |DFLOAT;rationalApproximation;$NniF;75| - |DFLOAT;atan;3$;76| |DFLOAT;retract;$F;77| - (|Union| 105 '"failed") |DFLOAT;retractIfCan;$U;78| - |DFLOAT;retract;$I;79| (|Union| 24 '"failed") - |DFLOAT;retractIfCan;$U;80| |DFLOAT;sign;$I;81| - |DFLOAT;abs;2$;82| (63 . |Zero|) (67 . /) (73 . *) - (79 . |coerce|) (84 . |zero?|) (89 . |negative?|) - (94 . |one?|) (99 . |numer|) (104 . |denom|) - |DFLOAT;**;$F$;85| (|PatternMatchResult| 102 $) - (|Pattern| 102) (|Factored| $) - (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 131 '"failed") (|List| $) (|Union| 133 '"failed") + |DFLOAT;rationalApproximation;$NniF;75| (100 . |Zero|) + |DFLOAT;abs;2$;82| |DFLOAT;atan;3$;76| (104 . |One|) + |DFLOAT;retract;$F;77| (|Union| 112 '"failed") + |DFLOAT;retractIfCan;$U;78| |DFLOAT;retract;$I;79| + (|Union| 26 '"failed") |DFLOAT;retractIfCan;$U;80| + |DFLOAT;sign;$I;81| (108 . *) (114 . **) (120 . |Zero|) + (124 . |Zero|) (128 . <) (134 . -) (139 . **) (145 . <) + (151 . **) + (|Record| (|:| |quotient| $) (|:| |remainder| $)) + (157 . |divide|) (163 . =) (169 . /) (175 . |abs|) + (180 . *) (186 . |coerce|) (191 . |zero?|) + (196 . |negative?|) (201 . |one?|) (206 . |numer|) + (211 . |denom|) (216 . |odd?|) |DFLOAT;**;$F$;85| + (|PatternMatchResult| 109 $) (|Pattern| 109) + (|Factored| $) (|Record| (|:| |coef1| $) (|:| |coef2| $)) + (|Union| 153 '"failed") (|List| $) (|Union| 155 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) - (|Record| (|:| |quotient| $) (|:| |remainder| $)) (|SparseUnivariatePolynomial| $) - (|Record| (|:| |coef| 133) (|:| |generator| $)) + (|Record| (|:| |coef| 155) (|:| |generator| $)) (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))) - '#(~= 109 |zero?| 115 |wholePart| 120 |unitNormal| 125 - |unitCanonical| 130 |unit?| 135 |truncate| 140 |tanh| 145 - |tan| 150 |subtractIfCan| 155 |squareFreePart| 161 - |squareFree| 166 |sqrt| 171 |sizeLess?| 176 |sinh| 182 - |sin| 187 |sign| 192 |sech| 197 |sec| 202 |sample| 207 - |round| 211 |retractIfCan| 216 |retract| 226 |rem| 236 - |recip| 242 |rationalApproximation| 247 |quo| 260 - |principalIdeal| 266 |prime?| 271 |precision| 276 - |positive?| 280 |pi| 285 |patternMatch| 289 |order| 296 - |one?| 301 |nthRoot| 306 |norm| 312 |negative?| 317 - |multiEuclidean| 322 |min| 328 |max| 338 |mantissa| 348 - |log2| 353 |log10| 358 |log| 363 |lcm| 368 |latex| 379 - |inv| 384 |hash| 389 |gcdPolynomial| 394 |gcd| 400 - |fractionPart| 411 |floor| 416 |float| 421 |factor| 434 - |extendedEuclidean| 439 |exquo| 452 |expressIdealMember| - 458 |exponent| 464 |exp1| 469 |exp| 473 |euclideanSize| - 478 |divide| 483 |digits| 489 |differentiate| 493 |csch| - 504 |csc| 509 |coth| 514 |cot| 519 |cosh| 524 |cos| 529 - |convert| 534 |coerce| 554 |characteristic| 584 |ceiling| - 588 |bits| 593 |base| 597 |atanh| 601 |atan| 606 - |associates?| 617 |asinh| 623 |asin| 628 |asech| 633 - |asec| 638 |acsch| 643 |acsc| 648 |acoth| 653 |acot| 658 - |acosh| 663 |acos| 668 |abs| 673 |Zero| 678 |One| 682 - |OMwrite| 686 |Gamma| 710 D 715 |Beta| 726 >= 732 > 738 = - 744 <= 750 < 756 / 762 - 774 + 785 ** 791 * 821) + '#(~= 221 |zero?| 227 |wholePart| 232 |unitNormal| 237 + |unitCanonical| 242 |unit?| 247 |truncate| 252 |tanh| 257 + |tan| 262 |subtractIfCan| 267 |squareFreePart| 273 + |squareFree| 278 |sqrt| 283 |sizeLess?| 288 |sinh| 294 + |sin| 299 |sign| 304 |sech| 309 |sec| 314 |sample| 319 + |round| 323 |retractIfCan| 328 |retract| 338 |rem| 348 + |recip| 354 |rationalApproximation| 359 |quo| 372 + |principalIdeal| 378 |prime?| 383 |precision| 388 + |positive?| 392 |pi| 397 |patternMatch| 401 |order| 408 + |one?| 413 |nthRoot| 418 |norm| 424 |negative?| 429 + |multiEuclidean| 434 |min| 440 |max| 450 |mantissa| 460 + |log2| 465 |log10| 470 |log| 475 |lcm| 480 |latex| 491 + |inv| 496 |hash| 501 |gcdPolynomial| 506 |gcd| 512 + |fractionPart| 523 |floor| 528 |float| 533 |factor| 546 + |extendedEuclidean| 551 |exquo| 564 |expressIdealMember| + 570 |exponent| 576 |exp1| 581 |exp| 585 |euclideanSize| + 590 |divide| 595 |digits| 601 |differentiate| 605 |csch| + 616 |csc| 621 |coth| 626 |cot| 631 |cosh| 636 |cos| 641 + |convert| 646 |coerce| 666 |characteristic| 696 |ceiling| + 700 |bits| 705 |base| 709 |atanh| 713 |atan| 718 + |associates?| 729 |asinh| 735 |asin| 740 |asech| 745 + |asec| 750 |acsch| 755 |acsc| 760 |acoth| 765 |acot| 770 + |acosh| 775 |acos| 780 |abs| 785 |Zero| 790 |One| 794 + |OMwrite| 798 |Gamma| 822 D 827 |Beta| 838 >= 844 > 850 = + 856 <= 862 < 868 / 874 - 886 + 897 ** 903 * 933) '((|approximate| . 0) (|canonicalsClosed| . 0) (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0) ((|commutative| "*") . 0) (|rightUnitary| . 0) @@ -1058,14 +1061,14 @@ (|PrincipalIdealDomain|) (|UniqueFactorizationDomain|) (|GcdDomain|) (|DivisionRing|) - (|IntegralDomain|) (|Algebra| 105) + (|IntegralDomain|) (|Algebra| 112) (|Algebra| $$) (|DifferentialRing|) (|CharacteristicZero|) (|OrderedRing|) - (|Module| 105) (|EntireRing|) + (|Module| 112) (|EntireRing|) (|CommutativeRing|) (|Module| $$) - (|BiModule| 105 105) (|BiModule| $$ $$) + (|BiModule| 112 112) (|BiModule| $$ $$) (|Ring|) (|OrderedAbelianGroup|) - (|RightModule| 105) (|LeftModule| 105) + (|RightModule| 112) (|LeftModule| 112) (|LeftModule| $$) (|Rng|) (|RightModule| $$) (|OrderedCancellationAbelianMonoid|) @@ -1074,81 +1077,89 @@ (|CancellationAbelianMonoid|) (|OrderedAbelianSemiGroup|) (|AbelianMonoid|) (|Monoid|) - (|PatternMatchable| 102) (|OrderedSet|) + (|PatternMatchable| 109) (|OrderedSet|) (|AbelianSemiGroup|) (|SemiGroup|) (|TranscendentalFunctionCategory|) - (|RetractableTo| 105) - (|RetractableTo| 24) (|RealConstant|) - (|SetCategory|) (|ConvertibleTo| 41) + (|RetractableTo| 112) + (|RetractableTo| 26) (|RealConstant|) + (|SetCategory|) (|ConvertibleTo| 51) (|ElementaryFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|TrigonometricFunctionCategory|) - (|OpenMath|) (|ConvertibleTo| 129) + (|OpenMath|) (|ConvertibleTo| 151) (|RadicalCategory|) - (|ConvertibleTo| 102) + (|ConvertibleTo| 109) (|ConvertibleTo| 13) - (|CoercibleFrom| 105) + (|CoercibleFrom| 112) (|CoercibleFrom| $$) - (|CoercibleFrom| 24) (|BasicType|) - (|CoercibleTo| 38)) - (|makeByteWordVec2| 139 + (|CoercibleFrom| 26) (|BasicType|) + (|CoercibleTo| 48)) + (|makeByteWordVec2| 160 '(0 6 0 7 2 9 0 8 6 10 1 9 11 0 12 2 9 - 11 0 13 14 1 9 11 0 15 1 9 11 0 16 2 - 0 0 22 0 29 1 38 0 13 39 1 41 0 13 42 - 1 94 13 13 95 2 94 13 13 13 97 1 102 - 0 13 103 0 105 0 118 2 105 0 24 24 - 119 2 24 0 106 0 120 1 105 0 24 121 1 - 105 18 0 122 1 105 18 0 123 1 105 18 - 0 124 1 105 24 0 125 1 105 24 0 126 2 - 0 18 0 0 1 1 0 18 0 87 1 0 24 0 99 1 - 0 139 0 1 1 0 0 0 1 1 0 18 0 1 1 0 0 - 0 1 1 0 0 0 75 1 0 0 0 63 2 0 91 0 0 - 1 1 0 0 0 1 1 0 130 0 1 1 0 0 0 54 2 - 0 18 0 0 1 1 0 0 0 73 1 0 0 0 61 1 0 - 24 0 116 1 0 0 0 78 1 0 0 0 65 0 0 0 - 1 1 0 0 0 1 1 0 111 0 112 1 0 114 0 - 115 1 0 105 0 110 1 0 24 0 113 2 0 0 - 0 0 1 1 0 91 0 92 2 0 105 0 106 108 3 - 0 105 0 106 106 107 2 0 0 0 0 1 1 0 - 138 133 1 1 0 18 0 1 0 0 22 27 1 0 18 - 0 1 0 0 0 37 3 0 128 0 129 128 1 1 0 - 24 0 33 1 0 18 0 88 2 0 0 0 24 1 1 0 - 0 0 1 1 0 18 0 86 2 0 134 133 0 1 0 0 - 0 32 2 0 0 0 0 51 0 0 0 31 2 0 0 0 0 - 50 1 0 24 0 25 1 0 0 0 28 1 0 0 0 55 - 1 0 0 0 60 2 0 0 0 0 1 1 0 0 133 1 1 - 0 8 0 1 1 0 0 0 1 1 0 89 0 90 2 0 137 - 137 137 1 1 0 0 133 1 2 0 0 0 0 1 1 0 - 0 0 1 1 0 0 0 1 3 0 0 24 24 22 100 2 - 0 0 24 24 1 1 0 130 0 1 3 0 132 0 0 0 - 1 2 0 135 0 0 1 2 0 91 0 0 1 2 0 134 - 133 0 1 1 0 24 0 26 0 0 0 36 1 0 0 0 - 59 1 0 106 0 1 2 0 136 0 0 1 0 0 22 1 - 1 0 0 0 93 2 0 0 0 106 1 1 0 0 0 76 1 - 0 0 0 66 1 0 0 0 77 1 0 0 0 64 1 0 0 - 0 74 1 0 0 0 62 1 0 41 0 43 1 0 129 0 - 1 1 0 102 0 104 1 0 13 0 101 1 0 0 - 105 1 1 0 0 24 58 1 0 0 105 1 1 0 0 0 - 1 1 0 0 24 58 1 0 38 0 40 0 0 106 1 1 - 0 0 0 1 0 0 22 30 0 0 22 23 1 0 0 0 - 81 2 0 0 0 0 109 1 0 0 0 69 2 0 18 0 - 0 1 1 0 0 0 79 1 0 0 0 67 1 0 0 0 84 - 1 0 0 0 72 1 0 0 0 82 1 0 0 0 70 1 0 - 0 0 83 1 0 0 0 71 1 0 0 0 80 1 0 0 0 - 68 1 0 0 0 117 0 0 0 34 0 0 0 35 2 0 - 11 9 0 20 3 0 11 9 0 18 21 1 0 8 0 17 - 2 0 8 0 18 19 1 0 0 0 96 1 0 0 0 1 2 - 0 0 0 106 1 2 0 0 0 0 98 2 0 18 0 0 1 - 2 0 18 0 0 1 2 0 18 0 0 52 2 0 18 0 0 - 1 2 0 18 0 0 44 2 0 0 0 24 53 2 0 0 0 - 0 85 2 0 0 0 0 47 1 0 0 0 45 2 0 0 0 - 0 46 2 0 0 0 0 57 2 0 0 0 105 127 2 0 - 0 0 24 56 2 0 0 0 106 1 2 0 0 0 22 1 - 2 0 0 105 0 1 2 0 0 0 105 1 2 0 0 0 0 - 48 2 0 0 24 0 49 2 0 0 106 0 1 2 0 0 - 22 0 29))))) + 11 0 13 15 1 9 11 0 16 1 9 11 0 17 0 + 26 0 30 2 24 19 0 0 31 2 24 0 24 0 32 + 1 0 0 26 33 2 0 0 24 0 35 2 26 0 0 0 + 40 0 26 0 41 2 26 0 0 0 42 1 48 0 13 + 49 1 51 0 13 52 1 103 13 13 104 2 103 + 13 13 13 106 1 109 0 13 110 0 26 0 + 116 0 24 0 119 2 26 0 26 0 127 2 26 0 + 0 113 128 0 112 0 129 0 113 0 130 2 + 26 19 0 0 131 1 26 0 0 132 2 24 0 0 + 113 133 2 113 19 0 0 134 2 113 0 0 + 113 135 2 26 136 0 0 137 2 26 19 0 0 + 138 2 112 0 26 26 139 1 26 0 0 140 2 + 26 0 113 0 141 1 112 0 26 142 1 112 + 19 0 143 1 112 19 0 144 1 112 19 0 + 145 1 112 26 0 146 1 112 26 0 147 1 + 26 19 0 148 2 0 19 0 0 1 1 0 19 0 96 + 1 0 26 0 36 1 0 160 0 1 1 0 0 0 1 1 0 + 19 0 1 1 0 0 0 1 1 0 0 0 85 1 0 0 0 + 73 2 0 100 0 0 1 1 0 0 0 1 1 0 152 0 + 1 1 0 0 0 64 2 0 19 0 0 1 1 0 0 0 83 + 1 0 0 0 71 1 0 26 0 126 1 0 0 0 88 1 + 0 0 0 75 0 0 0 1 1 0 0 0 1 1 0 121 0 + 122 1 0 124 0 125 1 0 112 0 120 1 0 + 26 0 123 2 0 0 0 0 1 1 0 100 0 101 2 + 0 112 0 113 115 3 0 112 0 113 113 114 + 2 0 0 0 0 1 1 0 159 155 1 1 0 19 0 1 + 0 0 24 29 1 0 19 0 1 0 0 0 47 3 0 150 + 0 151 150 1 1 0 26 0 43 1 0 19 0 97 2 + 0 0 0 26 1 1 0 0 0 1 1 0 19 0 95 2 0 + 156 155 0 1 0 0 0 39 2 0 0 0 0 61 0 0 + 0 38 2 0 0 0 0 60 1 0 26 0 27 1 0 0 0 + 34 1 0 0 0 65 1 0 0 0 70 2 0 0 0 0 1 + 1 0 0 155 1 1 0 8 0 1 1 0 0 0 1 1 0 + 98 0 99 2 0 158 158 158 1 1 0 0 155 1 + 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 3 0 0 + 26 26 24 108 2 0 0 26 26 1 1 0 152 0 + 1 3 0 154 0 0 0 1 2 0 157 0 0 1 2 0 + 100 0 0 1 2 0 156 155 0 1 1 0 26 0 28 + 0 0 0 46 1 0 0 0 69 1 0 113 0 1 2 0 + 136 0 0 1 0 0 24 1 1 0 0 0 102 2 0 0 + 0 113 1 1 0 0 0 86 1 0 0 0 76 1 0 0 0 + 87 1 0 0 0 74 1 0 0 0 84 1 0 0 0 72 1 + 0 51 0 53 1 0 151 0 1 1 0 109 0 111 1 + 0 13 0 14 1 0 0 112 1 1 0 0 26 68 1 0 + 0 112 1 1 0 0 0 1 1 0 0 26 68 1 0 48 + 0 50 0 0 113 1 1 0 0 0 1 0 0 24 37 0 + 0 24 25 1 0 0 0 91 2 0 0 0 0 118 1 0 + 0 0 79 2 0 19 0 0 1 1 0 0 0 89 1 0 0 + 0 77 1 0 0 0 94 1 0 0 0 82 1 0 0 0 92 + 1 0 0 0 80 1 0 0 0 93 1 0 0 0 81 1 0 + 0 0 90 1 0 0 0 78 1 0 0 0 117 0 0 0 + 23 0 0 0 44 2 0 11 9 0 21 3 0 11 9 0 + 19 22 1 0 8 0 18 2 0 8 0 19 20 1 0 0 + 0 105 1 0 0 0 1 2 0 0 0 113 1 2 0 0 0 + 0 107 2 0 19 0 0 1 2 0 19 0 0 1 2 0 + 19 0 0 62 2 0 19 0 0 1 2 0 19 0 0 54 + 2 0 0 0 26 63 2 0 0 0 0 45 2 0 0 0 0 + 57 1 0 0 0 55 2 0 0 0 0 56 2 0 0 0 0 + 67 2 0 0 0 112 149 2 0 0 0 26 66 2 0 + 0 0 113 1 2 0 0 0 24 1 2 0 0 112 0 1 + 2 0 0 0 112 1 2 0 0 0 0 58 2 0 0 26 0 + 59 2 0 0 113 0 1 2 0 0 24 0 35))))) '|lookupComplete|)) (MAKEPROP '|DoubleFloat| 'NILADIC T) diff --git a/src/algebra/strap/DIFRING-.lsp b/src/algebra/strap/DIFRING-.lsp index 1c9f8444..b3562e91 100644 --- a/src/algebra/strap/DIFRING-.lsp +++ b/src/algebra/strap/DIFRING-.lsp @@ -28,7 +28,7 @@ (EXIT |r|))))) (DEFUN |DIFRING-;D;SNniS;3| (|r| |n| $) - (SPADCALL |r| |n| (|getShellEntry| $ 11))) + (SPADCALL |r| |n| (|getShellEntry| $ 14))) (DEFUN |DifferentialRing&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -36,7 +36,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|DifferentialRing&|)) (LETT |dv$| (LIST '|DifferentialRing&| |dv$1|) . #0#) - (LETT $ (|newShell| 13) . #0#) + (LETT $ (|newShell| 16) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -46,14 +46,16 @@ (MAKEPROP '|DifferentialRing&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) - (0 . |differentiate|) |DIFRING-;D;2S;1| - (|NonNegativeInteger|) |DIFRING-;differentiate;SNniS;2| - (5 . |differentiate|) |DIFRING-;D;SNniS;3|) - '#(|differentiate| 11 D 17) 'NIL + (0 . |differentiate|) |DIFRING-;D;2S;1| (|SingleInteger|) + (5 . |One|) (|NonNegativeInteger|) (9 . |One|) + |DIFRING-;differentiate;SNniS;2| (13 . |differentiate|) + |DIFRING-;D;SNniS;3|) + '#(|differentiate| 19 D 25) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 12 - '(1 6 0 0 7 2 6 0 0 9 11 2 0 0 0 9 10 2 - 0 0 0 9 12 1 0 0 0 8))))) + (|makeByteWordVec2| 15 + '(1 6 0 0 7 0 9 0 10 0 11 0 12 2 6 0 0 + 11 14 2 0 0 0 11 13 2 0 0 0 11 15 1 0 + 0 0 8))))) '|lookupComplete|)) diff --git a/src/algebra/strap/DIVRING-.lsp b/src/algebra/strap/DIVRING-.lsp index 4a61885c..219bf0ab 100644 --- a/src/algebra/strap/DIVRING-.lsp +++ b/src/algebra/strap/DIVRING-.lsp @@ -9,23 +9,23 @@ (DEFUN |DIVRING-;**;SIS;1| (|x| |n| $) (COND - ((ZEROP |n|) (|spadConstant| $ 7)) - ((SPADCALL |x| (|getShellEntry| $ 9)) + ((ZEROP |n|) (|spadConstant| $ 10)) + ((SPADCALL |x| (|getShellEntry| $ 11)) (COND ((< |n| 0) (|error| "division by zero")) ('T |x|))) ((< |n| 0) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 11)) (- |n|) - (|getShellEntry| $ 14))) - ('T (SPADCALL |x| |n| (|getShellEntry| $ 14))))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 15)) (- |n|) + (|getShellEntry| $ 19))) + ('T (SPADCALL |x| |n| (|getShellEntry| $ 19))))) (DEFUN |DIVRING-;*;F2S;2| (|q| |x| $) (SPADCALL - (SPADCALL (SPADCALL |q| (|getShellEntry| $ 18)) + (SPADCALL (SPADCALL |q| (|getShellEntry| $ 22)) (SPADCALL - (SPADCALL (SPADCALL |q| (|getShellEntry| $ 19)) - (|getShellEntry| $ 20)) - (|getShellEntry| $ 11)) - (|getShellEntry| $ 21)) - |x| (|getShellEntry| $ 22))) + (SPADCALL (SPADCALL |q| (|getShellEntry| $ 23)) + (|getShellEntry| $ 24)) + (|getShellEntry| $ 15)) + (|getShellEntry| $ 25)) + |x| (|getShellEntry| $ 26))) (DEFUN |DivisionRing&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -33,7 +33,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|DivisionRing&|)) (LETT |dv$| (LIST '|DivisionRing&| |dv$1|) . #0#) - (LETT $ (|newShell| 25) . #0#) + (LETT $ (|newShell| 29) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -42,19 +42,21 @@ $)))) (MAKEPROP '|DivisionRing&| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |One|) - (|Boolean|) (4 . |zero?|) (9 . |Zero|) (13 . |inv|) - (|PositiveInteger|) (|RepeatedSquaring| 6) (18 . |expt|) - (|Integer|) |DIVRING-;**;SIS;1| (|Fraction| 15) - (24 . |numer|) (29 . |denom|) (34 . |coerce|) (39 . *) - (45 . *) |DIVRING-;*;F2S;2| (|NonNegativeInteger|)) - '#(** 51 * 57) 'NIL + (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Boolean|) + (|Integer|) (0 . |zero?|) (5 . |One|) (9 . |zero?|) + (14 . |Zero|) (18 . |Zero|) (22 . <) (28 . |inv|) (33 . -) + (|PositiveInteger|) (|RepeatedSquaring| 6) (38 . |expt|) + |DIVRING-;**;SIS;1| (|Fraction| 8) (44 . |numer|) + (49 . |denom|) (54 . |coerce|) (59 . *) (65 . *) + |DIVRING-;*;F2S;2| (|NonNegativeInteger|)) + '#(** 71 * 77) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 23 - '(0 6 0 7 1 6 8 0 9 0 6 0 10 1 6 0 0 11 - 2 13 6 6 12 14 1 17 15 0 18 1 17 15 0 - 19 1 6 0 15 20 2 6 0 15 0 21 2 6 0 0 - 0 22 2 0 0 0 15 16 2 0 0 17 0 23))))) + (|makeByteWordVec2| 27 + '(1 8 7 0 9 0 6 0 10 1 6 7 0 11 0 6 0 + 12 0 8 0 13 2 8 7 0 0 14 1 6 0 0 15 1 + 8 0 0 16 2 18 6 6 17 19 1 21 8 0 22 1 + 21 8 0 23 1 6 0 8 24 2 6 0 8 0 25 2 6 + 0 0 0 26 2 0 0 0 8 20 2 0 0 21 0 27))))) '|lookupComplete|)) diff --git a/src/algebra/strap/ES-.lsp b/src/algebra/strap/ES-.lsp index 0d783c8e..e7eed238 100644 --- a/src/algebra/strap/ES-.lsp +++ b/src/algebra/strap/ES-.lsp @@ -153,15 +153,15 @@ ('T (SPADCALL |op| (|getShellEntry| $ 14) (|getShellEntry| $ 21))))) (DEFUN |ES-;listk| (|f| $) - (SPADCALL (|ES-;allKernels| |f| $) (|getShellEntry| $ 26))) + (SPADCALL (|ES-;allKernels| |f| $) (|getShellEntry| $ 27))) (DEFUN |ES-;tower;SL;5| (|f| $) - (SPADCALL (|ES-;listk| |f| $) (|getShellEntry| $ 27))) + (SPADCALL (|ES-;listk| |f| $) (|getShellEntry| $ 28))) (DEFUN |ES-;allk| (|l| $) (PROG (#0=#:G1579 |f| #1=#:G1580) (RETURN - (SEQ (SPADCALL (ELT $ 32) + (SEQ (SPADCALL (ELT $ 33) (PROGN (LETT #0# NIL |ES-;allk|) (SEQ (LETT |f| NIL |ES-;allk|) @@ -178,8 +178,8 @@ |ES-;allk|))) (LETT #1# (CDR #1#) |ES-;allk|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (SPADCALL NIL (|getShellEntry| $ 31)) - (|getShellEntry| $ 35)))))) + (SPADCALL NIL (|getShellEntry| $ 32)) + (|getShellEntry| $ 36)))))) (DEFUN |ES-;operators;SL;7| (|f| $) (PROG (#0=#:G1581 |k| #1=#:G1582) @@ -198,7 +198,7 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |k| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 37)) #0#) |ES-;operators;SL;7|))) (LETT #1# (CDR #1#) |ES-;operators;SL;7|) (GO G190) @@ -207,11 +207,11 @@ (DEFUN |ES-;height;SNni;8| (|f| $) (PROG (#0=#:G1583 |k| #1=#:G1584) (RETURN - (SEQ (SPADCALL (ELT $ 42) + (SEQ (SPADCALL (ELT $ 44) (PROGN (LETT #0# NIL |ES-;height;SNni;8|) (SEQ (LETT |k| NIL |ES-;height;SNni;8|) - (LETT #1# (SPADCALL |f| (|getShellEntry| $ 39)) + (LETT #1# (SPADCALL |f| (|getShellEntry| $ 40)) |ES-;height;SNni;8|) G190 (COND @@ -223,12 +223,12 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |k| - (|getShellEntry| $ 41)) + (|getShellEntry| $ 42)) #0#) |ES-;height;SNni;8|))) (LETT #1# (CDR #1#) |ES-;height;SNni;8|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - 0 (|getShellEntry| $ 45)))))) + 0 (|getShellEntry| $ 47)))))) (DEFUN |ES-;freeOf?;SSB;9| (|x| |s| $) (PROG (#0=#:G1585 |k| #1=#:G1586) @@ -250,12 +250,12 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |k| - (|getShellEntry| $ 47)) + (|getShellEntry| $ 49)) #0#) |ES-;freeOf?;SSB;9|))) (LETT #1# (CDR #1#) |ES-;freeOf?;SSB;9|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 49))))))) + (|getShellEntry| $ 51))))))) (DEFUN |ES-;distribute;2S;10| (|x| $) (PROG (#0=#:G1587 |k| #1=#:G1588) @@ -277,7 +277,7 @@ (SEQ (EXIT (COND ((SPADCALL |k| (|getShellEntry| $ 13) - (|getShellEntry| $ 51)) + (|getShellEntry| $ 53)) (LETT #0# (CONS |k| #0#) |ES-;distribute;2S;10|))))) (LETT #1# (CDR #1#) |ES-;distribute;2S;10|) @@ -285,57 +285,57 @@ |x| $))))) (DEFUN |ES-;box;LS;11| (|l| $) - (SPADCALL (|getShellEntry| $ 14) |l| (|getShellEntry| $ 53))) + (SPADCALL (|getShellEntry| $ 14) |l| (|getShellEntry| $ 55))) (DEFUN |ES-;paren;LS;12| (|l| $) - (SPADCALL (|getShellEntry| $ 13) |l| (|getShellEntry| $ 53))) + (SPADCALL (|getShellEntry| $ 13) |l| (|getShellEntry| $ 55))) (DEFUN |ES-;freeOf?;2SB;13| (|x| |k| $) - (NOT (SPADCALL (SPADCALL |k| (|getShellEntry| $ 56)) - (|ES-;listk| |x| $) (|getShellEntry| $ 57)))) + (NOT (SPADCALL (SPADCALL |k| (|getShellEntry| $ 58)) + (|ES-;listk| |x| $) (|getShellEntry| $ 59)))) (DEFUN |ES-;kernel;Bo2S;14| (|op| |arg| $) - (SPADCALL |op| (LIST |arg|) (|getShellEntry| $ 59))) + (SPADCALL |op| (LIST |arg|) (|getShellEntry| $ 61))) (DEFUN |ES-;elt;Bo2S;15| (|op| |x| $) - (SPADCALL |op| (LIST |x|) (|getShellEntry| $ 53))) + (SPADCALL |op| (LIST |x|) (|getShellEntry| $ 55))) (DEFUN |ES-;elt;Bo3S;16| (|op| |x| |y| $) - (SPADCALL |op| (LIST |x| |y|) (|getShellEntry| $ 53))) + (SPADCALL |op| (LIST |x| |y|) (|getShellEntry| $ 55))) (DEFUN |ES-;elt;Bo4S;17| (|op| |x| |y| |z| $) - (SPADCALL |op| (LIST |x| |y| |z|) (|getShellEntry| $ 53))) + (SPADCALL |op| (LIST |x| |y| |z|) (|getShellEntry| $ 55))) (DEFUN |ES-;elt;Bo5S;18| (|op| |x| |y| |z| |t| $) - (SPADCALL |op| (LIST |x| |y| |z| |t|) (|getShellEntry| $ 53))) + (SPADCALL |op| (LIST |x| |y| |z| |t|) (|getShellEntry| $ 55))) (DEFUN |ES-;eval;SSMS;19| (|x| |s| |f| $) - (SPADCALL |x| (LIST |s|) (LIST |f|) (|getShellEntry| $ 67))) + (SPADCALL |x| (LIST |s|) (LIST |f|) (|getShellEntry| $ 69))) (DEFUN |ES-;eval;SBoMS;20| (|x| |s| |f| $) - (SPADCALL |x| (LIST (SPADCALL |s| (|getShellEntry| $ 69))) (LIST |f|) - (|getShellEntry| $ 67))) + (SPADCALL |x| (LIST (SPADCALL |s| (|getShellEntry| $ 71))) (LIST |f|) + (|getShellEntry| $ 69))) (DEFUN |ES-;eval;SSMS;21| (|x| |s| |f| $) (SPADCALL |x| (LIST |s|) (LIST (CONS #'|ES-;eval;SSMS;21!0| (VECTOR |f| $))) - (|getShellEntry| $ 67))) + (|getShellEntry| $ 69))) (DEFUN |ES-;eval;SSMS;21!0| (|#1| $$) - (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 72)) + (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 74)) (|getShellEntry| $$ 0))) (DEFUN |ES-;eval;SBoMS;22| (|x| |s| |f| $) (SPADCALL |x| (LIST |s|) (LIST (CONS #'|ES-;eval;SBoMS;22!0| (VECTOR |f| $))) - (|getShellEntry| $ 75))) + (|getShellEntry| $ 77))) (DEFUN |ES-;eval;SBoMS;22!0| (|#1| $$) - (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 72)) + (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 74)) (|getShellEntry| $$ 0))) (DEFUN |ES-;subst;SES;23| (|x| |e| $) - (SPADCALL |x| (LIST |e|) (|getShellEntry| $ 79))) + (SPADCALL |x| (LIST |e|) (|getShellEntry| $ 81))) (DEFUN |ES-;eval;SLLS;24| (|x| |ls| |lf| $) (PROG (#0=#:G1589 |f| #1=#:G1590) @@ -359,10 +359,10 @@ |ES-;eval;SLLS;24|))) (LETT #1# (CDR #1#) |ES-;eval;SLLS;24|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 75)))))) + (|getShellEntry| $ 77)))))) (DEFUN |ES-;eval;SLLS;24!0| (|#1| $$) - (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 72)) + (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 74)) (|getShellEntry| $$ 0))) (DEFUN |ES-;eval;SLLS;25| (|x| |ls| |lf| $) @@ -387,10 +387,10 @@ |ES-;eval;SLLS;25|))) (LETT #1# (CDR #1#) |ES-;eval;SLLS;25|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 67)))))) + (|getShellEntry| $ 69)))))) (DEFUN |ES-;eval;SLLS;25!0| (|#1| $$) - (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 72)) + (SPADCALL (SPADCALL |#1| (|getShellEntry| (|getShellEntry| $$ 1) 74)) (|getShellEntry| $$ 0))) (DEFUN |ES-;eval;SLLS;26| (|x| |ls| |lf| $) @@ -410,12 +410,12 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |s| - (|getShellEntry| $ 69)) + (|getShellEntry| $ 71)) #0#) |ES-;eval;SLLS;26|))) (LETT #1# (CDR #1#) |ES-;eval;SLLS;26|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - |lf| (|getShellEntry| $ 67)))))) + |lf| (|getShellEntry| $ 69)))))) (DEFUN |ES-;map;MKS;27| (|fn| |k| $) (PROG (#0=#:G1595 |x| #1=#:G1596 |l|) @@ -428,7 +428,7 @@ (SEQ (LETT |x| NIL |ES-;map;MKS;27|) (LETT #1# (SPADCALL |k| - (|getShellEntry| $ 85)) + (|getShellEntry| $ 87)) |ES-;map;MKS;27|) G190 (COND @@ -445,20 +445,20 @@ (LETT #1# (CDR #1#) |ES-;map;MKS;27|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) |ES-;map;MKS;27|) - (SPADCALL |k| (|getShellEntry| $ 85)) - (|getShellEntry| $ 86)) - (SPADCALL |k| (|getShellEntry| $ 87))) + (SPADCALL |k| (|getShellEntry| $ 87)) + (|getShellEntry| $ 88)) + (SPADCALL |k| (|getShellEntry| $ 89))) ('T - (SPADCALL (SPADCALL |k| (|getShellEntry| $ 36)) |l| - (|getShellEntry| $ 53)))))))) + (SPADCALL (SPADCALL |k| (|getShellEntry| $ 37)) |l| + (|getShellEntry| $ 55)))))))) (DEFUN |ES-;operator;2Bo;28| (|op| $) (COND ((SPADCALL |op| (SPADCALL "%paren" (|getShellEntry| $ 9)) - (|getShellEntry| $ 89)) + (|getShellEntry| $ 91)) (|getShellEntry| $ 13)) ((SPADCALL |op| (SPADCALL "%box" (|getShellEntry| $ 9)) - (|getShellEntry| $ 89)) + (|getShellEntry| $ 91)) (|getShellEntry| $ 14)) ('T (|error| "Unknown operator")))) @@ -466,7 +466,7 @@ (PROG (|l| |kk| #0=#:G1597 |n| |k|) (RETURN (SEQ (COND - ((NULL (LETT |l| (SPADCALL |x| (|getShellEntry| $ 39)) + ((NULL (LETT |l| (SPADCALL |x| (|getShellEntry| $ 40)) |ES-;mainKernel;SU;29|)) (CONS 1 "failed")) ('T @@ -474,7 +474,7 @@ (SPADCALL (LETT |k| (|SPADfirst| |l|) |ES-;mainKernel;SU;29|) - (|getShellEntry| $ 41)) + (|getShellEntry| $ 42)) |ES-;mainKernel;SU;29|) (SEQ (LETT |kk| NIL |ES-;mainKernel;SU;29|) (LETT #0# (CDR |l|) |ES-;mainKernel;SU;29|) @@ -489,11 +489,11 @@ (SEQ (EXIT (COND ((< |n| (SPADCALL |kk| - (|getShellEntry| $ 41))) + (|getShellEntry| $ 42))) (SEQ (LETT |n| (SPADCALL |kk| - (|getShellEntry| $ 41)) + (|getShellEntry| $ 42)) |ES-;mainKernel;SU;29|) (EXIT (LETT |k| |kk| @@ -507,9 +507,9 @@ (RETURN (SEQ (LETT |s| (SPADCALL - (LETT |l| (SPADCALL |f| (|getShellEntry| $ 39)) + (LETT |l| (SPADCALL |f| (|getShellEntry| $ 40)) |ES-;allKernels|) - (|getShellEntry| $ 31)) + (|getShellEntry| $ 32)) |ES-;allKernels|) (SEQ (LETT |k| NIL |ES-;allKernels|) (LETT #0# |l| |ES-;allKernels|) G190 @@ -523,26 +523,26 @@ (SEQ (LETT |u| (SPADCALL (SPADCALL |k| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 37)) "%dummyVar" - (|getShellEntry| $ 95)) + (|getShellEntry| $ 101)) |ES-;allKernels|) (EXIT (COND ((QEQCAR |u| 0) (SEQ (LETT |arg| (SPADCALL |k| - (|getShellEntry| $ 85)) + (|getShellEntry| $ 87)) |ES-;allKernels|) (LETT |s0| (SPADCALL (SPADCALL (SPADCALL |arg| - (|getShellEntry| $ 96)) - (|getShellEntry| $ 56)) + (|getShellEntry| $ 102)) + (|getShellEntry| $ 58)) (|ES-;allKernels| (|SPADfirst| |arg|) $) - (|getShellEntry| $ 97)) + (|getShellEntry| $ 103)) |ES-;allKernels|) (LETT |arg| (CDR (CDR |arg|)) |ES-;allKernels|) @@ -555,16 +555,16 @@ (EXIT (SPADCALL |s0| (|ES-;allk| |arg| $) - (|getShellEntry| $ 32))))) + (|getShellEntry| $ 33))))) ('T (|ES-;allk| (SPADCALL |k| - (|getShellEntry| $ 85)) + (|getShellEntry| $ 87)) $))))) |ES-;allKernels|) (EXIT (LETT |s| (SPADCALL |s| |t| - (|getShellEntry| $ 32)) + (|getShellEntry| $ 33)) |ES-;allKernels|))) (LETT #0# (CDR #0#) |ES-;allKernels|) (GO G190) G191 (EXIT NIL)) @@ -572,7 +572,7 @@ (DEFUN |ES-;kernel;BoLS;31| (|op| |args| $) (COND - ((NULL (SPADCALL |op| (|getShellEntry| $ 98))) + ((NULL (SPADCALL |op| (|getShellEntry| $ 108))) (|error| "Unknown operator")) ('T (|ES-;okkernel| |op| |args| $)))) @@ -582,7 +582,7 @@ (SEQ (SPADCALL (SPADCALL |op| |l| (+ 1 - (SPADCALL (ELT $ 42) + (SPADCALL (ELT $ 44) (PROGN (LETT #0# NIL |ES-;okkernel|) (SEQ (LETT |f| NIL |ES-;okkernel|) @@ -598,32 +598,32 @@ (LETT #0# (CONS (SPADCALL |f| - (|getShellEntry| $ 100)) + (|getShellEntry| $ 110)) #0#) |ES-;okkernel|))) (LETT #1# (CDR #1#) |ES-;okkernel|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - 0 (|getShellEntry| $ 45))) - (|getShellEntry| $ 101)) - (|getShellEntry| $ 87)))))) + 0 (|getShellEntry| $ 47))) + (|getShellEntry| $ 112)) + (|getShellEntry| $ 89)))))) (DEFUN |ES-;elt;BoLS;33| (|op| |args| $) (PROG (|u| #0=#:G1522 |v|) (RETURN (SEQ (EXIT (COND - ((NULL (SPADCALL |op| (|getShellEntry| $ 98))) + ((NULL (SPADCALL |op| (|getShellEntry| $ 108))) (|error| "Unknown operator")) ('T (SEQ (SEQ (LETT |u| (SPADCALL |op| - (|getShellEntry| $ 103)) + (|getShellEntry| $ 114)) |ES-;elt;BoLS;33|) (EXIT (COND ((QEQCAR |u| 0) (COND ((SPADCALL (LENGTH |args|) (QCDR |u|) - (|getShellEntry| $ 104)) + (|getShellEntry| $ 116)) (PROGN (LETT #0# (|error| @@ -632,7 +632,7 @@ (GO #0#)))))))) (LETT |v| (SPADCALL |op| |args| - (|getShellEntry| $ 107)) + (|getShellEntry| $ 119)) |ES-;elt;BoLS;33|) (EXIT (COND ((QEQCAR |v| 0) (QCDR |v|)) @@ -642,50 +642,50 @@ (DEFUN |ES-;retract;SK;34| (|f| $) (PROG (|k|) (RETURN - (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 109)) + (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 121)) |ES-;retract;SK;34|) (EXIT (COND ((OR (QEQCAR |k| 1) (SPADCALL (SPADCALL (QCDR |k|) - (|getShellEntry| $ 87)) - |f| (|getShellEntry| $ 110))) + (|getShellEntry| $ 89)) + |f| (|getShellEntry| $ 122))) (|error| "not a kernel")) ('T (QCDR |k|)))))))) (DEFUN |ES-;retractIfCan;SU;35| (|f| $) (PROG (|k|) (RETURN - (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 109)) + (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 121)) |ES-;retractIfCan;SU;35|) (EXIT (COND ((OR (QEQCAR |k| 1) (SPADCALL (SPADCALL (QCDR |k|) - (|getShellEntry| $ 87)) - |f| (|getShellEntry| $ 110))) + (|getShellEntry| $ 89)) + |f| (|getShellEntry| $ 122))) (CONS 1 "failed")) ('T |k|))))))) (DEFUN |ES-;is?;SSB;36| (|f| |s| $) (PROG (|k|) (RETURN - (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 113)) + (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 125)) |ES-;is?;SSB;36|) (EXIT (COND ((QEQCAR |k| 1) 'NIL) ('T - (SPADCALL (QCDR |k|) |s| (|getShellEntry| $ 114))))))))) + (SPADCALL (QCDR |k|) |s| (|getShellEntry| $ 127))))))))) (DEFUN |ES-;is?;SBoB;37| (|f| |op| $) (PROG (|k|) (RETURN - (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 113)) + (SEQ (LETT |k| (SPADCALL |f| (|getShellEntry| $ 125)) |ES-;is?;SBoB;37|) (EXIT (COND ((QEQCAR |k| 1) 'NIL) ('T - (SPADCALL (QCDR |k|) |op| (|getShellEntry| $ 51))))))))) + (SPADCALL (QCDR |k|) |op| (|getShellEntry| $ 53))))))))) (DEFUN |ES-;unwrap| (|l| |x| $) (PROG (|k| #0=#:G1601) @@ -700,8 +700,8 @@ (SPADCALL |x| |k| (|SPADfirst| (SPADCALL |k| - (|getShellEntry| $ 85))) - (|getShellEntry| $ 117)) + (|getShellEntry| $ 87))) + (|getShellEntry| $ 131)) |ES-;unwrap|))) (LETT #0# (CDR #0#) |ES-;unwrap|) (GO G190) G191 (EXIT NIL)) @@ -710,7 +710,7 @@ (DEFUN |ES-;distribute;3S;39| (|x| |y| $) (PROG (|ky| #0=#:G1602 |k| #1=#:G1603) (RETURN - (SEQ (LETT |ky| (SPADCALL |y| (|getShellEntry| $ 56)) + (SEQ (LETT |ky| (SPADCALL |y| (|getShellEntry| $ 58)) |ES-;distribute;3S;39|) (EXIT (|ES-;unwrap| (PROGN @@ -731,13 +731,13 @@ ((SPADCALL |k| (SPADCALL "%paren" (|getShellEntry| $ 9)) - (|getShellEntry| $ 114)) + (|getShellEntry| $ 127)) (SPADCALL |ky| (|ES-;listk| (SPADCALL |k| - (|getShellEntry| $ 87)) + (|getShellEntry| $ 89)) $) - (|getShellEntry| $ 57))) + (|getShellEntry| $ 59))) ('T 'NIL)) (LETT #0# (CONS |k| #0#) |ES-;distribute;3S;39|))))) @@ -750,14 +750,14 @@ (RETURN (SEQ (LETT |rec| (|ES-;mkKerLists| |leq| $) |ES-;eval;SLS;40|) (EXIT (SPADCALL |f| (QCAR |rec|) (QCDR |rec|) - (|getShellEntry| $ 119))))))) + (|getShellEntry| $ 133))))))) (DEFUN |ES-;subst;SLS;41| (|f| |leq| $) (PROG (|rec|) (RETURN (SEQ (LETT |rec| (|ES-;mkKerLists| |leq| $) |ES-;subst;SLS;41|) (EXIT (SPADCALL |f| (QCAR |rec|) (QCDR |rec|) - (|getShellEntry| $ 121))))))) + (|getShellEntry| $ 135))))))) (DEFUN |ES-;mkKerLists| (|leq| $) (PROG (|eq| #0=#:G1604 |k| |lk| |lv|) @@ -774,35 +774,35 @@ (GO G191))) (SEQ (LETT |k| (SPADCALL - (SPADCALL |eq| (|getShellEntry| $ 124)) - (|getShellEntry| $ 113)) + (SPADCALL |eq| (|getShellEntry| $ 140)) + (|getShellEntry| $ 125)) |ES-;mkKerLists|) (EXIT (COND ((QEQCAR |k| 1) (|error| "left hand side must be a single kernel")) ((NULL (SPADCALL (QCDR |k|) |lk| - (|getShellEntry| $ 57))) + (|getShellEntry| $ 59))) (SEQ (LETT |lk| (CONS (QCDR |k|) |lk|) |ES-;mkKerLists|) (EXIT (LETT |lv| (CONS (SPADCALL |eq| - (|getShellEntry| $ 125)) + (|getShellEntry| $ 142)) |lv|) |ES-;mkKerLists|))))))) (LETT #0# (CDR #0#) |ES-;mkKerLists|) (GO G190) G191 (EXIT NIL)) (EXIT (CONS |lk| |lv|)))))) -(DEFUN |ES-;even?;SB;43| (|x| $) (|ES-;intpred?| |x| (ELT $ 127) $)) +(DEFUN |ES-;even?;SB;43| (|x| $) (|ES-;intpred?| |x| (ELT $ 144) $)) -(DEFUN |ES-;odd?;SB;44| (|x| $) (|ES-;intpred?| |x| (ELT $ 129) $)) +(DEFUN |ES-;odd?;SB;44| (|x| $) (|ES-;intpred?| |x| (ELT $ 146) $)) (DEFUN |ES-;intpred?| (|x| |pred?| $) (PROG (|u|) (RETURN - (SEQ (LETT |u| (SPADCALL |x| (|getShellEntry| $ 132)) + (SEQ (LETT |u| (SPADCALL |x| (|getShellEntry| $ 149)) |ES-;intpred?|) (EXIT (COND ((QEQCAR |u| 0) (SPADCALL (QCDR |u|) |pred?|)) @@ -814,7 +814,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|ExpressionSpace&|)) (LETT |dv$| (LIST '|ExpressionSpace&| |dv$1|) . #0#) - (LETT $ (|newShell| 133) . #0#) + (LETT $ (|newShell| 150) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -833,9 +833,9 @@ (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 128 + (|setShellEntry| $ 145 (CONS (|dispatchFunction| |ES-;even?;SB;43|) $)) - (|setShellEntry| $ 130 + (|setShellEntry| $ 147 (CONS (|dispatchFunction| |ES-;odd?;SB;44|) $))))) $)))) @@ -844,88 +844,99 @@ (|Symbol|) (0 . |coerce|) (|BasicOperator|) (|CommonOperators|) (5 . |operator|) '|oppren| '|opbox| (|List| $) (10 . |box|) |ES-;box;2S;1| (15 . |paren|) - |ES-;paren;2S;2| (|Boolean|) (20 . =) |ES-;belong?;BoB;3| - (|Kernel| 6) (|List| 23) (|Set| 23) (26 . |parts|) - (31 . |sort!|) (|Kernel| $) (|List| 28) |ES-;tower;SL;5| - (36 . |brace|) (41 . |union|) (|Mapping| 25 25 25) - (|List| 25) (47 . |reduce|) (54 . |operator|) (|List| 10) - |ES-;operators;SL;7| (59 . |kernels|) - (|NonNegativeInteger|) (64 . |height|) (69 . |max|) - (|Mapping| 40 40 40) (|List| 40) (75 . |reduce|) - |ES-;height;SNni;8| (82 . |name|) (|List| 8) - (87 . |member?|) |ES-;freeOf?;SSB;9| (93 . |is?|) - |ES-;distribute;2S;10| (99 . |elt|) |ES-;box;LS;11| - |ES-;paren;LS;12| (105 . |retract|) (110 . |member?|) - |ES-;freeOf?;2SB;13| (116 . |kernel|) |ES-;kernel;Bo2S;14| - |ES-;elt;Bo2S;15| |ES-;elt;Bo3S;16| |ES-;elt;Bo4S;17| - |ES-;elt;Bo5S;18| (|Mapping| $ 15) (|List| 65) - (122 . |eval|) |ES-;eval;SSMS;19| (129 . |name|) - |ES-;eval;SBoMS;20| (|List| 6) (134 . |first|) - (|Mapping| $ $) |ES-;eval;SSMS;21| (139 . |eval|) - |ES-;eval;SBoMS;22| (|Equation| $) (|List| 77) - (146 . |subst|) |ES-;subst;SES;23| (|List| 73) - |ES-;eval;SLLS;24| |ES-;eval;SLLS;25| |ES-;eval;SLLS;26| - (152 . |argument|) (157 . =) (163 . |coerce|) - |ES-;map;MKS;27| (168 . |is?|) |ES-;operator;2Bo;28| - (|Union| 28 '"failed") |ES-;mainKernel;SU;29| (|None|) - (|Union| 93 '"failed") (174 . |property|) (180 . |second|) - (185 . |remove!|) (191 . |belong?|) |ES-;kernel;BoLS;31| - (196 . |height|) (201 . |kernel|) (|Union| 40 '"failed") - (208 . |arity|) (213 . ~=) (|Union| 6 '"failed") - (|BasicOperatorFunctions1| 6) (219 . |evaluate|) - |ES-;elt;BoLS;33| (225 . |mainKernel|) (230 . ~=) - |ES-;retract;SK;34| |ES-;retractIfCan;SU;35| - (236 . |retractIfCan|) (241 . |is?|) |ES-;is?;SSB;36| - |ES-;is?;SBoB;37| (247 . |eval|) |ES-;distribute;3S;39| - (254 . |eval|) |ES-;eval;SLS;40| (261 . |subst|) - |ES-;subst;SLS;41| (|Equation| 6) (268 . |lhs|) - (273 . |rhs|) (|Integer|) (278 . |even?|) (283 . |even?|) - (288 . |odd?|) (293 . |odd?|) (|Union| 126 '"failed") - (298 . |retractIfCan|)) - '#(|tower| 303 |subst| 308 |retractIfCan| 320 |retract| 325 - |paren| 330 |operators| 340 |operator| 345 |odd?| 350 - |map| 355 |mainKernel| 361 |kernel| 366 |is?| 378 |height| - 390 |freeOf?| 395 |even?| 407 |eval| 412 |elt| 467 - |distribute| 503 |box| 514 |belong?| 524) + |ES-;paren;2S;2| (|Boolean|) (20 . =) (26 . |true|) + |ES-;belong?;BoB;3| (|Kernel| 6) (|List| 24) (|Set| 24) + (30 . |parts|) (35 . |sort!|) (|Kernel| $) (|List| 29) + |ES-;tower;SL;5| (40 . |brace|) (45 . |union|) + (|Mapping| 26 26 26) (|List| 26) (51 . |reduce|) + (58 . |operator|) (|List| 10) |ES-;operators;SL;7| + (63 . |kernels|) (|NonNegativeInteger|) (68 . |height|) + (73 . |Zero|) (77 . |max|) (|Mapping| 41 41 41) + (|List| 41) (83 . |reduce|) |ES-;height;SNni;8| + (90 . |name|) (|List| 8) (95 . |member?|) + |ES-;freeOf?;SSB;9| (101 . |is?|) |ES-;distribute;2S;10| + (107 . |elt|) |ES-;box;LS;11| |ES-;paren;LS;12| + (113 . |retract|) (118 . |member?|) |ES-;freeOf?;2SB;13| + (124 . |kernel|) |ES-;kernel;Bo2S;14| |ES-;elt;Bo2S;15| + |ES-;elt;Bo3S;16| |ES-;elt;Bo4S;17| |ES-;elt;Bo5S;18| + (|Mapping| $ 15) (|List| 67) (130 . |eval|) + |ES-;eval;SSMS;19| (137 . |name|) |ES-;eval;SBoMS;20| + (|List| 6) (142 . |first|) (|Mapping| $ $) + |ES-;eval;SSMS;21| (147 . |eval|) |ES-;eval;SBoMS;22| + (|Equation| $) (|List| 79) (154 . |subst|) + |ES-;subst;SES;23| (|List| 75) |ES-;eval;SLLS;24| + |ES-;eval;SLLS;25| |ES-;eval;SLLS;26| (160 . |argument|) + (165 . =) (171 . |coerce|) |ES-;map;MKS;27| (176 . |is?|) + |ES-;operator;2Bo;28| (182 . |empty?|) (187 . |first|) + (192 . |rest|) (197 . <) (|Union| 29 '"failed") + |ES-;mainKernel;SU;29| (|None|) (|Union| 99 '"failed") + (203 . |property|) (209 . |second|) (214 . |remove!|) + (220 . |rest|) (225 . |One|) (|Integer|) (229 . |One|) + (233 . |belong?|) |ES-;kernel;BoLS;31| (238 . |height|) + (243 . +) (249 . |kernel|) (|Union| 41 '"failed") + (256 . |arity|) (261 . |#|) (266 . ~=) + (|Union| 6 '"failed") (|BasicOperatorFunctions1| 6) + (272 . |evaluate|) |ES-;elt;BoLS;33| (278 . |mainKernel|) + (283 . ~=) |ES-;retract;SK;34| |ES-;retractIfCan;SU;35| + (289 . |retractIfCan|) (294 . |false|) (298 . |is?|) + |ES-;is?;SSB;36| |ES-;is?;SBoB;37| (304 . |reverse!|) + (309 . |eval|) |ES-;distribute;3S;39| (316 . |eval|) + |ES-;eval;SLS;40| (323 . |subst|) |ES-;subst;SLS;41| + (330 . |empty|) (334 . |empty|) (|Equation| 6) + (338 . |lhs|) (343 . |concat|) (349 . |rhs|) + (354 . |concat|) (360 . |even?|) (365 . |even?|) + (370 . |odd?|) (375 . |odd?|) (|Union| 106 '"failed") + (380 . |retractIfCan|)) + '#(|tower| 385 |subst| 390 |retractIfCan| 402 |retract| 407 + |paren| 412 |operators| 422 |operator| 427 |odd?| 432 + |map| 437 |mainKernel| 443 |kernel| 448 |is?| 460 |height| + 472 |freeOf?| 477 |even?| 489 |eval| 494 |elt| 549 + |distribute| 585 |box| 596 |belong?| 606) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 132 + (|makeByteWordVec2| 149 '(1 8 0 7 9 1 11 10 8 12 1 6 0 15 16 1 - 6 0 15 18 2 10 20 0 0 21 1 25 24 0 26 - 1 24 0 0 27 1 25 0 24 31 2 25 0 0 0 - 32 3 34 25 33 0 25 35 1 23 10 0 36 1 - 6 29 0 39 1 23 40 0 41 2 40 0 0 0 42 - 3 44 40 43 0 40 45 1 23 8 0 47 2 48 - 20 8 0 49 2 23 20 0 10 51 2 6 0 10 15 - 53 1 6 28 0 56 2 24 20 23 0 57 2 6 0 - 10 15 59 3 6 0 0 48 66 67 1 10 8 0 69 - 1 71 6 0 72 3 6 0 0 37 66 75 2 6 0 0 - 78 79 1 23 71 0 85 2 71 20 0 0 86 1 6 - 0 28 87 2 10 20 0 8 89 2 10 94 0 7 95 - 1 71 6 0 96 2 25 0 23 0 97 1 6 20 10 - 98 1 6 40 0 100 3 23 0 10 71 40 101 1 - 10 102 0 103 2 40 20 0 0 104 2 106 - 105 10 71 107 1 6 91 0 109 2 6 20 0 0 - 110 1 6 91 0 113 2 23 20 0 8 114 3 6 - 0 0 28 0 117 3 6 0 0 29 15 119 3 6 0 - 0 29 15 121 1 123 6 0 124 1 123 6 0 - 125 1 126 20 0 127 1 0 20 0 128 1 126 - 20 0 129 1 0 20 0 130 1 6 131 0 132 1 - 0 29 0 30 2 0 0 0 78 122 2 0 0 0 77 - 80 1 0 91 0 112 1 0 28 0 111 1 0 0 0 - 19 1 0 0 15 55 1 0 37 0 38 1 0 10 10 - 90 1 0 20 0 130 2 0 0 73 28 88 1 0 91 - 0 92 2 0 0 10 15 99 2 0 0 10 0 60 2 0 - 20 0 8 115 2 0 20 0 10 116 1 0 40 0 - 46 2 0 20 0 8 50 2 0 20 0 0 58 1 0 20 - 0 128 3 0 0 0 10 73 76 3 0 0 0 37 66 - 84 3 0 0 0 10 65 70 3 0 0 0 37 81 82 - 3 0 0 0 8 65 68 3 0 0 0 8 73 74 3 0 0 - 0 48 81 83 2 0 0 0 78 120 2 0 0 10 15 - 108 5 0 0 10 0 0 0 0 64 3 0 0 10 0 0 - 62 4 0 0 10 0 0 0 63 2 0 0 10 0 61 2 - 0 0 0 0 118 1 0 0 0 52 1 0 0 15 54 1 - 0 0 0 17 1 0 20 10 22))))) + 6 0 15 18 2 10 20 0 0 21 0 20 0 22 1 + 26 25 0 27 1 25 0 0 28 1 26 0 25 32 2 + 26 0 0 0 33 3 35 26 34 0 26 36 1 24 + 10 0 37 1 6 30 0 40 1 24 41 0 42 0 41 + 0 43 2 41 0 0 0 44 3 46 41 45 0 41 47 + 1 24 8 0 49 2 50 20 8 0 51 2 24 20 0 + 10 53 2 6 0 10 15 55 1 6 29 0 58 2 25 + 20 24 0 59 2 6 0 10 15 61 3 6 0 0 50 + 68 69 1 10 8 0 71 1 73 6 0 74 3 6 0 0 + 38 68 77 2 6 0 0 80 81 1 24 73 0 87 2 + 73 20 0 0 88 1 6 0 29 89 2 10 20 0 8 + 91 1 25 20 0 93 1 25 24 0 94 1 25 0 0 + 95 2 41 20 0 0 96 2 10 100 0 7 101 1 + 73 6 0 102 2 26 0 24 0 103 1 73 0 0 + 104 0 41 0 105 0 106 0 107 1 6 20 10 + 108 1 6 41 0 110 2 41 0 0 0 111 3 24 + 0 10 73 41 112 1 10 113 0 114 1 73 41 + 0 115 2 41 20 0 0 116 2 118 117 10 73 + 119 1 6 97 0 121 2 6 20 0 0 122 1 6 + 97 0 125 0 20 0 126 2 24 20 0 8 127 1 + 25 0 0 130 3 6 0 0 29 0 131 3 6 0 0 + 30 15 133 3 6 0 0 30 15 135 0 25 0 + 137 0 73 0 138 1 139 6 0 140 2 25 0 + 24 0 141 1 139 6 0 142 2 73 0 6 0 143 + 1 106 20 0 144 1 0 20 0 145 1 106 20 + 0 146 1 0 20 0 147 1 6 148 0 149 1 0 + 30 0 31 2 0 0 0 80 136 2 0 0 0 79 82 + 1 0 97 0 124 1 0 29 0 123 1 0 0 0 19 + 1 0 0 15 57 1 0 38 0 39 1 0 10 10 92 + 1 0 20 0 147 2 0 0 75 29 90 1 0 97 0 + 98 2 0 0 10 15 109 2 0 0 10 0 62 2 0 + 20 0 8 128 2 0 20 0 10 129 1 0 41 0 + 48 2 0 20 0 8 52 2 0 20 0 0 60 1 0 20 + 0 145 3 0 0 0 10 75 78 3 0 0 0 38 68 + 86 3 0 0 0 10 67 72 3 0 0 0 38 83 84 + 3 0 0 0 8 67 70 3 0 0 0 8 75 76 3 0 0 + 0 50 83 85 2 0 0 0 80 134 2 0 0 10 15 + 120 5 0 0 10 0 0 0 0 66 3 0 0 10 0 0 + 64 4 0 0 10 0 0 0 65 2 0 0 10 0 63 2 + 0 0 0 0 132 1 0 0 0 54 1 0 0 15 56 1 + 0 0 0 17 1 0 20 10 23))))) '|lookupComplete|)) diff --git a/src/algebra/strap/EUCDOM-.lsp b/src/algebra/strap/EUCDOM-.lsp index ba98d42c..1f2691f3 100644 --- a/src/algebra/strap/EUCDOM-.lsp +++ b/src/algebra/strap/EUCDOM-.lsp @@ -40,24 +40,24 @@ ((SPADCALL |y| (|getShellEntry| $ 8)) 'NIL) ((SPADCALL |x| (|getShellEntry| $ 8)) 'T) ('T - (< (SPADCALL |x| (|getShellEntry| $ 10)) - (SPADCALL |y| (|getShellEntry| $ 10)))))) + (< (SPADCALL |x| (|getShellEntry| $ 12)) + (SPADCALL |y| (|getShellEntry| $ 12)))))) (DEFUN |EUCDOM-;quo;3S;2| (|x| |y| $) - (QCAR (SPADCALL |x| |y| (|getShellEntry| $ 13)))) + (QCAR (SPADCALL |x| |y| (|getShellEntry| $ 16)))) (DEFUN |EUCDOM-;rem;3S;3| (|x| |y| $) - (QCDR (SPADCALL |x| |y| (|getShellEntry| $ 13)))) + (QCDR (SPADCALL |x| |y| (|getShellEntry| $ 16)))) (DEFUN |EUCDOM-;exquo;2SU;4| (|x| |y| $) (PROG (|qr|) (RETURN (SEQ (COND ((SPADCALL |x| (|getShellEntry| $ 8)) - (CONS 0 (|spadConstant| $ 16))) + (CONS 0 (|spadConstant| $ 19))) ((SPADCALL |y| (|getShellEntry| $ 8)) (CONS 1 "failed")) ('T - (SEQ (LETT |qr| (SPADCALL |x| |y| (|getShellEntry| $ 13)) + (SEQ (LETT |qr| (SPADCALL |x| |y| (|getShellEntry| $ 16)) |EUCDOM-;exquo;2SU;4|) (EXIT (COND ((SPADCALL (QCDR |qr|) @@ -68,9 +68,9 @@ (DEFUN |EUCDOM-;gcd;3S;5| (|x| |y| $) (PROG (|#G13| |#G14|) (RETURN - (SEQ (LETT |x| (SPADCALL |x| (|getShellEntry| $ 19)) + (SEQ (LETT |x| (SPADCALL |x| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|) - (LETT |y| (SPADCALL |y| (|getShellEntry| $ 19)) + (LETT |y| (SPADCALL |y| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|) (SEQ G190 (COND @@ -79,12 +79,12 @@ (SEQ (PROGN (LETT |#G13| |y| |EUCDOM-;gcd;3S;5|) (LETT |#G14| - (SPADCALL |x| |y| (|getShellEntry| $ 20)) + (SPADCALL |x| |y| (|getShellEntry| $ 23)) |EUCDOM-;gcd;3S;5|) (LETT |x| |#G13| |EUCDOM-;gcd;3S;5|) (LETT |y| |#G14| |EUCDOM-;gcd;3S;5|)) (EXIT (LETT |y| - (SPADCALL |y| (|getShellEntry| $ 19)) + (SPADCALL |y| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |x|))))) @@ -94,7 +94,7 @@ (RETURN (SEQ (PROGN (LETT |#G16| - (SPADCALL (QVELT |s| 2) (|getShellEntry| $ 23)) + (SPADCALL (QVELT |s| 2) (|getShellEntry| $ 26)) |EUCDOM-;unitNormalizeIdealElt|) (LETT |u| (QVELT |#G16| 0) |EUCDOM-;unitNormalizeIdealElt|) @@ -104,12 +104,12 @@ |EUCDOM-;unitNormalizeIdealElt|) |#G16|) (EXIT (COND - ((SPADCALL |a| (|getShellEntry| $ 24)) |s|) + ((SPADCALL |a| (|getShellEntry| $ 27)) |s|) ('T (VECTOR (SPADCALL |a| (QVELT |s| 0) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) (SPADCALL |a| (QVELT |s| 1) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) |c|)))))))) (DEFUN |EUCDOM-;extendedEuclidean;2SR;7| (|x| |y| $) @@ -117,14 +117,14 @@ (RETURN (SEQ (LETT |s1| (|EUCDOM-;unitNormalizeIdealElt| - (VECTOR (|spadConstant| $ 26) - (|spadConstant| $ 16) |x|) + (VECTOR (|spadConstant| $ 29) + (|spadConstant| $ 19) |x|) $) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s2| (|EUCDOM-;unitNormalizeIdealElt| - (VECTOR (|spadConstant| $ 16) - (|spadConstant| $ 26) |y|) + (VECTOR (|spadConstant| $ 19) + (|spadConstant| $ 29) |y|) $) |EUCDOM-;extendedEuclidean;2SR;7|) (EXIT (COND @@ -140,20 +140,20 @@ (SEQ (LETT |qr| (SPADCALL (QVELT |s1| 2) (QVELT |s2| 2) - (|getShellEntry| $ 13)) + (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s3| (VECTOR (SPADCALL (QVELT |s1| 0) (SPADCALL (QCAR |qr|) (QVELT |s2| 0) - (|getShellEntry| $ 25)) - (|getShellEntry| $ 27)) + (|getShellEntry| $ 28)) + (|getShellEntry| $ 30)) (SPADCALL (QVELT |s1| 1) (SPADCALL (QCAR |qr|) (QVELT |s2| 1) - (|getShellEntry| $ 25)) - (|getShellEntry| $ 27)) + (|getShellEntry| $ 28)) + (|getShellEntry| $ 30)) (QCDR |qr|)) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s1| |s2| @@ -169,17 +169,17 @@ (|getShellEntry| $ 8))) (COND ((NULL (SPADCALL (QVELT |s1| 0) |y| - (|getShellEntry| $ 28))) + (|getShellEntry| $ 31))) (SEQ (LETT |qr| (SPADCALL (QVELT |s1| 0) |y| - (|getShellEntry| $ 13)) + (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;2SR;7|) (QSETVELT |s1| 0 (QCDR |qr|)) (QSETVELT |s1| 1 (SPADCALL (QVELT |s1| 1) (SPADCALL (QCAR |qr|) |x| - (|getShellEntry| $ 25)) - (|getShellEntry| $ 29))) + (|getShellEntry| $ 28)) + (|getShellEntry| $ 32))) (EXIT (LETT |s1| (|EUCDOM-;unitNormalizeIdealElt| @@ -193,13 +193,13 @@ (SEQ (COND ((SPADCALL |z| (|getShellEntry| $ 8)) (CONS 0 - (CONS (|spadConstant| $ 16) (|spadConstant| $ 16)))) + (CONS (|spadConstant| $ 19) (|spadConstant| $ 19)))) ('T - (SEQ (LETT |s| (SPADCALL |x| |y| (|getShellEntry| $ 32)) + (SEQ (LETT |s| (SPADCALL |x| |y| (|getShellEntry| $ 35)) |EUCDOM-;extendedEuclidean;3SU;8|) (LETT |w| (SPADCALL |z| (QVELT |s| 2) - (|getShellEntry| $ 33)) + (|getShellEntry| $ 36)) |EUCDOM-;extendedEuclidean;3SU;8|) (EXIT (COND ((QEQCAR |w| 1) (CONS 1 "failed")) @@ -207,55 +207,55 @@ (CONS 0 (CONS (SPADCALL (QVELT |s| 0) (QCDR |w|) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) (SPADCALL (QVELT |s| 1) (QCDR |w|) - (|getShellEntry| $ 25))))) + (|getShellEntry| $ 28))))) ('T (SEQ (LETT |qr| (SPADCALL (SPADCALL (QVELT |s| 0) (QCDR |w|) - (|getShellEntry| $ 25)) - |y| (|getShellEntry| $ 13)) + (|getShellEntry| $ 28)) + |y| (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;3SU;8|) (EXIT (CONS 0 (CONS (QCDR |qr|) (SPADCALL (SPADCALL (QVELT |s| 1) (QCDR |w|) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) (SPADCALL (QCAR |qr|) |x| - (|getShellEntry| $ 25)) - (|getShellEntry| $ 29)))))))))))))))) + (|getShellEntry| $ 28)) + (|getShellEntry| $ 32)))))))))))))))) (DEFUN |EUCDOM-;principalIdeal;LR;9| (|l| $) (PROG (|uca| |v| |u| #0=#:G1519 |vv| #1=#:G1520) (RETURN (SEQ (COND - ((SPADCALL |l| NIL (|getShellEntry| $ 38)) + ((SPADCALL |l| NIL (|getShellEntry| $ 41)) (|error| "empty list passed to principalIdeal")) - ((SPADCALL (CDR |l|) NIL (|getShellEntry| $ 38)) + ((SPADCALL (CDR |l|) NIL (|getShellEntry| $ 41)) (SEQ (LETT |uca| (SPADCALL (|SPADfirst| |l|) - (|getShellEntry| $ 23)) + (|getShellEntry| $ 26)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (LIST (QVELT |uca| 0)) (QVELT |uca| 1))))) - ((SPADCALL (CDR (CDR |l|)) NIL (|getShellEntry| $ 38)) + ((SPADCALL (CDR (CDR |l|)) NIL (|getShellEntry| $ 41)) (SEQ (LETT |u| (SPADCALL (|SPADfirst| |l|) - (SPADCALL |l| (|getShellEntry| $ 39)) - (|getShellEntry| $ 32)) + (SPADCALL |l| (|getShellEntry| $ 44)) + (|getShellEntry| $ 35)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (LIST (QVELT |u| 0) (QVELT |u| 1)) (QVELT |u| 2))))) ('T (SEQ (LETT |v| - (SPADCALL (CDR |l|) (|getShellEntry| $ 42)) + (SPADCALL (CDR |l|) (|getShellEntry| $ 47)) |EUCDOM-;principalIdeal;LR;9|) (LETT |u| (SPADCALL (|SPADfirst| |l|) (QCDR |v|) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 35)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (CONS (QVELT |u| 0) (PROGN @@ -280,7 +280,7 @@ (CONS (SPADCALL (QVELT |u| 1) |vv| - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) #0#) |EUCDOM-;principalIdeal;LR;9|))) (LETT #1# (CDR #1#) @@ -293,8 +293,8 @@ (PROG (#0=#:G1521 #1=#:G1522 |pid| |q| #2=#:G1523 |v| #3=#:G1524) (RETURN (SEQ (COND - ((SPADCALL |z| (|spadConstant| $ 16) - (|getShellEntry| $ 44)) + ((SPADCALL |z| (|spadConstant| $ 19) + (|getShellEntry| $ 50)) (CONS 0 (PROGN (LETT #0# NIL @@ -312,17 +312,17 @@ NIL)) (GO G191))) (SEQ (EXIT (LETT #0# - (CONS (|spadConstant| $ 16) #0#) + (CONS (|spadConstant| $ 19) #0#) |EUCDOM-;expressIdealMember;LSU;10|))) (LETT #1# (CDR #1#) |EUCDOM-;expressIdealMember;LSU;10|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))))) ('T - (SEQ (LETT |pid| (SPADCALL |l| (|getShellEntry| $ 42)) + (SEQ (LETT |pid| (SPADCALL |l| (|getShellEntry| $ 47)) |EUCDOM-;expressIdealMember;LSU;10|) (LETT |q| (SPADCALL |z| (QCDR |pid|) - (|getShellEntry| $ 33)) + (|getShellEntry| $ 36)) |EUCDOM-;expressIdealMember;LSU;10|) (EXIT (COND ((QEQCAR |q| 1) (CONS 1 "failed")) @@ -349,7 +349,7 @@ (LETT #2# (CONS (SPADCALL (QCDR |q|) |v| - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) #2#) |EUCDOM-;expressIdealMember;LSU;10|))) (LETT #3# (CDR #3#) @@ -369,11 +369,11 @@ ((EQL |n| 1) (CONS 0 (LIST |z|))) ('T (SEQ (LETT |l1| - (SPADCALL |l| (|getShellEntry| $ 47)) + (SPADCALL |l| (|getShellEntry| $ 57)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |l2| (SPADCALL |l1| (QUOTIENT2 |n| 2) - (|getShellEntry| $ 49)) + (|getShellEntry| $ 60)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |u| (SPADCALL @@ -402,7 +402,7 @@ (#4# (LETT #3# (SPADCALL #3# #2# - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) |EUCDOM-;multiEuclidean;LSU;11|)) ('T (PROGN @@ -415,7 +415,7 @@ (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) - ('T (|spadConstant| $ 26)))) + ('T (|spadConstant| $ 29)))) (PROGN (LETT #9# NIL |EUCDOM-;multiEuclidean;LSU;11|) @@ -441,7 +441,7 @@ (#9# (LETT #8# (SPADCALL #8# #7# - (|getShellEntry| $ 25)) + (|getShellEntry| $ 28)) |EUCDOM-;multiEuclidean;LSU;11|)) ('T (PROGN @@ -454,8 +454,8 @@ (GO G190) G191 (EXIT NIL)) (COND (#9# #8#) - ('T (|spadConstant| $ 26)))) - |z| (|getShellEntry| $ 50)) + ('T (|spadConstant| $ 29)))) + |z| (|getShellEntry| $ 61)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((QEQCAR |u| 1) (CONS 1 "failed")) @@ -463,7 +463,7 @@ (SEQ (LETT |v1| (SPADCALL |l1| (QCDR (QCDR |u|)) - (|getShellEntry| $ 51)) + (|getShellEntry| $ 62)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND @@ -474,7 +474,7 @@ (LETT |v2| (SPADCALL |l2| (QCAR (QCDR |u|)) - (|getShellEntry| $ 51)) + (|getShellEntry| $ 62)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND @@ -485,7 +485,7 @@ (SPADCALL (QCDR |v1|) (QCDR |v2|) (|getShellEntry| $ - 52)))))))))))))))))))))) + 63)))))))))))))))))))))) (DEFUN |EuclideanDomain&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -493,7 +493,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|EuclideanDomain&|)) (LETT |dv$| (LIST '|EuclideanDomain&| |dv$1|) . #0#) - (LETT $ (|newShell| 54) . #0#) + (LETT $ (|newShell| 65) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -503,48 +503,55 @@ (MAKEPROP '|EuclideanDomain&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Boolean|) - (0 . |zero?|) (|NonNegativeInteger|) (5 . |euclideanSize|) + (0 . |zero?|) (5 . |false|) (9 . |true|) + (|NonNegativeInteger|) (13 . |euclideanSize|) (18 . <) |EUCDOM-;sizeLess?;2SB;1| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - (10 . |divide|) |EUCDOM-;quo;3S;2| |EUCDOM-;rem;3S;3| - (16 . |Zero|) (|Union| $ '"failed") |EUCDOM-;exquo;2SU;4| - (20 . |unitCanonical|) (25 . |rem|) |EUCDOM-;gcd;3S;5| + (24 . |divide|) |EUCDOM-;quo;3S;2| |EUCDOM-;rem;3S;3| + (30 . |Zero|) (|Union| $ '"failed") |EUCDOM-;exquo;2SU;4| + (34 . |unitCanonical|) (39 . |rem|) |EUCDOM-;gcd;3S;5| (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) - (31 . |unitNormal|) (36 . |one?|) (41 . *) (47 . |One|) - (51 . -) (57 . |sizeLess?|) (63 . +) + (45 . |unitNormal|) (50 . |one?|) (55 . *) (61 . |One|) + (65 . -) (71 . |sizeLess?|) (77 . +) (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) |EUCDOM-;extendedEuclidean;2SR;7| - (69 . |extendedEuclidean|) (75 . |exquo|) + (83 . |extendedEuclidean|) (89 . |exquo|) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 34 '"failed") |EUCDOM-;extendedEuclidean;3SU;8| - (|List| 6) (81 . =) (87 . |second|) (|List| $) - (|Record| (|:| |coef| 40) (|:| |generator| $)) - (92 . |principalIdeal|) |EUCDOM-;principalIdeal;LR;9| - (97 . =) (|Union| 40 '"failed") - |EUCDOM-;expressIdealMember;LSU;10| (103 . |copy|) - (|Integer|) (108 . |split!|) (114 . |extendedEuclidean|) - (121 . |multiEuclidean|) (127 . |concat|) - |EUCDOM-;multiEuclidean;LSU;11|) - '#(|sizeLess?| 133 |rem| 139 |quo| 145 |principalIdeal| 151 - |multiEuclidean| 156 |gcd| 162 |extendedEuclidean| 168 - |exquo| 181 |expressIdealMember| 187) + (|Union| 37 '"failed") |EUCDOM-;extendedEuclidean;3SU;8| + (|List| 6) (95 . =) (101 . |rest|) (106 . |first|) + (111 . |second|) (|List| $) + (|Record| (|:| |coef| 45) (|:| |generator| $)) + (116 . |principalIdeal|) (121 . |cons|) + |EUCDOM-;principalIdeal;LR;9| (127 . =) + (|Union| 45 '"failed") |EUCDOM-;expressIdealMember;LSU;10| + (133 . |#|) (138 . |zero?|) (143 . |One|) (147 . =) + (153 . |copy|) (158 . |quo|) (|Integer|) (164 . |split!|) + (170 . |extendedEuclidean|) (177 . |multiEuclidean|) + (183 . |concat|) |EUCDOM-;multiEuclidean;LSU;11|) + '#(|sizeLess?| 189 |rem| 195 |quo| 201 |principalIdeal| 207 + |multiEuclidean| 212 |gcd| 218 |extendedEuclidean| 224 + |exquo| 237 |expressIdealMember| 243) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 53 - '(1 6 7 0 8 1 6 9 0 10 2 6 12 0 0 13 0 - 6 0 16 1 6 0 0 19 2 6 0 0 0 20 1 6 22 - 0 23 1 6 7 0 24 2 6 0 0 0 25 0 6 0 26 - 2 6 0 0 0 27 2 6 7 0 0 28 2 6 0 0 0 - 29 2 6 30 0 0 32 2 6 17 0 0 33 2 37 7 - 0 0 38 1 37 6 0 39 1 6 41 40 42 2 6 7 - 0 0 44 1 37 0 0 47 2 37 0 0 48 49 3 6 - 35 0 0 0 50 2 6 45 40 0 51 2 37 0 0 0 - 52 2 0 7 0 0 11 2 0 0 0 0 15 2 0 0 0 - 0 14 1 0 41 40 43 2 0 45 40 0 53 2 0 - 0 0 0 21 3 0 35 0 0 0 36 2 0 30 0 0 - 31 2 0 17 0 0 18 2 0 45 40 0 46))))) + (|makeByteWordVec2| 64 + '(1 6 7 0 8 0 7 0 9 0 7 0 10 1 6 11 0 + 12 2 11 7 0 0 13 2 6 15 0 0 16 0 6 0 + 19 1 6 0 0 22 2 6 0 0 0 23 1 6 25 0 + 26 1 6 7 0 27 2 6 0 0 0 28 0 6 0 29 2 + 6 0 0 0 30 2 6 7 0 0 31 2 6 0 0 0 32 + 2 6 33 0 0 35 2 6 20 0 0 36 2 40 7 0 + 0 41 1 40 0 0 42 1 40 6 0 43 1 40 6 0 + 44 1 6 46 45 47 2 40 0 6 0 48 2 6 7 0 + 0 50 1 40 11 0 53 1 11 7 0 54 0 11 0 + 55 2 11 7 0 0 56 1 40 0 0 57 2 11 0 0 + 0 58 2 40 0 0 59 60 3 6 38 0 0 0 61 2 + 6 51 45 0 62 2 40 0 0 0 63 2 0 7 0 0 + 14 2 0 0 0 0 18 2 0 0 0 0 17 1 0 46 + 45 49 2 0 51 45 0 64 2 0 0 0 0 24 3 0 + 38 0 0 0 39 2 0 33 0 0 34 2 0 20 0 0 + 21 2 0 51 45 0 52))))) '|lookupComplete|)) diff --git a/src/algebra/strap/FFIELDC-.lsp b/src/algebra/strap/FFIELDC-.lsp index 2a3322ff..6742951f 100644 --- a/src/algebra/strap/FFIELDC-.lsp +++ b/src/algebra/strap/FFIELDC-.lsp @@ -57,45 +57,45 @@ ((SPADCALL (LETT |a| (SPADCALL (+ (SPADCALL |a| (|getShellEntry| $ 11)) 1) - (|getShellEntry| $ 12)) + (|getShellEntry| $ 14)) |FFIELDC-;nextItem;SU;3|) - (|getShellEntry| $ 14)) + (|getShellEntry| $ 16)) (CONS 1 "failed")) ('T (CONS 0 |a|)))) (DEFUN |FFIELDC-;order;SOpc;4| (|e| $) - (SPADCALL (SPADCALL |e| (|getShellEntry| $ 17)) - (|getShellEntry| $ 20))) + (SPADCALL (SPADCALL |e| (|getShellEntry| $ 19)) + (|getShellEntry| $ 22))) (DEFUN |FFIELDC-;conditionP;MU;5| (|mat| $) (PROG (|l|) (RETURN - (SEQ (LETT |l| (SPADCALL |mat| (|getShellEntry| $ 25)) + (SEQ (LETT |l| (SPADCALL |mat| (|getShellEntry| $ 27)) |FFIELDC-;conditionP;MU;5|) (COND ((OR (NULL |l|) - (SPADCALL (ELT $ 14) (|SPADfirst| |l|) - (|getShellEntry| $ 27))) + (SPADCALL (ELT $ 16) (|SPADfirst| |l|) + (|getShellEntry| $ 31))) (EXIT (CONS 1 "failed")))) (EXIT (CONS 0 - (SPADCALL (ELT $ 28) (|SPADfirst| |l|) - (|getShellEntry| $ 30)))))))) + (SPADCALL (ELT $ 32) (|SPADfirst| |l|) + (|getShellEntry| $ 34)))))))) (DEFUN |FFIELDC-;charthRoot;2S;6| (|x| $) - (SPADCALL |x| (QUOTIENT2 2 0) (|getShellEntry| $ 36))) + (SPADCALL |x| (QUOTIENT2 2 0) (|getShellEntry| $ 43))) (DEFUN |FFIELDC-;charthRoot;SU;7| (|x| $) - (CONS 0 (SPADCALL |x| (|getShellEntry| $ 28)))) + (CONS 0 (SPADCALL |x| (|getShellEntry| $ 32)))) (DEFUN |FFIELDC-;createPrimitiveElement;S;8| ($) (PROG (|sm1| |start| |i| |e| |found|) (RETURN - (SEQ (LETT |sm1| (- (SPADCALL (|getShellEntry| $ 39)) 1) + (SEQ (LETT |sm1| (- (SPADCALL (|getShellEntry| $ 46)) 1) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |start| (COND - ((SPADCALL (SPADCALL (|getShellEntry| $ 41)) - (CONS 1 "polynomial") (|getShellEntry| $ 42)) + ((SPADCALL (SPADCALL (|getShellEntry| $ 49)) + (CONS 1 "polynomial") (|getShellEntry| $ 50)) 0) ('T 1)) |FFIELDC-;createPrimitiveElement;S;8|) @@ -111,11 +111,11 @@ (COND ((< |i| 0) 'NIL) ('T 'T)) (< 0 |i|)) '(|PositiveInteger|) |i|)) - (|getShellEntry| $ 12)) + (|getShellEntry| $ 14)) |FFIELDC-;createPrimitiveElement;S;8|) (EXIT (LETT |found| (EQL (SPADCALL |e| - (|getShellEntry| $ 17)) + (|getShellEntry| $ 19)) |sm1|) |FFIELDC-;createPrimitiveElement;S;8|))) (LETT |i| (+ |i| 1) @@ -127,9 +127,9 @@ (PROG (|explist| |q| |exp| #0=#:G1514 |equalone|) (RETURN (SEQ (COND - ((SPADCALL |a| (|getShellEntry| $ 14)) 'NIL) + ((SPADCALL |a| (|getShellEntry| $ 16)) 'NIL) ('T - (SEQ (LETT |explist| (SPADCALL (|getShellEntry| $ 46)) + (SEQ (LETT |explist| (SPADCALL (|getShellEntry| $ 56)) |FFIELDC-;primitive?;SB;9|) (LETT |q| (- 2 1) |FFIELDC-;primitive?;SB;9|) (LETT |equalone| 'NIL |FFIELDC-;primitive?;SB;9|) @@ -148,8 +148,8 @@ (SPADCALL (SPADCALL |a| (QUOTIENT2 |q| (QCAR |exp|)) - (|getShellEntry| $ 47)) - (|getShellEntry| $ 48)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;primitive?;SB;9|))) (LETT #0# (CDR #0#) |FFIELDC-;primitive?;SB;9|) (GO G190) G191 (EXIT NIL)) @@ -161,12 +161,12 @@ (RETURN (SEQ (COND ((SPADCALL |e| (|spadConstant| $ 7) - (|getShellEntry| $ 50)) + (|getShellEntry| $ 63)) (|error| "order(0) is not defined ")) ('T (SEQ (LETT |ord| (- 2 1) |FFIELDC-;order;SPi;10|) (LETT |a| 0 |FFIELDC-;order;SPi;10|) - (LETT |lof| (SPADCALL (|getShellEntry| $ 46)) + (LETT |lof| (SPADCALL (|getShellEntry| $ 56)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |rec| NIL |FFIELDC-;order;SPi;10|) (LETT #0# |lof| |FFIELDC-;order;SPi;10|) G190 @@ -185,8 +185,8 @@ (LETT |goon| (SPADCALL (SPADCALL |e| |a| - (|getShellEntry| $ 47)) - (|getShellEntry| $ 48)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |j| 0 |FFIELDC-;order;SPi;10|) (LETT #1# (- (QCDR |rec|) 2) @@ -206,8 +206,8 @@ (LETT |goon| (SPADCALL (SPADCALL |e| |a| - (|getShellEntry| $ 47)) - (|getShellEntry| $ 48)) + (|getShellEntry| $ 58)) + (|getShellEntry| $ 59)) |FFIELDC-;order;SPi;10|))) (LETT |j| (QSADD1 |j|) |FFIELDC-;order;SPi;10|) @@ -226,16 +226,16 @@ |mult| |disclog| |a|) (RETURN (SEQ (COND - ((SPADCALL |b| (|getShellEntry| $ 14)) + ((SPADCALL |b| (|getShellEntry| $ 16)) (|error| "discreteLog: logarithm of zero")) ('T - (SEQ (LETT |faclist| (SPADCALL (|getShellEntry| $ 46)) + (SEQ (LETT |faclist| (SPADCALL (|getShellEntry| $ 56)) |FFIELDC-;discreteLog;SNni;11|) (LETT |a| |b| |FFIELDC-;discreteLog;SNni;11|) - (LETT |gen| (SPADCALL (|getShellEntry| $ 52)) + (LETT |gen| (SPADCALL (|getShellEntry| $ 67)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND - ((SPADCALL |b| |gen| (|getShellEntry| $ 50)) + ((SPADCALL |b| |gen| (|getShellEntry| $ 63)) 1) ('T (SEQ (LETT |disclog| 0 @@ -277,15 +277,15 @@ |FFIELDC-;discreteLog;SNni;11|) (LETT |exptable| (SPADCALL |fac| - (|getShellEntry| $ 54)) + (|getShellEntry| $ 69)) |FFIELDC-;discreteLog;SNni;11|) (LETT |n| (SPADCALL |exptable| - (|getShellEntry| $ 55)) + (|getShellEntry| $ 70)) |FFIELDC-;discreteLog;SNni;11|) (LETT |c| (SPADCALL |a| |exp| - (|getShellEntry| $ 47)) + (|getShellEntry| $ 58)) |FFIELDC-;discreteLog;SNni;11|) (LETT |end| (QUOTIENT2 (- |fac| 1) |n|) @@ -309,7 +309,7 @@ (SPADCALL |c| (|getShellEntry| $ 11)) |exptable| - (|getShellEntry| $ 57)) + (|getShellEntry| $ 73)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND @@ -333,9 +333,9 @@ |groupord| |fac|) (- |n|)) (|getShellEntry| $ - 47)) + 58)) (|getShellEntry| $ - 58)) + 79)) |FFIELDC-;discreteLog;SNni;11|))))) (LETT |i| (QSADD1 |i|) |FFIELDC-;discreteLog;SNni;11|) @@ -356,9 +356,9 @@ (SPADCALL |gen| (- |disc1|) (|getShellEntry| $ - 47)) + 58)) (|getShellEntry| $ - 58)) + 79)) |FFIELDC-;discreteLog;SNni;11|)))) ('T (|error| @@ -377,36 +377,36 @@ |mult| |a|) (RETURN (SEQ (EXIT (COND - ((SPADCALL |b| (|getShellEntry| $ 14)) + ((SPADCALL |b| (|getShellEntry| $ 16)) (SEQ (SPADCALL "discreteLog: logarithm of zero" - (|getShellEntry| $ 63)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) - ((SPADCALL |logbase| (|getShellEntry| $ 14)) + ((SPADCALL |logbase| (|getShellEntry| $ 16)) (SEQ (SPADCALL "discreteLog: logarithm to base zero" - (|getShellEntry| $ 63)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) - ((SPADCALL |b| |logbase| (|getShellEntry| $ 50)) + ((SPADCALL |b| |logbase| (|getShellEntry| $ 63)) (CONS 0 1)) ('T (COND ((NULL (ZEROP (REMAINDER2 (LETT |groupord| (SPADCALL |logbase| - (|getShellEntry| $ 17)) + (|getShellEntry| $ 19)) |FFIELDC-;discreteLog;2SU;12|) (SPADCALL |b| - (|getShellEntry| $ 17))))) + (|getShellEntry| $ 19))))) (SEQ (SPADCALL "discreteLog: second argument not in cyclic group generated by first argument" - (|getShellEntry| $ 63)) + (|getShellEntry| $ 85)) (EXIT (CONS 1 "failed")))) ('T (SEQ (LETT |faclist| (SPADCALL (SPADCALL |groupord| - (|getShellEntry| $ 65)) - (|getShellEntry| $ 67)) + (|getShellEntry| $ 89)) + (|getShellEntry| $ 91)) |FFIELDC-;discreteLog;2SU;12|) (LETT |a| |b| |FFIELDC-;discreteLog;2SU;12|) @@ -433,7 +433,7 @@ (LETT |primroot| (SPADCALL |logbase| (QUOTIENT2 |groupord| |fac|) - (|getShellEntry| $ 47)) + (|getShellEntry| $ 58)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (SEQ @@ -452,9 +452,9 @@ (LETT |rhoHelp| (SPADCALL |primroot| (SPADCALL |a| |exp| - (|getShellEntry| $ 47)) + (|getShellEntry| $ 58)) |fac| - (|getShellEntry| $ 69)) + (|getShellEntry| $ 93)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (COND @@ -482,8 +482,8 @@ (SPADCALL |logbase| (- |rho|) (|getShellEntry| $ - 47)) - (|getShellEntry| $ 58)) + 58)) + (|getShellEntry| $ 79)) |FFIELDC-;discreteLog;2SU;12|))))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;2SU;12|) @@ -495,25 +495,25 @@ #2# (EXIT #2#))))) (DEFUN |FFIELDC-;squareFreePolynomial| (|f| $) - (SPADCALL |f| (|getShellEntry| $ 74))) + (SPADCALL |f| (|getShellEntry| $ 98))) (DEFUN |FFIELDC-;factorPolynomial| (|f| $) - (SPADCALL |f| (|getShellEntry| $ 76))) + (SPADCALL |f| (|getShellEntry| $ 100))) (DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) (PROG (|flist| |u| #0=#:G1521 #1=#:G1510 #2=#:G1508 #3=#:G1509) (RETURN (SEQ (COND - ((SPADCALL |f| (|spadConstant| $ 77) - (|getShellEntry| $ 78)) - (|spadConstant| $ 79)) + ((SPADCALL |f| (|spadConstant| $ 101) + (|getShellEntry| $ 102)) + (|spadConstant| $ 103)) ('T (SEQ (LETT |flist| - (SPADCALL |f| 'T (|getShellEntry| $ 83)) + (SPADCALL |f| 'T (|getShellEntry| $ 107)) |FFIELDC-;factorSquareFreePolynomial|) (EXIT (SPADCALL (SPADCALL (QCAR |flist|) - (|getShellEntry| $ 84)) + (|getShellEntry| $ 108)) (PROGN (LETT #3# NIL |FFIELDC-;factorSquareFreePolynomial|) @@ -535,13 +535,13 @@ (LETT #1# (SPADCALL (QCAR |u|) (QCDR |u|) - (|getShellEntry| $ 85)) + (|getShellEntry| $ 109)) |FFIELDC-;factorSquareFreePolynomial|) (COND (#3# (LETT #2# (SPADCALL #2# #1# - (|getShellEntry| $ 86)) + (|getShellEntry| $ 110)) |FFIELDC-;factorSquareFreePolynomial|)) ('T (PROGN @@ -554,11 +554,11 @@ (GO G190) G191 (EXIT NIL)) (COND (#3# #2#) - ('T (|spadConstant| $ 87)))) - (|getShellEntry| $ 88)))))))))) + ('T (|spadConstant| $ 111)))) + (|getShellEntry| $ 112)))))))))) (DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) - (SPADCALL |f| |g| (|getShellEntry| $ 90))) + (SPADCALL |f| |g| (|getShellEntry| $ 114))) (DEFUN |FiniteFieldCategory&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -566,7 +566,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|FiniteFieldCategory&|)) (LETT |dv$| (LIST '|FiniteFieldCategory&| |dv$1|) . #0#) - (LETT $ (|newShell| 93) . #0#) + (LETT $ (|newShell| 117) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -577,68 +577,83 @@ (MAKEPROP '|FiniteFieldCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |Zero|) |FFIELDC-;differentiate;2S;1| |FFIELDC-;init;S;2| - (|PositiveInteger|) (4 . |lookup|) (9 . |index|) - (|Boolean|) (14 . |zero?|) (|Union| $ '"failed") - |FFIELDC-;nextItem;SU;3| (19 . |order|) (|Integer|) - (|OnePointCompletion| 10) (24 . |coerce|) - |FFIELDC-;order;SOpc;4| (|Vector| 6) (|List| 22) - (|Matrix| 6) (29 . |nullSpace|) (|Mapping| 13 6) - (34 . |every?|) (40 . |charthRoot|) (|Mapping| 6 6) - (45 . |map|) (|Vector| $) (|Union| 31 '"failed") + (|PositiveInteger|) (4 . |lookup|) (9 . |One|) (13 . +) + (19 . |index|) (|Boolean|) (24 . |zero?|) + (|Union| $ '"failed") |FFIELDC-;nextItem;SU;3| + (29 . |order|) (|Integer|) (|OnePointCompletion| 10) + (34 . |coerce|) |FFIELDC-;order;SOpc;4| (|Vector| 6) + (|List| 24) (|Matrix| 6) (39 . |nullSpace|) + (44 . |empty?|) (49 . |first|) (|Mapping| 15 6) + (54 . |every?|) (60 . |charthRoot|) (|Mapping| 6 6) + (65 . |map|) (|Vector| $) (|Union| 35 '"failed") (|Matrix| $) |FFIELDC-;conditionP;MU;5| - (|NonNegativeInteger|) (51 . **) + (|NonNegativeInteger|) (71 . |size|) + (75 . |characteristic|) (79 . |quo|) (85 . **) |FFIELDC-;charthRoot;2S;6| |FFIELDC-;charthRoot;SU;7| - (57 . |size|) + (91 . |size|) (95 . -) (|Union| '"prime" '"polynomial" '"normal" '"cyclic") - (61 . |representationType|) (65 . =) - |FFIELDC-;createPrimitiveElement;S;8| - (|Record| (|:| |factor| 18) (|:| |exponent| 18)) - (|List| 44) (71 . |factorsOfCyclicGroupSize|) (75 . **) - (81 . |one?|) |FFIELDC-;primitive?;SB;9| (86 . =) - |FFIELDC-;order;SPi;10| (92 . |primitiveElement|) - (|Table| 10 35) (96 . |tableForDiscreteLogarithm|) - (101 . |#|) (|Union| 35 '"failed") (106 . |search|) - (112 . *) |FFIELDC-;discreteLog;SNni;11| (|Void|) - (|String|) (|OutputForm|) (118 . |messagePrint|) - (|Factored| $) (123 . |factor|) (|Factored| 18) - (128 . |factors|) (|DiscreteLogarithmPackage| 6) - (133 . |shanksDiscLogAlgorithm|) + (101 . |representationType|) (105 . =) (111 . |false|) + (115 . =) |FFIELDC-;createPrimitiveElement;S;8| + (|Record| (|:| |factor| 20) (|:| |exponent| 20)) + (|List| 54) (121 . |factorsOfCyclicGroupSize|) + (125 . |quo|) (131 . **) (137 . |one?|) + |FFIELDC-;primitive?;SB;9| (142 . |Zero|) (146 . |Zero|) + (150 . =) (|SingleInteger|) (156 . |Zero|) + |FFIELDC-;order;SPi;10| (160 . |primitiveElement|) + (|Table| 10 39) (164 . |tableForDiscreteLogarithm|) + (169 . |#|) (174 . |One|) (|Union| 39 '"failed") + (178 . |search|) (184 . |true|) (188 . *) (194 . +) + (200 . *) (206 . -) (211 . *) (217 . +) + |FFIELDC-;discreteLog;SNni;11| (|Void|) (|String|) + (|OutputForm|) (223 . |messagePrint|) (228 . |rem|) + (234 . |zero?|) (|Factored| $) (239 . |factor|) + (|Factored| 20) (244 . |factors|) + (|DiscreteLogarithmPackage| 6) + (249 . |shanksDiscLogAlgorithm|) |FFIELDC-;discreteLog;2SU;12| - (|SparseUnivariatePolynomial| 6) (|Factored| 71) - (|UnivariatePolynomialSquareFree| 6 71) - (140 . |squareFree|) (|DistinctDegreeFactorize| 6 71) - (145 . |factor|) (150 . |Zero|) (154 . =) (160 . |Zero|) - (|Record| (|:| |irr| 71) (|:| |pow| 18)) (|List| 80) - (|Record| (|:| |cont| 6) (|:| |factors| 81)) - (164 . |distdfact|) (170 . |coerce|) (175 . |primeFactor|) - (181 . *) (187 . |One|) (191 . *) (|EuclideanDomain&| 71) - (197 . |gcd|) (|SparseUnivariatePolynomial| $) + (|SparseUnivariatePolynomial| 6) (|Factored| 95) + (|UnivariatePolynomialSquareFree| 6 95) + (256 . |squareFree|) (|DistinctDegreeFactorize| 6 95) + (261 . |factor|) (266 . |Zero|) (270 . =) (276 . |Zero|) + (|Record| (|:| |irr| 95) (|:| |pow| 20)) (|List| 104) + (|Record| (|:| |cont| 6) (|:| |factors| 105)) + (280 . |distdfact|) (286 . |coerce|) (291 . |primeFactor|) + (297 . *) (303 . |One|) (307 . *) (|EuclideanDomain&| 95) + (313 . |gcd|) (|SparseUnivariatePolynomial| $) |FFIELDC-;gcdPolynomial;3Sup;16|) - '#(|primitive?| 203 |order| 208 |nextItem| 218 |init| 223 - |gcdPolynomial| 227 |discreteLog| 233 |differentiate| 244 - |createPrimitiveElement| 249 |conditionP| 253 |charthRoot| - 258) + '#(|primitive?| 319 |order| 324 |nextItem| 334 |init| 339 + |gcdPolynomial| 343 |discreteLog| 349 |differentiate| 360 + |createPrimitiveElement| 365 |conditionP| 369 |charthRoot| + 374) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 92 - '(0 6 0 7 1 6 10 0 11 1 6 0 10 12 1 6 - 13 0 14 1 6 10 0 17 1 19 0 18 20 1 24 - 23 0 25 2 22 13 26 0 27 1 6 0 0 28 2 - 22 0 29 0 30 2 6 0 0 35 36 0 6 35 39 - 0 6 40 41 2 40 13 0 0 42 0 6 45 46 2 - 6 0 0 18 47 1 6 13 0 48 2 6 13 0 0 50 - 0 6 0 52 1 6 53 18 54 1 53 35 0 55 2 - 53 56 10 0 57 2 6 0 0 0 58 1 62 60 61 - 63 1 18 64 0 65 1 66 45 0 67 3 68 56 - 6 6 35 69 1 73 72 71 74 1 75 72 71 76 - 0 71 0 77 2 71 13 0 0 78 0 72 0 79 2 - 75 82 71 13 83 1 71 0 6 84 2 72 0 71 - 18 85 2 72 0 0 0 86 0 72 0 87 2 72 0 - 71 0 88 2 89 0 0 0 90 1 0 13 0 49 1 0 - 10 0 51 1 0 19 0 21 1 0 15 0 16 0 0 0 - 9 2 0 91 91 91 92 1 0 35 0 59 2 0 56 - 0 0 70 1 0 0 0 8 0 0 0 43 1 0 32 33 - 34 1 0 0 0 37 1 0 15 0 38))))) + (|makeByteWordVec2| 116 + '(0 6 0 7 1 6 10 0 11 0 10 0 12 2 10 0 + 0 0 13 1 6 0 10 14 1 6 15 0 16 1 6 10 + 0 19 1 21 0 20 22 1 26 25 0 27 1 25 + 15 0 28 1 25 24 0 29 2 24 15 30 0 31 + 1 6 0 0 32 2 24 0 33 0 34 0 15 39 40 + 0 20 39 41 2 39 0 0 0 42 2 6 0 0 39 + 43 0 6 39 46 2 20 0 0 0 47 0 6 48 49 + 2 48 15 0 0 50 0 15 0 51 2 10 15 0 0 + 52 0 6 55 56 2 20 0 0 0 57 2 6 0 0 20 + 58 1 6 15 0 59 0 39 0 61 0 20 0 62 2 + 6 15 0 0 63 0 64 0 65 0 6 0 67 1 6 68 + 20 69 1 68 39 0 70 0 39 0 71 2 68 72 + 10 0 73 0 15 0 74 2 39 0 39 0 75 2 39 + 0 0 0 76 2 20 0 20 0 77 1 20 0 0 78 2 + 6 0 0 0 79 2 20 0 0 0 80 1 84 82 83 + 85 2 39 0 0 0 86 1 39 15 0 87 1 20 88 + 0 89 1 90 55 0 91 3 92 72 6 6 39 93 1 + 97 96 95 98 1 99 96 95 100 0 95 0 101 + 2 95 15 0 0 102 0 96 0 103 2 99 106 + 95 15 107 1 95 0 6 108 2 96 0 95 20 + 109 2 96 0 0 0 110 0 96 0 111 2 96 0 + 95 0 112 2 113 0 0 0 114 1 0 15 0 60 + 1 0 10 0 66 1 0 21 0 23 1 0 17 0 18 0 + 0 0 9 2 0 115 115 115 116 1 0 39 0 81 + 2 0 72 0 0 94 1 0 0 0 8 0 0 0 53 1 0 + 36 37 38 1 0 0 0 44 1 0 17 0 45))))) '|lookupComplete|)) diff --git a/src/algebra/strap/FPS-.lsp b/src/algebra/strap/FPS-.lsp index d9a74d7e..c85e10be 100644 --- a/src/algebra/strap/FPS-.lsp +++ b/src/algebra/strap/FPS-.lsp @@ -18,8 +18,8 @@ (MAX 1 (QUOTIENT2 (SPADCALL 4004 - (- (SPADCALL (|getShellEntry| $ 13)) 1) - (|getShellEntry| $ 14)) + (- (SPADCALL (|getShellEntry| $ 14)) 1) + (|getShellEntry| $ 16)) 13301)) |FPS-;digits;Pi;2|) (|check-subtype| @@ -32,7 +32,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|FloatingPointSystem&|)) (LETT |dv$| (LIST '|FloatingPointSystem&| |dv$1|) . #0#) - (LETT $ (|newShell| 17) . #0#) + (LETT $ (|newShell| 21) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -46,14 +46,15 @@ (MAKEPROP '|FloatingPointSystem&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|PositiveInteger|) (0 . |base|) (|Integer|) (4 . |float|) |FPS-;float;2IS;1| - (11 . |One|) (15 . |bits|) (19 . *) (25 . |max|) - |FPS-;digits;Pi;2|) - '#(|float| 29 |digits| 35) 'NIL + (11 . |One|) (15 . |One|) (19 . |bits|) (23 . -) (29 . *) + (35 . |max|) (39 . |quo|) (45 . |max|) |FPS-;digits;Pi;2|) + '#(|float| 51 |digits| 57) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 16 - '(0 6 7 8 3 6 0 9 9 7 10 0 6 0 12 0 6 7 - 13 2 9 0 7 0 14 0 6 0 15 2 0 0 9 9 11 - 0 0 7 16))))) + (|makeByteWordVec2| 20 + '(0 6 7 8 3 6 0 9 9 7 10 0 6 0 12 0 7 0 + 13 0 6 7 14 2 9 0 0 0 15 2 9 0 7 0 16 + 0 6 0 17 2 9 0 0 0 18 2 9 0 0 0 19 2 + 0 0 9 9 11 0 0 7 20))))) '|lookupComplete|)) diff --git a/src/algebra/strap/GCDDOM-.lsp b/src/algebra/strap/GCDDOM-.lsp index e128bbb7..37c12aba 100644 --- a/src/algebra/strap/GCDDOM-.lsp +++ b/src/algebra/strap/GCDDOM-.lsp @@ -88,8 +88,8 @@ (SPADCALL |p1| (SPADCALL (|spadConstant| $ 16) |e1| - (|getShellEntry| $ 32)) - (|getShellEntry| $ 33)) + (|getShellEntry| $ 36)) + (|getShellEntry| $ 37)) |GCDDOM-;gcdPolynomial;3Sup;4|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -108,8 +108,8 @@ (SPADCALL |p2| (SPADCALL (|spadConstant| $ 16) |e2| - (|getShellEntry| $ 32)) - (|getShellEntry| $ 33)) + (|getShellEntry| $ 36)) + (|getShellEntry| $ 37)) |GCDDOM-;gcdPolynomial;3Sup;4|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -125,32 +125,32 @@ (LETT |p1| (COND ((OR (EQL (SPADCALL |p1| - (|getShellEntry| $ 34)) + (|getShellEntry| $ 39)) 0) (EQL (SPADCALL |p2| - (|getShellEntry| $ 34)) + (|getShellEntry| $ 39)) 0)) - (SPADCALL |c1| 0 (|getShellEntry| $ 32))) + (SPADCALL |c1| 0 (|getShellEntry| $ 36))) ('T (SEQ (LETT |p| (SPADCALL |p1| |p2| - (|getShellEntry| $ 35)) + (|getShellEntry| $ 41)) |GCDDOM-;gcdPolynomial;3Sup;4|) (EXIT (COND ((EQL (SPADCALL |p| - (|getShellEntry| $ 34)) + (|getShellEntry| $ 39)) 0) (SPADCALL |c1| 0 - (|getShellEntry| $ 32))) + (|getShellEntry| $ 36))) ('T (SEQ (LETT |c2| (SPADCALL (SPADCALL |p1| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 42)) (SPADCALL |p2| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 42)) (|getShellEntry| $ 10)) |GCDDOM-;gcdPolynomial;3Sup;4|) (EXIT @@ -162,10 +162,10 @@ (SPADCALL (SPADCALL |c2| |p| (|getShellEntry| $ - 37)) + 43)) (SPADCALL |p| (|getShellEntry| $ - 36)) + 42)) (|getShellEntry| $ 27)) |GCDDOM-;gcdPolynomial;3Sup;4|) @@ -176,8 +176,8 @@ (|getShellEntry| $ 6)) #0#)) - (|getShellEntry| $ 38)) - (|getShellEntry| $ 37)) + (|getShellEntry| $ 44)) + (|getShellEntry| $ 43)) (|getShellEntry| $ 25)))))))))) |GCDDOM-;gcdPolynomial;3Sup;4|) (EXIT (COND @@ -185,8 +185,8 @@ ('T (SPADCALL (SPADCALL (|spadConstant| $ 16) |e1| - (|getShellEntry| $ 32)) - |p1| (|getShellEntry| $ 39)))))))))))) + (|getShellEntry| $ 36)) + |p1| (|getShellEntry| $ 46)))))))))))) (DEFUN |GcdDomain&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -194,7 +194,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|GcdDomain&|)) (LETT |dv$| (LIST '|GcdDomain&| |dv$1|) . #0#) - (LETT $ (|newShell| 42) . #0#) + (LETT $ (|newShell| 49) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -211,25 +211,28 @@ (|SparseUnivariatePolynomial| 6) (46 . |zero?|) (51 . |unitCanonical|) (56 . |content|) (61 . |exquo|) (|NonNegativeInteger|) (67 . |minimumDegree|) - (72 . |Zero|) (76 . |One|) (80 . |monomial|) - (86 . |exquo|) (92 . |degree|) (97 . |subResultantGcd|) - (103 . |leadingCoefficient|) (108 . *) - (114 . |primitivePart|) (119 . *) - (|SparseUnivariatePolynomial| $) + (72 . |Zero|) (76 . |Zero|) (|Integer|) (80 . |Zero|) + (84 . <) (90 . |One|) (94 . |monomial|) (100 . |exquo|) + (106 . |min|) (112 . |degree|) (117 . =) + (123 . |subResultantGcd|) (129 . |leadingCoefficient|) + (134 . *) (140 . |primitivePart|) (145 . |zero?|) + (150 . *) (|SparseUnivariatePolynomial| $) |GCDDOM-;gcdPolynomial;3Sup;4|) - '#(|lcm| 125 |gcdPolynomial| 136 |gcd| 142) 'NIL + '#(|lcm| 156 |gcdPolynomial| 167 |gcd| 173) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 41 + (|makeByteWordVec2| 48 '(0 6 0 7 2 6 8 0 0 9 2 6 0 0 0 10 2 6 11 0 0 12 2 6 0 0 0 13 2 6 0 0 0 15 0 6 0 16 4 18 6 17 0 6 6 19 1 23 8 0 24 1 23 0 0 25 1 23 6 0 26 2 23 11 0 6 - 27 1 23 28 0 29 0 23 0 30 0 23 0 31 2 - 23 0 6 28 32 2 23 11 0 0 33 1 23 28 0 - 34 2 23 0 0 0 35 1 23 6 0 36 2 23 0 6 - 0 37 1 23 0 0 38 2 23 0 0 0 39 1 0 0 - 20 21 2 0 0 0 0 14 2 0 40 40 40 41 1 - 0 0 20 22))))) + 27 1 23 28 0 29 0 23 0 30 0 28 0 31 0 + 32 0 33 2 28 8 0 0 34 0 23 0 35 2 23 + 0 6 28 36 2 23 11 0 0 37 2 28 0 0 0 + 38 1 23 28 0 39 2 28 8 0 0 40 2 23 0 + 0 0 41 1 23 6 0 42 2 23 0 6 0 43 1 23 + 0 0 44 1 28 8 0 45 2 23 0 0 0 46 1 0 + 0 20 21 2 0 0 0 0 14 2 0 47 47 47 48 + 1 0 0 20 22))))) '|lookupComplete|)) diff --git a/src/algebra/strap/HOAGG-.lsp b/src/algebra/strap/HOAGG-.lsp index 5a895dee..713e069d 100644 --- a/src/algebra/strap/HOAGG-.lsp +++ b/src/algebra/strap/HOAGG-.lsp @@ -143,27 +143,27 @@ (DEFUN |HOAGG-;count;SANni;7| (|s| |x| $) (SPADCALL (CONS #'|HOAGG-;count;SANni;7!0| (VECTOR $ |s|)) |x| - (|getShellEntry| $ 25))) + (|getShellEntry| $ 31))) (DEFUN |HOAGG-;count;SANni;7!0| (|#1| $$) (SPADCALL (|getShellEntry| $$ 1) |#1| - (|getShellEntry| (|getShellEntry| $$ 0) 24))) + (|getShellEntry| (|getShellEntry| $$ 0) 30))) (DEFUN |HOAGG-;member?;SAB;8| (|e| |c| $) (SPADCALL (CONS #'|HOAGG-;member?;SAB;8!0| (VECTOR $ |e|)) |c| - (|getShellEntry| $ 27))) + (|getShellEntry| $ 33))) (DEFUN |HOAGG-;member?;SAB;8!0| (|#1| $$) (SPADCALL (|getShellEntry| $$ 1) |#1| - (|getShellEntry| (|getShellEntry| $$ 0) 24))) + (|getShellEntry| (|getShellEntry| $$ 0) 30))) (DEFUN |HOAGG-;=;2AB;9| (|x| |y| $) (PROG (|b| #0=#:G1433 |a| #1=#:G1432 #2=#:G1423 #3=#:G1421 #4=#:G1422) (RETURN (SEQ (COND - ((SPADCALL |x| (SPADCALL |y| (|getShellEntry| $ 29)) - (|getShellEntry| $ 30)) + ((SPADCALL |x| (SPADCALL |y| (|getShellEntry| $ 35)) + (|getShellEntry| $ 36)) (PROGN (LETT #4# NIL |HOAGG-;=;2AB;9|) (SEQ (LETT |b| NIL |HOAGG-;=;2AB;9|) @@ -186,7 +186,7 @@ (SEQ (EXIT (PROGN (LETT #2# (SPADCALL |a| |b| - (|getShellEntry| $ 24)) + (|getShellEntry| $ 30)) |HOAGG-;=;2AB;9|) (COND (#4# @@ -227,13 +227,13 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |a| - (|getShellEntry| $ 33)) + (|getShellEntry| $ 39)) #0#) |HOAGG-;coerce;AOf;10|))) (LETT #1# (CDR #1#) |HOAGG-;coerce;AOf;10|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 35)) - (|getShellEntry| $ 36)))))) + (|getShellEntry| $ 41)) + (|getShellEntry| $ 42)))))) (DEFUN |HomogeneousAggregate&| (|#1| |#2|) (PROG (|dv$1| |dv$2| |dv$| $ |pv$|) @@ -243,7 +243,7 @@ (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|HomogeneousAggregate&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 38) . #0#) + (LETT $ (|newShell| 44) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -265,30 +265,30 @@ (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 17 + (|setShellEntry| $ 18 (CONS (|dispatchFunction| |HOAGG-;#;ANni;2|) $)) - (|setShellEntry| $ 20 + (|setShellEntry| $ 23 (CONS (|dispatchFunction| |HOAGG-;any?;MAB;3|) $)) - (|setShellEntry| $ 21 + (|setShellEntry| $ 24 (CONS (|dispatchFunction| |HOAGG-;every?;MAB;4|) $)) - (|setShellEntry| $ 22 + (|setShellEntry| $ 28 (CONS (|dispatchFunction| |HOAGG-;count;MANni;5|) $)) - (|setShellEntry| $ 23 + (|setShellEntry| $ 29 (CONS (|dispatchFunction| |HOAGG-;members;AL;6|) $)) (COND ((|testBitVector| |pv$| 4) (PROGN - (|setShellEntry| $ 26 + (|setShellEntry| $ 32 (CONS (|dispatchFunction| |HOAGG-;count;SANni;7|) $)) - (|setShellEntry| $ 28 + (|setShellEntry| $ 34 (CONS (|dispatchFunction| |HOAGG-;member?;SAB;8|) $)) - (|setShellEntry| $ 31 + (|setShellEntry| $ 37 (CONS (|dispatchFunction| |HOAGG-;=;2AB;9|) $))))) (COND ((|testBitVector| |pv$| 5) - (|setShellEntry| $ 37 + (|setShellEntry| $ 43 (CONS (|dispatchFunction| |HOAGG-;coerce;AOf;10|) $))))))) $)))) @@ -297,30 +297,34 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|Equation| 7) (|List| 8) (0 . |eval|) (|Mapping| 7 7) (6 . |map|) (12 . |eval|) (|List| 7) (18 . |parts|) - (|NonNegativeInteger|) (23 . |#|) (|Boolean|) - (|Mapping| 18 7) (28 . |any?|) (34 . |every?|) - (40 . |count|) (46 . |members|) (51 . =) (57 . |count|) - (63 . |count|) (69 . |any?|) (75 . |member?|) (81 . |#|) - (86 . |size?|) (92 . =) (|OutputForm|) (98 . |coerce|) - (|List| $) (103 . |commaSeparate|) (108 . |bracket|) - (113 . |coerce|)) - '#(|members| 118 |member?| 123 |every?| 129 |eval| 135 - |count| 141 |coerce| 153 |any?| 158 = 164 |#| 170) + (|NonNegativeInteger|) (23 . |#|) (28 . |#|) (|Boolean|) + (33 . |true|) (37 . |false|) (|Mapping| 19 7) + (41 . |any?|) (47 . |every?|) (53 . |One|) (57 . +) + (63 . |Zero|) (67 . |count|) (73 . |members|) (78 . =) + (84 . |count|) (90 . |count|) (96 . |any?|) + (102 . |member?|) (108 . |#|) (113 . |size?|) (119 . =) + (|OutputForm|) (125 . |coerce|) (|List| $) + (130 . |commaSeparate|) (135 . |bracket|) + (140 . |coerce|)) + '#(|members| 145 |member?| 150 |every?| 156 |eval| 162 + |count| 168 |coerce| 180 |any?| 185 = 191 |#| 197) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 37 + (|makeByteWordVec2| 43 '(2 7 0 0 9 10 2 6 0 11 0 12 2 0 0 0 9 - 13 1 6 14 0 15 1 0 16 0 17 2 0 18 19 - 0 20 2 0 18 19 0 21 2 0 16 19 0 22 1 - 0 14 0 23 2 7 18 0 0 24 2 6 16 19 0 - 25 2 0 16 7 0 26 2 6 18 19 0 27 2 0 - 18 7 0 28 1 6 16 0 29 2 6 18 0 16 30 - 2 0 18 0 0 31 1 7 32 0 33 1 32 0 34 - 35 1 32 0 0 36 1 0 32 0 37 1 0 14 0 - 23 2 0 18 7 0 28 2 0 18 19 0 21 2 0 0 - 0 9 13 2 0 16 7 0 26 2 0 16 19 0 22 1 - 0 32 0 37 2 0 18 19 0 20 2 0 18 0 0 - 31 1 0 16 0 17))))) + 13 1 6 14 0 15 1 14 16 0 17 1 0 16 0 + 18 0 19 0 20 0 19 0 21 2 0 19 22 0 23 + 2 0 19 22 0 24 0 16 0 25 2 16 0 0 0 + 26 0 16 0 27 2 0 16 22 0 28 1 0 14 0 + 29 2 7 19 0 0 30 2 6 16 22 0 31 2 0 + 16 7 0 32 2 6 19 22 0 33 2 0 19 7 0 + 34 1 6 16 0 35 2 6 19 0 16 36 2 0 19 + 0 0 37 1 7 38 0 39 1 38 0 40 41 1 38 + 0 0 42 1 0 38 0 43 1 0 14 0 29 2 0 19 + 7 0 34 2 0 19 22 0 24 2 0 0 0 9 13 2 + 0 16 7 0 32 2 0 16 22 0 28 1 0 38 0 + 43 2 0 19 22 0 23 2 0 19 0 0 37 1 0 + 16 0 18))))) '|lookupComplete|)) diff --git a/src/algebra/strap/ILIST.lsp b/src/algebra/strap/ILIST.lsp index ee2b5370..2a1dfcbc 100644 --- a/src/algebra/strap/ILIST.lsp +++ b/src/algebra/strap/ILIST.lsp @@ -202,7 +202,7 @@ (SEQ (COND ((EQ |i| 1000) (COND - ((SPADCALL |x| (|getShellEntry| $ 33)) + ((SPADCALL |x| (|getShellEntry| $ 39)) (|error| "cyclic list"))))) (LETT |y| (CONS (QCAR |x|) |y|) |ILIST;copy;2$;20|) @@ -215,25 +215,25 @@ (PROG (|s| |y| |z|) (RETURN (SEQ (LETT |y| NIL |ILIST;coerce;$Of;21|) - (LETT |s| (SPADCALL |x| (|getShellEntry| $ 35)) + (LETT |s| (SPADCALL |x| (|getShellEntry| $ 44)) |ILIST;coerce;$Of;21|) (SEQ G190 (COND ((NULL (NEQ |x| |s|)) (GO G191))) (SEQ (LETT |y| (CONS (SPADCALL (|SPADfirst| |x|) - (|getShellEntry| $ 37)) + (|getShellEntry| $ 45)) |y|) |ILIST;coerce;$Of;21|) (EXIT (LETT |x| (CDR |x|) |ILIST;coerce;$Of;21|))) NIL (GO G190) G191 (EXIT NIL)) (LETT |y| (NREVERSE |y|) |ILIST;coerce;$Of;21|) (EXIT (COND - ((NULL |s|) (SPADCALL |y| (|getShellEntry| $ 39))) + ((NULL |s|) (SPADCALL |y| (|getShellEntry| $ 49))) ('T (SEQ (LETT |z| (SPADCALL (SPADCALL (|SPADfirst| |x|) - (|getShellEntry| $ 37)) - (|getShellEntry| $ 41)) + (|getShellEntry| $ 45)) + (|getShellEntry| $ 50)) |ILIST;coerce;$Of;21|) (SEQ G190 (COND @@ -244,7 +244,7 @@ (LETT |z| (CONS (SPADCALL (|SPADfirst| |x|) - (|getShellEntry| $ 37)) + (|getShellEntry| $ 45)) |z|) |ILIST;coerce;$Of;21|))) NIL (GO G190) G191 (EXIT NIL)) @@ -252,10 +252,10 @@ (SPADCALL |y| (SPADCALL (SPADCALL (NREVERSE |z|) - (|getShellEntry| $ 42)) - (|getShellEntry| $ 43)) - (|getShellEntry| $ 44)) - (|getShellEntry| $ 39))))))))))) + (|getShellEntry| $ 51)) + (|getShellEntry| $ 52)) + (|getShellEntry| $ 53)) + (|getShellEntry| $ 49))))))))))) (DEFUN |ILIST;=;2$B;22| (|x| |y| $) (PROG (#0=#:G1470) @@ -272,7 +272,7 @@ (SEQ (EXIT (COND ((SPADCALL (QCAR |x|) (QCAR |y|) - (|getShellEntry| $ 46)) + (|getShellEntry| $ 57)) (PROGN (LETT #0# 'NIL |ILIST;=;2$B;22|) @@ -298,7 +298,7 @@ (SEQ (LETT |s| (STRCONC |s| (SPADCALL (QCAR |x|) - (|getShellEntry| $ 49))) + (|getShellEntry| $ 60))) |ILIST;latex;$S;23|) (LETT |x| (QCDR |x|) |ILIST;latex;$S;23|) (EXIT (COND @@ -315,7 +315,7 @@ (COND ((NULL (NOT (NULL |x|))) (GO G191))) (SEQ (EXIT (COND ((SPADCALL |s| (QCAR |x|) - (|getShellEntry| $ 51)) + (|getShellEntry| $ 63)) (PROGN (LETT #0# 'T |ILIST;member?;S$B;24|) @@ -368,7 +368,7 @@ (SEQ (EXIT (COND ((SPADCALL (QCAR |pr|) |f| - (|getShellEntry| $ 51)) + (|getShellEntry| $ 63)) (QRPLACD |pp| (QCDR |pr|))) ('T (LETT |pp| |pr| @@ -501,7 +501,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|IndexedList|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|IndexedList| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 72) . #0#) + (LETT $ (|newShell| 88) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -543,20 +543,20 @@ (|setShellEntry| $ 7 |#2|) (COND ((|testBitVector| |pv$| 8) - (|setShellEntry| $ 45 + (|setShellEntry| $ 54 (CONS (|dispatchFunction| |ILIST;coerce;$Of;21|) $)))) (COND ((|testBitVector| |pv$| 7) (PROGN - (|setShellEntry| $ 47 + (|setShellEntry| $ 58 (CONS (|dispatchFunction| |ILIST;=;2$B;22|) $)) - (|setShellEntry| $ 50 + (|setShellEntry| $ 62 (CONS (|dispatchFunction| |ILIST;latex;$S;23|) $)) - (|setShellEntry| $ 52 + (|setShellEntry| $ 64 (CONS (|dispatchFunction| |ILIST;member?;S$B;24|) $))))) (COND ((|testBitVector| |pv$| 7) - (|setShellEntry| $ 54 + (|setShellEntry| $ 66 (CONS (|dispatchFunction| |ILIST;removeDuplicates!;2$;26|) $)))) @@ -573,43 +573,47 @@ |ILIST;setelt;$rest2$;13| (|List| 6) |ILIST;construct;L$;14| |ILIST;parts;$L;15| |ILIST;reverse!;2$;16| |ILIST;reverse;2$;17| (|Integer|) - |ILIST;minIndex;$I;18| |ILIST;rest;$Nni$;19| - (0 . |cyclic?|) |ILIST;copy;2$;20| (5 . |cycleEntry|) - (|OutputForm|) (10 . |coerce|) (|List| $) (15 . |bracket|) - (|List| 36) (20 . |list|) (25 . |commaSeparate|) - (30 . |overbar|) (35 . |concat!|) (41 . |coerce|) - (46 . ~=) (52 . =) (|String|) (58 . |latex|) - (63 . |latex|) (68 . =) (74 . |member?|) - |ILIST;concat!;3$;25| (80 . |removeDuplicates!|) - (|Mapping| 11 6 6) |ILIST;sort!;M2$;27| - |ILIST;merge!;M3$;28| |ILIST;split!;$I$;29| - (|Mapping| 6 6 6) (|Equation| 6) (|List| 60) + |ILIST;minIndex;$I;18| (|SingleInteger|) (0 . |One|) + (4 . |One|) |ILIST;rest;$Nni$;19| (8 . |Zero|) + (12 . |Zero|) (16 . |not|) (21 . |cyclic?|) + |ILIST;copy;2$;20| (|OutputForm|) (|List| 41) + (26 . |empty|) (30 . |cycleEntry|) (35 . |coerce|) + (40 . |concat|) (46 . |reverse!|) (|List| $) + (51 . |bracket|) (56 . |list|) (61 . |commaSeparate|) + (66 . |overbar|) (71 . |concat!|) (77 . |coerce|) + (82 . |true|) (86 . |false|) (90 . ~=) (96 . =) (|String|) + (102 . |latex|) (107 . |concat|) (113 . |latex|) (118 . =) + (124 . |member?|) |ILIST;concat!;3$;25| + (130 . |removeDuplicates!|) (|Mapping| 11 6 6) + |ILIST;sort!;M2$;27| |ILIST;merge!;M3$;28| (135 . |One|) + (139 . <) (145 . -) |ILIST;split!;$I$;29| (151 . =) + (157 . |quo|) (|Mapping| 6 6 6) (|Equation| 6) (|List| 77) (|Mapping| 11 6) (|Void|) (|UniversalSegment| 30) '"last" - '"value" (|Mapping| 6 6) (|InputForm|) (|SingleInteger|) - (|List| 30) (|Union| 6 '"failed")) - '#(~= 85 |value| 91 |third| 96 |tail| 101 |swap!| 106 - |split!| 113 |sorted?| 119 |sort!| 130 |sort| 141 |size?| - 152 |setvalue!| 158 |setrest!| 164 |setlast!| 170 - |setfirst!| 176 |setelt| 182 |setchildren!| 224 |select!| - 230 |select| 236 |second| 242 |sample| 247 |reverse!| 251 - |reverse| 256 |rest| 261 |removeDuplicates!| 272 - |removeDuplicates| 277 |remove!| 282 |remove| 294 |reduce| - 306 |qsetelt!| 327 |qelt| 334 |possiblyInfinite?| 340 - |position| 345 |parts| 364 |nodes| 369 |node?| 374 |new| - 380 |more?| 386 |minIndex| 392 |min| 397 |merge!| 403 - |merge| 416 |members| 429 |member?| 434 |maxIndex| 440 - |max| 445 |map!| 451 |map| 457 |list| 470 |less?| 475 - |leaves| 481 |leaf?| 486 |latex| 491 |last| 496 |insert!| - 507 |insert| 521 |indices| 535 |index?| 540 |hash| 546 - |first| 551 |find| 562 |fill!| 568 |explicitlyFinite?| 574 - |every?| 579 |eval| 585 |eq?| 611 |entry?| 617 |entries| - 623 |empty?| 628 |empty| 633 |elt| 637 |distance| 680 - |delete!| 686 |delete| 698 |cyclic?| 710 |cycleTail| 715 - |cycleSplit!| 720 |cycleLength| 725 |cycleEntry| 730 - |count| 735 |copyInto!| 747 |copy| 754 |convert| 759 - |construct| 764 |concat!| 769 |concat| 781 |coerce| 804 - |children| 809 |child?| 814 |any?| 820 >= 826 > 832 = 838 - <= 844 < 850 |#| 856) + '"value" (|Mapping| 6 6) (|InputForm|) (|List| 30) + (|Union| 6 '"failed")) + '#(~= 163 |value| 169 |third| 174 |tail| 179 |swap!| 184 + |split!| 191 |sorted?| 197 |sort!| 208 |sort| 219 |size?| + 230 |setvalue!| 236 |setrest!| 242 |setlast!| 248 + |setfirst!| 254 |setelt| 260 |setchildren!| 302 |select!| + 308 |select| 314 |second| 320 |sample| 325 |reverse!| 329 + |reverse| 334 |rest| 339 |removeDuplicates!| 350 + |removeDuplicates| 355 |remove!| 360 |remove| 372 |reduce| + 384 |qsetelt!| 405 |qelt| 412 |possiblyInfinite?| 418 + |position| 423 |parts| 442 |nodes| 447 |node?| 452 |new| + 458 |more?| 464 |minIndex| 470 |min| 475 |merge!| 481 + |merge| 494 |members| 507 |member?| 512 |maxIndex| 518 + |max| 523 |map!| 529 |map| 535 |list| 548 |less?| 553 + |leaves| 559 |leaf?| 564 |latex| 569 |last| 574 |insert!| + 585 |insert| 599 |indices| 613 |index?| 618 |hash| 624 + |first| 629 |find| 640 |fill!| 646 |explicitlyFinite?| 652 + |every?| 657 |eval| 663 |eq?| 689 |entry?| 695 |entries| + 701 |empty?| 706 |empty| 711 |elt| 715 |distance| 758 + |delete!| 764 |delete| 776 |cyclic?| 788 |cycleTail| 793 + |cycleSplit!| 798 |cycleLength| 803 |cycleEntry| 808 + |count| 813 |copyInto!| 825 |copy| 832 |convert| 837 + |construct| 842 |concat!| 847 |concat| 859 |coerce| 882 + |children| 887 |child?| 892 |any?| 898 >= 904 > 910 = 916 + <= 922 < 928 |#| 934) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 5 '(0 0 0 0 0 0 0 0 0 0 5 0 0 1 4 0 0 1 2 3 4)) @@ -636,58 +640,63 @@ (|EltableAggregate| 30 6) (|Evalable| 6) (|SetCategory|) (|Type|) (|Eltable| 30 6) (|InnerEvalable| 6 6) - (|CoercibleTo| 36) (|ConvertibleTo| 68) + (|CoercibleTo| 41) (|ConvertibleTo| 85) (|BasicType|)) - (|makeByteWordVec2| 71 - '(1 0 11 0 33 1 0 0 0 35 1 6 36 0 37 1 - 36 0 38 39 1 40 0 36 41 1 36 0 38 42 - 1 36 0 0 43 2 40 0 0 36 44 1 0 36 0 - 45 2 6 11 0 0 46 2 0 11 0 0 47 1 6 48 - 0 49 1 0 48 0 50 2 6 11 0 0 51 2 0 11 - 6 0 52 1 0 0 0 54 2 7 11 0 0 1 1 0 6 - 0 1 1 0 6 0 1 1 0 0 0 1 3 0 63 0 30 - 30 1 2 0 0 0 30 58 1 5 11 0 1 2 0 11 - 55 0 1 1 5 0 0 1 2 0 0 55 0 56 1 5 0 - 0 1 2 0 0 55 0 1 2 0 11 0 8 1 2 0 6 0 + (|makeByteWordVec2| 87 + '(0 32 0 33 0 8 0 34 0 32 0 36 0 8 0 37 + 1 11 0 0 38 1 0 11 0 39 0 42 0 43 1 0 + 0 0 44 1 6 41 0 45 2 42 0 41 0 46 1 + 42 0 0 47 1 41 0 48 49 1 42 0 41 50 1 + 41 0 48 51 1 41 0 0 52 2 42 0 0 41 53 + 1 0 41 0 54 0 11 0 55 0 11 0 56 2 6 + 11 0 0 57 2 0 11 0 0 58 1 6 59 0 60 2 + 59 0 0 0 61 1 0 59 0 62 2 6 11 0 0 63 + 2 0 11 6 0 64 1 0 0 0 66 0 30 0 70 2 + 30 11 0 0 71 2 30 0 0 0 72 2 30 11 0 + 0 74 2 30 0 0 0 75 2 7 11 0 0 1 1 0 6 + 0 1 1 0 6 0 1 1 0 0 0 1 3 0 80 0 30 + 30 1 2 0 0 0 30 73 1 5 11 0 1 2 0 11 + 67 0 1 1 5 0 0 1 2 0 0 67 0 68 1 5 0 + 0 1 2 0 0 67 0 1 2 0 11 0 8 1 2 0 6 0 6 1 2 0 0 0 0 23 2 0 6 0 6 1 2 0 6 0 - 6 21 3 0 6 0 30 6 1 3 0 6 0 64 6 1 3 - 0 6 0 65 6 1 3 0 0 0 19 0 24 3 0 6 0 - 14 6 22 3 0 6 0 66 6 1 2 0 0 0 38 1 2 - 0 0 62 0 1 2 0 0 62 0 1 1 0 6 0 1 0 0 + 6 21 3 0 6 0 30 6 1 3 0 6 0 81 6 1 3 + 0 6 0 82 6 1 3 0 0 0 19 0 24 3 0 6 0 + 14 6 22 3 0 6 0 83 6 1 2 0 0 0 48 1 2 + 0 0 79 0 1 2 0 0 79 0 1 1 0 6 0 1 0 0 0 1 1 0 0 0 28 1 0 0 0 29 2 0 0 0 8 - 32 1 0 0 0 18 1 7 0 0 54 1 7 0 0 1 2 - 7 0 6 0 1 2 0 0 62 0 1 2 7 0 6 0 1 2 - 0 0 62 0 1 4 7 6 59 0 6 6 1 2 0 6 59 - 0 1 3 0 6 59 0 6 1 3 0 6 0 30 6 1 2 0 + 35 1 0 0 0 18 1 7 0 0 66 1 7 0 0 1 2 + 7 0 6 0 1 2 0 0 79 0 1 2 7 0 6 0 1 2 + 0 0 79 0 1 4 7 6 76 0 6 6 1 2 0 6 76 + 0 1 3 0 6 76 0 6 1 3 0 6 0 30 6 1 2 0 6 0 30 1 1 0 11 0 1 2 7 30 6 0 1 3 7 - 30 6 0 30 1 2 0 30 62 0 1 1 0 25 0 27 - 1 0 38 0 1 2 7 11 0 0 1 2 0 0 8 6 1 2 + 30 6 0 30 1 2 0 30 79 0 1 1 0 25 0 27 + 1 0 48 0 1 2 7 11 0 0 1 2 0 0 8 6 1 2 0 11 0 8 1 1 6 30 0 31 2 5 0 0 0 1 2 - 5 0 0 0 1 3 0 0 55 0 0 57 2 5 0 0 0 1 - 3 0 0 55 0 0 1 1 0 25 0 1 2 7 11 6 0 - 52 1 6 30 0 1 2 5 0 0 0 1 2 0 0 67 0 - 1 3 0 0 59 0 0 1 2 0 0 67 0 1 1 0 0 6 + 5 0 0 0 1 3 0 0 67 0 0 69 2 5 0 0 0 1 + 3 0 0 67 0 0 1 1 0 25 0 1 2 7 11 6 0 + 64 1 6 30 0 1 2 5 0 0 0 1 2 0 0 84 0 + 1 3 0 0 76 0 0 1 2 0 0 84 0 1 1 0 0 6 1 2 0 11 0 8 1 1 0 25 0 1 1 0 11 0 1 - 1 7 48 0 50 2 0 0 0 8 1 1 0 6 0 1 3 0 + 1 7 59 0 62 2 0 0 0 8 1 1 0 6 0 1 3 0 0 6 0 30 1 3 0 0 0 0 30 1 3 0 0 0 0 - 30 1 3 0 0 6 0 30 1 1 0 70 0 1 2 0 11 - 30 0 1 1 7 69 0 1 2 0 0 0 8 1 1 0 6 0 - 13 2 0 71 62 0 1 2 0 0 0 6 1 1 0 11 0 - 1 2 0 11 62 0 1 3 9 0 0 6 6 1 3 9 0 0 - 25 25 1 2 9 0 0 60 1 2 9 0 0 61 1 2 0 + 30 1 3 0 0 6 0 30 1 1 0 86 0 1 2 0 11 + 30 0 1 1 7 32 0 1 2 0 0 0 8 1 1 0 6 0 + 13 2 0 87 79 0 1 2 0 0 0 6 1 1 0 11 0 + 1 2 0 11 79 0 1 3 9 0 0 6 6 1 3 9 0 0 + 25 25 1 2 9 0 0 77 1 2 9 0 0 78 1 2 0 11 0 0 12 2 7 11 6 0 1 1 0 25 0 1 1 0 11 0 17 0 0 0 16 2 0 6 0 30 1 3 0 6 0 - 30 6 1 2 0 0 0 64 1 2 0 6 0 65 1 2 0 - 0 0 19 20 2 0 6 0 14 15 2 0 6 0 66 1 - 2 0 30 0 0 1 2 0 0 0 64 1 2 0 0 0 30 - 1 2 0 0 0 64 1 2 0 0 0 30 1 1 0 11 0 - 33 1 0 0 0 1 1 0 0 0 1 1 0 8 0 1 1 0 - 0 0 35 2 7 8 6 0 1 2 0 8 62 0 1 3 0 0 - 0 0 30 1 1 0 0 0 34 1 3 68 0 1 1 0 0 - 25 26 2 0 0 0 0 53 2 0 0 0 6 1 1 0 0 - 38 1 2 0 0 0 6 1 2 0 0 6 0 10 2 0 0 0 - 0 1 1 8 36 0 45 1 0 38 0 1 2 7 11 0 0 - 1 2 0 11 62 0 1 2 5 11 0 0 1 2 5 11 0 - 0 1 2 7 11 0 0 47 2 5 11 0 0 1 2 5 11 + 30 6 1 2 0 0 0 81 1 2 0 6 0 82 1 2 0 + 0 0 19 20 2 0 6 0 14 15 2 0 6 0 83 1 + 2 0 30 0 0 1 2 0 0 0 81 1 2 0 0 0 30 + 1 2 0 0 0 81 1 2 0 0 0 30 1 1 0 11 0 + 39 1 0 0 0 1 1 0 0 0 1 1 0 8 0 1 1 0 + 0 0 44 2 7 8 6 0 1 2 0 8 79 0 1 3 0 0 + 0 0 30 1 1 0 0 0 40 1 3 85 0 1 1 0 0 + 25 26 2 0 0 0 0 65 2 0 0 0 6 1 1 0 0 + 48 1 2 0 0 0 6 1 2 0 0 6 0 10 2 0 0 0 + 0 1 1 8 41 0 54 1 0 48 0 1 2 7 11 0 0 + 1 2 0 11 79 0 1 2 5 11 0 0 1 2 5 11 0 + 0 1 2 7 11 0 0 58 2 5 11 0 0 1 2 5 11 0 0 1 1 0 8 0 9))))) '|lookupComplete|)) diff --git a/src/algebra/strap/INS-.lsp b/src/algebra/strap/INS-.lsp index 234dfc24..da1d5f67 100644 --- a/src/algebra/strap/INS-.lsp +++ b/src/algebra/strap/INS-.lsp @@ -97,25 +97,25 @@ (DEFUN |INS-;characteristic;Nni;1| ($) (DECLARE (IGNORE $)) 0) -(DEFUN |INS-;differentiate;2S;2| (|x| $) (|spadConstant| $ 9)) +(DEFUN |INS-;differentiate;2S;2| (|x| $) (|spadConstant| $ 10)) (DEFUN |INS-;even?;SB;3| (|x| $) - (NOT (SPADCALL |x| (|getShellEntry| $ 12)))) + (NOT (SPADCALL |x| (|getShellEntry| $ 13)))) (DEFUN |INS-;positive?;SB;4| (|x| $) - (SPADCALL (|spadConstant| $ 9) |x| (|getShellEntry| $ 14))) + (SPADCALL (|spadConstant| $ 10) |x| (|getShellEntry| $ 15))) (DEFUN |INS-;copy;2S;5| (|x| $) (DECLARE (IGNORE $)) |x|) (DEFUN |INS-;bit?;2SB;6| (|x| |i| $) (SPADCALL - (SPADCALL |x| (SPADCALL |i| (|getShellEntry| $ 17)) - (|getShellEntry| $ 18)) - (|getShellEntry| $ 12))) + (SPADCALL |x| (SPADCALL |i| (|getShellEntry| $ 18)) + (|getShellEntry| $ 19)) + (|getShellEntry| $ 13))) (DEFUN |INS-;mask;2S;7| (|n| $) - (SPADCALL (SPADCALL (|spadConstant| $ 20) |n| (|getShellEntry| $ 18)) - (|getShellEntry| $ 21))) + (SPADCALL (SPADCALL (|spadConstant| $ 21) |n| (|getShellEntry| $ 19)) + (|getShellEntry| $ 22))) (DEFUN |INS-;rational?;SB;8| (|x| $) (DECLARE (IGNORE $)) 'T) @@ -123,148 +123,148 @@ (PROG (#0=#:G1426 #1=#:G1427) (RETURN (COND - ((SPADCALL |x| (|spadConstant| $ 9) (|getShellEntry| $ 24)) + ((SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 26)) (|error| "euclideanSize called on zero")) - ((SPADCALL |x| (|spadConstant| $ 9) (|getShellEntry| $ 14)) - (PROG1 (LETT #0# (- (SPADCALL |x| (|getShellEntry| $ 26))) + ((SPADCALL |x| (|spadConstant| $ 10) (|getShellEntry| $ 15)) + (PROG1 (LETT #0# (- (SPADCALL |x| (|getShellEntry| $ 28))) |INS-;euclideanSize;SNni;9|) (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#))) ('T - (PROG1 (LETT #1# (SPADCALL |x| (|getShellEntry| $ 26)) + (PROG1 (LETT #1# (SPADCALL |x| (|getShellEntry| $ 28)) |INS-;euclideanSize;SNni;9|) (|check-subtype| (COND ((< #1# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #1#))))))) (DEFUN |INS-;convert;SF;10| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 29))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 28)) + (|getShellEntry| $ 32))) (DEFUN |INS-;convert;SDf;11| (|x| $) - (FLOAT (SPADCALL |x| (|getShellEntry| $ 26)) |$DoubleFloatMaximum|)) + (FLOAT (SPADCALL |x| (|getShellEntry| $ 28)) |$DoubleFloatMaximum|)) (DEFUN |INS-;convert;SIf;12| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 34))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 28)) + (|getShellEntry| $ 38))) (DEFUN |INS-;retract;SI;13| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 26))) + (SPADCALL |x| (|getShellEntry| $ 28))) (DEFUN |INS-;convert;SP;14| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 38))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 28)) + (|getShellEntry| $ 42))) (DEFUN |INS-;factor;SF;15| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 42))) + (SPADCALL |x| (|getShellEntry| $ 46))) (DEFUN |INS-;squareFree;SF;16| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 45))) + (SPADCALL |x| (|getShellEntry| $ 49))) (DEFUN |INS-;prime?;SB;17| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 48))) + (SPADCALL |x| (|getShellEntry| $ 52))) (DEFUN |INS-;factorial;2S;18| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 51))) + (SPADCALL |x| (|getShellEntry| $ 55))) (DEFUN |INS-;binomial;3S;19| (|n| |m| $) - (SPADCALL |n| |m| (|getShellEntry| $ 53))) + (SPADCALL |n| |m| (|getShellEntry| $ 57))) (DEFUN |INS-;permutation;3S;20| (|n| |m| $) - (SPADCALL |n| |m| (|getShellEntry| $ 55))) + (SPADCALL |n| |m| (|getShellEntry| $ 59))) (DEFUN |INS-;retractIfCan;SU;21| (|x| $) - (CONS 0 (SPADCALL |x| (|getShellEntry| $ 26)))) + (CONS 0 (SPADCALL |x| (|getShellEntry| $ 28)))) -(DEFUN |INS-;init;S;22| ($) (|spadConstant| $ 9)) +(DEFUN |INS-;init;S;22| ($) (|spadConstant| $ 10)) (DEFUN |INS-;nextItem;SU;23| (|n| $) (COND - ((SPADCALL |n| (|getShellEntry| $ 60)) - (CONS 0 (|spadConstant| $ 20))) - ((SPADCALL (|spadConstant| $ 9) |n| (|getShellEntry| $ 14)) - (CONS 0 (SPADCALL |n| (|getShellEntry| $ 17)))) + ((SPADCALL |n| (|getShellEntry| $ 64)) + (CONS 0 (|spadConstant| $ 21))) + ((SPADCALL (|spadConstant| $ 10) |n| (|getShellEntry| $ 15)) + (CONS 0 (SPADCALL |n| (|getShellEntry| $ 18)))) ('T (CONS 0 - (SPADCALL (|spadConstant| $ 20) |n| (|getShellEntry| $ 61)))))) + (SPADCALL (|spadConstant| $ 21) |n| (|getShellEntry| $ 65)))))) (DEFUN |INS-;patternMatch;SP2Pmr;24| (|x| |p| |l| $) - (SPADCALL |x| |p| |l| (|getShellEntry| $ 66))) + (SPADCALL |x| |p| |l| (|getShellEntry| $ 70))) (DEFUN |INS-;rational;SF;25| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 70))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 28)) + (|getShellEntry| $ 74))) (DEFUN |INS-;rationalIfCan;SU;26| (|x| $) (CONS 0 - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 70)))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 28)) + (|getShellEntry| $ 74)))) (DEFUN |INS-;symmetricRemainder;3S;27| (|x| |n| $) (PROG (|r|) (RETURN - (SEQ (LETT |r| (SPADCALL |x| |n| (|getShellEntry| $ 74)) + (SEQ (LETT |r| (SPADCALL |x| |n| (|getShellEntry| $ 78)) |INS-;symmetricRemainder;3S;27|) (EXIT (COND - ((SPADCALL |r| (|spadConstant| $ 9) - (|getShellEntry| $ 24)) + ((SPADCALL |r| (|spadConstant| $ 10) + (|getShellEntry| $ 26)) |r|) ('T (SEQ (COND - ((SPADCALL |n| (|spadConstant| $ 9) - (|getShellEntry| $ 14)) + ((SPADCALL |n| (|spadConstant| $ 10) + (|getShellEntry| $ 15)) (LETT |n| - (SPADCALL |n| (|getShellEntry| $ 17)) + (SPADCALL |n| (|getShellEntry| $ 18)) |INS-;symmetricRemainder;3S;27|))) (EXIT (COND - ((SPADCALL (|spadConstant| $ 9) |r| - (|getShellEntry| $ 14)) + ((SPADCALL (|spadConstant| $ 10) |r| + (|getShellEntry| $ 15)) (COND ((SPADCALL |n| (SPADCALL 2 |r| - (|getShellEntry| $ 76)) - (|getShellEntry| $ 14)) + (|getShellEntry| $ 80)) + (|getShellEntry| $ 15)) (SPADCALL |r| |n| - (|getShellEntry| $ 61))) + (|getShellEntry| $ 65))) ('T |r|))) - ((NULL (SPADCALL (|spadConstant| $ 9) + ((NULL (SPADCALL (|spadConstant| $ 10) (SPADCALL (SPADCALL 2 |r| - (|getShellEntry| $ 76)) - |n| (|getShellEntry| $ 77)) - (|getShellEntry| $ 14))) + (|getShellEntry| $ 80)) + |n| (|getShellEntry| $ 81)) + (|getShellEntry| $ 15))) (SPADCALL |r| |n| - (|getShellEntry| $ 77))) + (|getShellEntry| $ 81))) ('T |r|))))))))))) (DEFUN |INS-;invmod;3S;28| (|a| |b| $) (PROG (|q| |r| |r1| |c| |c1| |d| |d1|) (RETURN (SEQ (COND - ((SPADCALL |a| (|getShellEntry| $ 79)) - (LETT |a| (SPADCALL |a| |b| (|getShellEntry| $ 80)) + ((SPADCALL |a| (|getShellEntry| $ 83)) + (LETT |a| (SPADCALL |a| |b| (|getShellEntry| $ 84)) |INS-;invmod;3S;28|))) (LETT |c| |a| |INS-;invmod;3S;28|) - (LETT |c1| (|spadConstant| $ 20) |INS-;invmod;3S;28|) + (LETT |c1| (|spadConstant| $ 21) |INS-;invmod;3S;28|) (LETT |d| |b| |INS-;invmod;3S;28|) - (LETT |d1| (|spadConstant| $ 9) |INS-;invmod;3S;28|) + (LETT |d1| (|spadConstant| $ 10) |INS-;invmod;3S;28|) (SEQ G190 (COND - ((NULL (NOT (SPADCALL |d| (|getShellEntry| $ 60)))) + ((NULL (NOT (SPADCALL |d| (|getShellEntry| $ 64)))) (GO G191))) (SEQ (LETT |q| - (SPADCALL |c| |d| (|getShellEntry| $ 81)) + (SPADCALL |c| |d| (|getShellEntry| $ 85)) |INS-;invmod;3S;28|) (LETT |r| (SPADCALL |c| (SPADCALL |q| |d| - (|getShellEntry| $ 82)) - (|getShellEntry| $ 61)) + (|getShellEntry| $ 86)) + (|getShellEntry| $ 65)) |INS-;invmod;3S;28|) (LETT |r1| (SPADCALL |c1| (SPADCALL |q| |d1| - (|getShellEntry| $ 82)) - (|getShellEntry| $ 61)) + (|getShellEntry| $ 86)) + (|getShellEntry| $ 65)) |INS-;invmod;3S;28|) (LETT |c| |d| |INS-;invmod;3S;28|) (LETT |c1| |d1| |INS-;invmod;3S;28|) @@ -272,29 +272,29 @@ (EXIT (LETT |d1| |r1| |INS-;invmod;3S;28|))) NIL (GO G190) G191 (EXIT NIL)) (COND - ((NULL (SPADCALL |c| (|getShellEntry| $ 83))) + ((NULL (SPADCALL |c| (|getShellEntry| $ 87))) (EXIT (|error| "inverse does not exist")))) (EXIT (COND - ((SPADCALL |c1| (|getShellEntry| $ 79)) - (SPADCALL |c1| |b| (|getShellEntry| $ 77))) + ((SPADCALL |c1| (|getShellEntry| $ 83)) + (SPADCALL |c1| |b| (|getShellEntry| $ 81))) ('T |c1|))))))) (DEFUN |INS-;powmod;4S;29| (|x| |n| |p| $) (PROG (|y| #0=#:G1484 |z|) (RETURN (SEQ (EXIT (SEQ (COND - ((SPADCALL |x| (|getShellEntry| $ 79)) + ((SPADCALL |x| (|getShellEntry| $ 83)) (LETT |x| (SPADCALL |x| |p| - (|getShellEntry| $ 80)) + (|getShellEntry| $ 84)) |INS-;powmod;4S;29|))) (EXIT (COND - ((SPADCALL |x| (|getShellEntry| $ 60)) - (|spadConstant| $ 9)) - ((SPADCALL |n| (|getShellEntry| $ 60)) - (|spadConstant| $ 20)) + ((SPADCALL |x| (|getShellEntry| $ 64)) + (|spadConstant| $ 10)) + ((SPADCALL |n| (|getShellEntry| $ 64)) + (|spadConstant| $ 21)) ('T - (SEQ (LETT |y| (|spadConstant| $ 20) + (SEQ (LETT |y| (|spadConstant| $ 21) |INS-;powmod;4S;29|) (LETT |z| |x| |INS-;powmod;4S;29|) (EXIT @@ -302,10 +302,10 @@ (SEQ (COND ((SPADCALL |n| - (|getShellEntry| $ 12)) + (|getShellEntry| $ 13)) (LETT |y| (SPADCALL |y| |z| |p| - (|getShellEntry| $ 85)) + (|getShellEntry| $ 89)) |INS-;powmod;4S;29|))) (EXIT (COND @@ -313,11 +313,11 @@ (LETT |n| (SPADCALL |n| (SPADCALL - (|spadConstant| $ 20) - (|getShellEntry| $ 17)) - (|getShellEntry| $ 18)) + (|spadConstant| $ 21) + (|getShellEntry| $ 18)) + (|getShellEntry| $ 19)) |INS-;powmod;4S;29|) - (|getShellEntry| $ 60)) + (|getShellEntry| $ 64)) (PROGN (LETT #0# |y| |INS-;powmod;4S;29|) @@ -325,7 +325,7 @@ ('T (LETT |z| (SPADCALL |z| |z| |p| - (|getShellEntry| $ 85)) + (|getShellEntry| $ 89)) |INS-;powmod;4S;29|))))) NIL (GO G190) G191 (EXIT NIL))))))))) #0# (EXIT #0#))))) @@ -336,7 +336,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|IntegerNumberSystem&|)) (LETT |dv$| (LIST '|IntegerNumberSystem&| |dv$1|) . #0#) - (LETT $ (|newShell| 87) . #0#) + (LETT $ (|newShell| 91) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -346,71 +346,73 @@ (MAKEPROP '|IntegerNumberSystem&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) - (|NonNegativeInteger|) |INS-;characteristic;Nni;1| - (0 . |Zero|) |INS-;differentiate;2S;2| (|Boolean|) - (4 . |odd?|) |INS-;even?;SB;3| (9 . <) - |INS-;positive?;SB;4| |INS-;copy;2S;5| (15 . -) - (20 . |shift|) |INS-;bit?;2SB;6| (26 . |One|) (30 . |dec|) - |INS-;mask;2S;7| |INS-;rational?;SB;8| (35 . =) - (|Integer|) (41 . |convert|) |INS-;euclideanSize;SNni;9| - (|Float|) (46 . |coerce|) |INS-;convert;SF;10| - (|DoubleFloat|) |INS-;convert;SDf;11| (|InputForm|) - (51 . |convert|) |INS-;convert;SIf;12| - |INS-;retract;SI;13| (|Pattern| 25) (56 . |coerce|) + (|NonNegativeInteger|) (0 . |Zero|) + |INS-;characteristic;Nni;1| (4 . |Zero|) + |INS-;differentiate;2S;2| (|Boolean|) (8 . |odd?|) + |INS-;even?;SB;3| (13 . <) |INS-;positive?;SB;4| + |INS-;copy;2S;5| (19 . -) (24 . |shift|) |INS-;bit?;2SB;6| + (30 . |One|) (34 . |dec|) |INS-;mask;2S;7| (39 . |true|) + |INS-;rational?;SB;8| (43 . =) (|Integer|) + (49 . |convert|) (54 . -) |INS-;euclideanSize;SNni;9| + (|Float|) (59 . |coerce|) |INS-;convert;SF;10| + (|DoubleFloat|) (64 . |coerce|) |INS-;convert;SDf;11| + (|InputForm|) (69 . |convert|) |INS-;convert;SIf;12| + |INS-;retract;SI;13| (|Pattern| 27) (74 . |coerce|) |INS-;convert;SP;14| (|Factored| 6) - (|IntegerFactorizationPackage| 6) (61 . |factor|) - (|Factored| $) |INS-;factor;SF;15| (66 . |squareFree|) + (|IntegerFactorizationPackage| 6) (79 . |factor|) + (|Factored| $) |INS-;factor;SF;15| (84 . |squareFree|) |INS-;squareFree;SF;16| (|IntegerPrimesPackage| 6) - (71 . |prime?|) |INS-;prime?;SB;17| - (|IntegerCombinatoricFunctions| 6) (76 . |factorial|) - |INS-;factorial;2S;18| (81 . |binomial|) - |INS-;binomial;3S;19| (87 . |permutation|) - |INS-;permutation;3S;20| (|Union| 25 '"failed") - |INS-;retractIfCan;SU;21| |INS-;init;S;22| (93 . |zero?|) - (98 . -) (|Union| $ '"failed") |INS-;nextItem;SU;23| - (|PatternMatchResult| 25 6) + (89 . |prime?|) |INS-;prime?;SB;17| + (|IntegerCombinatoricFunctions| 6) (94 . |factorial|) + |INS-;factorial;2S;18| (99 . |binomial|) + |INS-;binomial;3S;19| (105 . |permutation|) + |INS-;permutation;3S;20| (|Union| 27 '"failed") + |INS-;retractIfCan;SU;21| |INS-;init;S;22| (111 . |zero?|) + (116 . -) (|Union| $ '"failed") |INS-;nextItem;SU;23| + (|PatternMatchResult| 27 6) (|PatternMatchIntegerNumberSystem| 6) - (104 . |patternMatch|) (|PatternMatchResult| 25 $) - |INS-;patternMatch;SP2Pmr;24| (|Fraction| 25) - (111 . |coerce|) |INS-;rational;SF;25| - (|Union| 69 '"failed") |INS-;rationalIfCan;SU;26| - (116 . |rem|) (|PositiveInteger|) (122 . *) (128 . +) - |INS-;symmetricRemainder;3S;27| (134 . |negative?|) - (139 . |positiveRemainder|) (145 . |quo|) (151 . *) - (157 . |one?|) |INS-;invmod;3S;28| (162 . |mulmod|) + (122 . |patternMatch|) (|PatternMatchResult| 27 $) + |INS-;patternMatch;SP2Pmr;24| (|Fraction| 27) + (129 . |coerce|) |INS-;rational;SF;25| + (|Union| 73 '"failed") |INS-;rationalIfCan;SU;26| + (134 . |rem|) (|PositiveInteger|) (140 . *) (146 . +) + |INS-;symmetricRemainder;3S;27| (152 . |negative?|) + (157 . |positiveRemainder|) (163 . |quo|) (169 . *) + (175 . |one?|) |INS-;invmod;3S;28| (180 . |mulmod|) |INS-;powmod;4S;29|) - '#(|symmetricRemainder| 169 |squareFree| 175 |retractIfCan| - 180 |retract| 185 |rationalIfCan| 190 |rational?| 195 - |rational| 200 |prime?| 205 |powmod| 210 |positive?| 217 - |permutation| 222 |patternMatch| 228 |nextItem| 235 |mask| - 240 |invmod| 245 |init| 251 |factorial| 255 |factor| 260 - |even?| 265 |euclideanSize| 270 |differentiate| 275 |copy| - 280 |convert| 285 |characteristic| 305 |bit?| 309 - |binomial| 315) + '#(|symmetricRemainder| 187 |squareFree| 193 |retractIfCan| + 198 |retract| 203 |rationalIfCan| 208 |rational?| 213 + |rational| 218 |prime?| 223 |powmod| 228 |positive?| 235 + |permutation| 240 |patternMatch| 246 |nextItem| 253 |mask| + 258 |invmod| 263 |init| 269 |factorial| 273 |factor| 278 + |even?| 283 |euclideanSize| 288 |differentiate| 293 |copy| + 298 |convert| 303 |characteristic| 323 |bit?| 327 + |binomial| 333) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 86 - '(0 6 0 9 1 6 11 0 12 2 6 11 0 0 14 1 6 - 0 0 17 2 6 0 0 0 18 0 6 0 20 1 6 0 0 - 21 2 6 11 0 0 24 1 6 25 0 26 1 28 0 - 25 29 1 33 0 25 34 1 37 0 25 38 1 41 - 40 6 42 1 41 40 6 45 1 47 11 6 48 1 - 50 6 6 51 2 50 6 6 6 53 2 50 6 6 6 55 - 1 6 11 0 60 2 6 0 0 0 61 3 65 64 6 37 - 64 66 1 69 0 25 70 2 6 0 0 0 74 2 6 0 - 75 0 76 2 6 0 0 0 77 1 6 11 0 79 2 6 - 0 0 0 80 2 6 0 0 0 81 2 6 0 0 0 82 1 - 6 11 0 83 3 6 0 0 0 0 85 2 0 0 0 0 78 - 1 0 43 0 46 1 0 57 0 58 1 0 25 0 36 1 - 0 72 0 73 1 0 11 0 23 1 0 69 0 71 1 0 - 11 0 49 3 0 0 0 0 0 86 1 0 11 0 15 2 - 0 0 0 0 56 3 0 67 0 37 67 68 1 0 62 0 - 63 1 0 0 0 22 2 0 0 0 0 84 0 0 0 59 1 - 0 0 0 52 1 0 43 0 44 1 0 11 0 13 1 0 - 7 0 27 1 0 0 0 10 1 0 0 0 16 1 0 31 0 - 32 1 0 28 0 30 1 0 37 0 39 1 0 33 0 - 35 0 0 7 8 2 0 11 0 0 19 2 0 0 0 0 - 54))))) + (|makeByteWordVec2| 90 + '(0 7 0 8 0 6 0 10 1 6 12 0 13 2 6 12 0 + 0 15 1 6 0 0 18 2 6 0 0 0 19 0 6 0 21 + 1 6 0 0 22 0 12 0 24 2 6 12 0 0 26 1 + 6 27 0 28 1 27 0 0 29 1 31 0 27 32 1 + 34 0 27 35 1 37 0 27 38 1 41 0 27 42 + 1 45 44 6 46 1 45 44 6 49 1 51 12 6 + 52 1 54 6 6 55 2 54 6 6 6 57 2 54 6 6 + 6 59 1 6 12 0 64 2 6 0 0 0 65 3 69 68 + 6 41 68 70 1 73 0 27 74 2 6 0 0 0 78 + 2 6 0 79 0 80 2 6 0 0 0 81 1 6 12 0 + 83 2 6 0 0 0 84 2 6 0 0 0 85 2 6 0 0 + 0 86 1 6 12 0 87 3 6 0 0 0 0 89 2 0 0 + 0 0 82 1 0 47 0 50 1 0 61 0 62 1 0 27 + 0 40 1 0 76 0 77 1 0 12 0 25 1 0 73 0 + 75 1 0 12 0 53 3 0 0 0 0 0 90 1 0 12 + 0 16 2 0 0 0 0 60 3 0 71 0 41 71 72 1 + 0 66 0 67 1 0 0 0 23 2 0 0 0 0 88 0 0 + 0 63 1 0 0 0 56 1 0 47 0 48 1 0 12 0 + 14 1 0 7 0 30 1 0 0 0 11 1 0 0 0 17 1 + 0 34 0 36 1 0 31 0 33 1 0 41 0 43 1 0 + 37 0 39 0 0 7 9 2 0 12 0 0 20 2 0 0 0 + 0 58))))) '|lookupComplete|)) diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp index fd48fd1a..c7ad0701 100644 --- a/src/algebra/strap/INT.lsp +++ b/src/algebra/strap/INT.lsp @@ -249,12 +249,12 @@ (DEFUN |INT;writeOMInt| (|dev| |x| $) (SEQ (COND ((< |x| 0) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 8)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 13)) (SPADCALL |dev| "arith1" "unary_minus" - (|getShellEntry| $ 10)) - (SPADCALL |dev| (- |x|) (|getShellEntry| $ 12)) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 13))))) - ('T (SPADCALL |dev| |x| (|getShellEntry| $ 12)))))) + (|getShellEntry| $ 15)) + (SPADCALL |dev| (- |x|) (|getShellEntry| $ 18)) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 19))))) + ('T (SPADCALL |dev| |x| (|getShellEntry| $ 18)))))) (DEFUN |INT;OMwrite;$S;2| (|x| $) (PROG (|sp| |dev| |s|) @@ -262,13 +262,13 @@ (SEQ (LETT |s| "" |INT;OMwrite;$S;2|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |INT;OMwrite;$S;2|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 15)) - (|getShellEntry| $ 16)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 21)) + (|getShellEntry| $ 22)) |INT;OMwrite;$S;2|) - (SPADCALL |dev| (|getShellEntry| $ 17)) + (SPADCALL |dev| (|getShellEntry| $ 23)) (|INT;writeOMInt| |dev| |x| $) - (SPADCALL |dev| (|getShellEntry| $ 18)) - (SPADCALL |dev| (|getShellEntry| $ 19)) + (SPADCALL |dev| (|getShellEntry| $ 24)) + (SPADCALL |dev| (|getShellEntry| $ 25)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |INT;OMwrite;$S;2|) (EXIT |s|))))) @@ -278,26 +278,26 @@ (SEQ (LETT |s| "" |INT;OMwrite;$BS;3|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |INT;OMwrite;$BS;3|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 15)) - (|getShellEntry| $ 16)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 21)) + (|getShellEntry| $ 22)) |INT;OMwrite;$BS;3|) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17)))) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23)))) (|INT;writeOMInt| |dev| |x| $) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18)))) - (SPADCALL |dev| (|getShellEntry| $ 19)) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 24)))) + (SPADCALL |dev| (|getShellEntry| $ 25)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |INT;OMwrite;$BS;3|) (EXIT |s|))))) (DEFUN |INT;OMwrite;Omd$V;4| (|dev| |x| $) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 17)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 23)) (|INT;writeOMInt| |dev| |x| $) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 18))))) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 24))))) (DEFUN |INT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $) - (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17)))) + (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23)))) (|INT;writeOMInt| |dev| |x| $) (EXIT (COND - (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18))))))) + (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 24))))))) (DEFUN |INT;zero?;$B;6| (|x| $) (DECLARE (IGNORE $)) (ZEROP |x|)) @@ -322,7 +322,7 @@ (MINUSP |x|)) (DEFUN |INT;coerce;$Of;16| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 37))) + (SPADCALL |x| (|getShellEntry| $ 45))) (DEFUN |INT;coerce;2$;17| (|m| $) (DECLARE (IGNORE $)) |m|) @@ -355,14 +355,14 @@ (REMAINDER2 (* |a| |b|) |p|)) (DEFUN |INT;convert;$F;23| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 46))) + (SPADCALL |x| (|getShellEntry| $ 56))) (DEFUN |INT;convert;$Df;24| (|x| $) (DECLARE (IGNORE $)) (FLOAT |x| |$DoubleFloatMaximum|)) (DEFUN |INT;convert;$If;25| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 51))) + (SPADCALL |x| (|getShellEntry| $ 62))) (DEFUN |INT;convert;$S;26| (|x| $) (DECLARE (IGNORE $)) @@ -449,51 +449,51 @@ (ABS |x|)) (DEFUN |INT;solveLinearPolynomialEquation| (|lp| |p| $) - (SPADCALL |lp| |p| (|getShellEntry| $ 93))) + (SPADCALL |lp| |p| (|getShellEntry| $ 99))) (DEFUN |INT;squareFreePolynomial| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 97))) + (SPADCALL |p| (|getShellEntry| $ 103))) (DEFUN |INT;factorPolynomial| (|p| $) (PROG (|pp| #0=#:G1498) (RETURN - (SEQ (LETT |pp| (SPADCALL |p| (|getShellEntry| $ 98)) + (SEQ (LETT |pp| (SPADCALL |p| (|getShellEntry| $ 104)) |INT;factorPolynomial|) (EXIT (COND - ((EQL (SPADCALL |pp| (|getShellEntry| $ 99)) - (SPADCALL |p| (|getShellEntry| $ 99))) - (SPADCALL |p| (|getShellEntry| $ 101))) + ((EQL (SPADCALL |pp| (|getShellEntry| $ 105)) + (SPADCALL |p| (|getShellEntry| $ 105))) + (SPADCALL |p| (|getShellEntry| $ 107))) ('T - (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 101)) + (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 107)) (SPADCALL (CONS #'|INT;factorPolynomial!0| $) (SPADCALL (PROG2 (LETT #0# (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 99)) + (|getShellEntry| $ 105)) (SPADCALL |pp| - (|getShellEntry| $ 99)) - (|getShellEntry| $ 103)) + (|getShellEntry| $ 105)) + (|getShellEntry| $ 109)) |INT;factorPolynomial|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) $ #0#)) - (|getShellEntry| $ 105)) - (|getShellEntry| $ 109)) - (|getShellEntry| $ 111))))))))) + (|getShellEntry| $ 111)) + (|getShellEntry| $ 115)) + (|getShellEntry| $ 117))))))))) (DEFUN |INT;factorPolynomial!0| (|#1| $) - (SPADCALL |#1| (|getShellEntry| $ 102))) + (SPADCALL |#1| (|getShellEntry| $ 108))) (DEFUN |INT;factorSquareFreePolynomial| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 112))) + (SPADCALL |p| (|getShellEntry| $ 118))) (DEFUN |INT;gcdPolynomial;3Sup;57| (|p| |q| $) (COND - ((SPADCALL |p| (|getShellEntry| $ 113)) - (SPADCALL |q| (|getShellEntry| $ 114))) - ((SPADCALL |q| (|getShellEntry| $ 113)) - (SPADCALL |p| (|getShellEntry| $ 114))) - ('T (SPADCALL (LIST |p| |q|) (|getShellEntry| $ 117))))) + ((SPADCALL |p| (|getShellEntry| $ 119)) + (SPADCALL |q| (|getShellEntry| $ 120))) + ((SPADCALL |q| (|getShellEntry| $ 119)) + (SPADCALL |p| (|getShellEntry| $ 120))) + ('T (SPADCALL (LIST |p| |q|) (|getShellEntry| $ 123))))) (DEFUN |Integer| () (PROG () @@ -517,100 +517,103 @@ (RETURN (PROGN (LETT |dv$| '(|Integer|) . #0=(|Integer|)) - (LETT $ (|newShell| 132) . #0#) + (LETT $ (|newShell| 138) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) (|haddProp| |$ConstructorCache| '|Integer| NIL (CONS 1 $)) (|stuffDomainSlots| $) - (|setShellEntry| $ 72 - (|setShellEntry| $ 71 + (|setShellEntry| $ 80 + (|setShellEntry| $ 52 (CONS (|dispatchFunction| |INT;*;3$;40|) $))) $)))) (MAKEPROP '|Integer| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL NIL (|Void|) (|OpenMathDevice|) - (0 . |OMputApp|) (|String|) (5 . |OMputSymbol|) - (|Integer|) (12 . |OMputInteger|) (18 . |OMputEndApp|) - (|OpenMathEncoding|) (23 . |OMencodingXML|) - (27 . |OMopenString|) (33 . |OMputObject|) - (38 . |OMputEndObject|) (43 . |OMclose|) - |INT;OMwrite;$S;2| (|Boolean|) |INT;OMwrite;$BS;3| - |INT;OMwrite;Omd$V;4| |INT;OMwrite;Omd$BV;5| - |INT;zero?;$B;6| |INT;one?;$B;7| + (LIST '#(NIL NIL NIL NIL NIL NIL (CONS IDENTITY (FUNCALL (|dispatchFunction| |INT;Zero;$;8|) $)) + (|NonNegativeInteger|) (0 . |Zero|) (|Boolean|) + |INT;<;2$B;35| (|Void|) (|OpenMathDevice|) + (4 . |OMputApp|) (|String|) (9 . |OMputSymbol|) + |INT;-;2$;36| (|Integer|) (16 . |OMputInteger|) + (22 . |OMputEndApp|) (|OpenMathEncoding|) + (27 . |OMencodingXML|) (31 . |OMopenString|) + (37 . |OMputObject|) (42 . |OMputEndObject|) + (47 . |OMclose|) |INT;OMwrite;$S;2| |INT;OMwrite;$BS;3| + |INT;OMwrite;Omd$V;4| |INT;OMwrite;Omd$BV;5| + |INT;zero?;$B;6| (CONS IDENTITY (FUNCALL (|dispatchFunction| |INT;One;$;9|) $)) - |INT;base;$;10| |INT;copy;2$;11| |INT;inc;2$;12| - |INT;dec;2$;13| (|SingleInteger|) |INT;hash;$Si;14| - |INT;negative?;$B;15| (|OutputForm|) (48 . |outputForm|) - |INT;coerce;$Of;16| |INT;coerce;2$;17| |INT;convert;2$;18| - |INT;length;2$;19| |INT;addmod;4$;20| |INT;submod;4$;21| - |INT;mulmod;4$;22| (|Float|) (53 . |coerce|) - |INT;convert;$F;23| (|DoubleFloat|) |INT;convert;$Df;24| - (|InputForm|) (58 . |convert|) |INT;convert;$If;25| - |INT;convert;$S;26| |INT;latex;$S;27| - |INT;positiveRemainder;3$;28| (|Matrix| 11) (|Matrix| $) - |INT;reducedSystem;2M;29| (|Vector| 11) - (|Record| (|:| |mat| 56) (|:| |vec| 59)) (|Vector| $) + (52 . |One|) |INT;=;2$B;34| |INT;one?;$B;7| + |INT;base;$;10| |INT;copy;2$;11| |INT;+;3$;37| + |INT;inc;2$;12| |INT;-;3$;38| |INT;dec;2$;13| + (|SingleInteger|) |INT;hash;$Si;14| |INT;negative?;$B;15| + (|OutputForm|) (56 . |outputForm|) |INT;coerce;$Of;16| + |INT;coerce;2$;17| |INT;convert;2$;18| |INT;length;2$;19| + |INT;addmod;4$;20| |INT;submod;4$;21| NIL |INT;rem;3$;47| + |INT;mulmod;4$;22| (|Float|) (61 . |coerce|) + |INT;convert;$F;23| (|DoubleFloat|) (66 . |coerce|) + |INT;convert;$Df;24| (|InputForm|) (71 . |convert|) + |INT;convert;$If;25| (76 . |string|) |INT;convert;$S;26| + (81 . <) (87 . |concat|) |INT;latex;$S;27| + |INT;positiveRemainder;3$;28| (|Matrix| 17) (|Matrix| $) + |INT;reducedSystem;2M;29| (|Vector| 17) + (|Record| (|:| |mat| 70) (|:| |vec| 73)) (|Vector| $) |INT;reducedSystem;MVR;30| |INT;abs;2$;31| - |INT;random;$;32| |INT;random;2$;33| |INT;=;2$B;34| - |INT;<;2$B;35| |INT;-;2$;36| |INT;+;3$;37| |INT;-;3$;38| - NIL NIL (|NonNegativeInteger|) |INT;**;$Nni$;41| + |INT;random;$;32| |INT;random;2$;33| NIL |INT;**;$Nni$;41| |INT;odd?;$B;42| |INT;max;3$;43| |INT;min;3$;44| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - |INT;divide;2$R;45| |INT;quo;3$;46| |INT;rem;3$;47| - |INT;shift;3$;48| (|Union| $ '"failed") |INT;recip;$U;49| - |INT;gcd;3$;50| + |INT;divide;2$R;45| |INT;quo;3$;46| |INT;shift;3$;48| + (|Union| $ '"failed") |INT;recip;$U;49| |INT;gcd;3$;50| (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) |INT;unitNormal;$R;51| |INT;unitCanonical;2$;52| - (|SparseUnivariatePolynomial| 11) (|List| 89) - (|Union| 90 '"failed") + (|SparseUnivariatePolynomial| 17) (|List| 95) + (|Union| 96 '"failed") (|IntegerSolveLinearPolynomialEquation|) - (63 . |solveLinearPolynomialEquation|) - (|SparseUnivariatePolynomial| $$) (|Factored| 94) - (|UnivariatePolynomialSquareFree| $$ 94) - (69 . |squareFree|) (74 . |primitivePart|) - (79 . |leadingCoefficient|) (|GaloisGroupFactorizer| 94) - (84 . |factor|) (89 . |coerce|) (94 . |exquo|) - (|Factored| $) (100 . |factor|) (|Mapping| 94 $$) - (|Factored| $$) (|FactoredFunctions2| $$ 94) (105 . |map|) - (|FactoredFunctionUtilities| 94) (111 . |mergeFactors|) - (117 . |factorSquareFree|) (122 . |zero?|) - (127 . |unitCanonical|) (|List| 94) (|HeuGcd| 94) - (132 . |gcd|) (|SparseUnivariatePolynomial| $) - |INT;gcdPolynomial;3Sup;57| (|Fraction| 11) - (|Union| 120 '"failed") (|PatternMatchResult| 11 $) - (|Pattern| 11) (|Union| 11 '"failed") (|List| $) - (|Record| (|:| |coef| 125) (|:| |generator| $)) - (|Union| 125 '"failed") + (93 . |solveLinearPolynomialEquation|) + (|SparseUnivariatePolynomial| $$) (|Factored| 100) + (|UnivariatePolynomialSquareFree| $$ 100) + (99 . |squareFree|) (104 . |primitivePart|) + (109 . |leadingCoefficient|) (|GaloisGroupFactorizer| 100) + (114 . |factor|) (119 . |coerce|) (124 . |exquo|) + (|Factored| $) (130 . |factor|) (|Mapping| 100 $$) + (|Factored| $$) (|FactoredFunctions2| $$ 100) + (135 . |map|) (|FactoredFunctionUtilities| 100) + (141 . |mergeFactors|) (147 . |factorSquareFree|) + (152 . |zero?|) (157 . |unitCanonical|) (|List| 100) + (|HeuGcd| 100) (162 . |gcd|) + (|SparseUnivariatePolynomial| $) + |INT;gcdPolynomial;3Sup;57| (|Fraction| 17) + (|Union| 126 '"failed") (|PatternMatchResult| 17 $) + (|Pattern| 17) (|Union| 17 '"failed") (|List| $) + (|Record| (|:| |coef| 131) (|:| |generator| $)) + (|Union| 131 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 129 '"failed") (|PositiveInteger|)) - '#(~= 137 |zero?| 143 |unitNormal| 148 |unitCanonical| 153 - |unit?| 158 |symmetricRemainder| 163 |subtractIfCan| 169 - |submod| 175 |squareFreePart| 182 |squareFree| 187 - |sizeLess?| 192 |sign| 198 |shift| 203 |sample| 209 - |retractIfCan| 213 |retract| 218 |rem| 223 |reducedSystem| - 229 |recip| 240 |rationalIfCan| 245 |rational?| 250 - |rational| 255 |random| 260 |quo| 269 |principalIdeal| 275 - |prime?| 280 |powmod| 285 |positiveRemainder| 292 - |positive?| 298 |permutation| 303 |patternMatch| 309 - |one?| 316 |odd?| 321 |nextItem| 326 |negative?| 331 - |multiEuclidean| 336 |mulmod| 342 |min| 349 |max| 355 - |mask| 361 |length| 366 |lcm| 371 |latex| 382 |invmod| 387 - |init| 393 |inc| 397 |hash| 402 |gcdPolynomial| 407 |gcd| - 413 |factorial| 424 |factor| 429 |extendedEuclidean| 434 - |exquo| 447 |expressIdealMember| 453 |even?| 459 - |euclideanSize| 464 |divide| 469 |differentiate| 475 |dec| - 486 |copy| 491 |convert| 496 |coerce| 526 |characteristic| - 546 |bit?| 550 |binomial| 556 |base| 562 |associates?| 566 - |addmod| 572 |abs| 579 |Zero| 584 |One| 588 |OMwrite| 592 - D 616 >= 627 > 633 = 639 <= 645 < 651 - 657 + 668 ** 674 * - 686) + (|Union| 135 '"failed") (|PositiveInteger|)) + '#(~= 167 |zero?| 173 |unitNormal| 178 |unitCanonical| 183 + |unit?| 188 |symmetricRemainder| 193 |subtractIfCan| 199 + |submod| 205 |squareFreePart| 212 |squareFree| 217 + |sizeLess?| 222 |sign| 228 |shift| 233 |sample| 239 + |retractIfCan| 243 |retract| 248 |rem| 253 |reducedSystem| + 259 |recip| 270 |rationalIfCan| 275 |rational?| 280 + |rational| 285 |random| 290 |quo| 299 |principalIdeal| 305 + |prime?| 310 |powmod| 315 |positiveRemainder| 322 + |positive?| 328 |permutation| 333 |patternMatch| 339 + |one?| 346 |odd?| 351 |nextItem| 356 |negative?| 361 + |multiEuclidean| 366 |mulmod| 372 |min| 379 |max| 385 + |mask| 391 |length| 396 |lcm| 401 |latex| 412 |invmod| 417 + |init| 423 |inc| 427 |hash| 432 |gcdPolynomial| 437 |gcd| + 443 |factorial| 454 |factor| 459 |extendedEuclidean| 464 + |exquo| 477 |expressIdealMember| 483 |even?| 489 + |euclideanSize| 494 |divide| 499 |differentiate| 505 |dec| + 516 |copy| 521 |convert| 526 |coerce| 556 |characteristic| + 576 |bit?| 580 |binomial| 586 |base| 592 |associates?| 596 + |addmod| 602 |abs| 609 |Zero| 614 |One| 618 |OMwrite| 622 + D 646 >= 657 > 663 = 669 <= 675 < 681 - 687 + 698 ** 704 * + 716) '((|infinite| . 0) (|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) @@ -637,7 +640,7 @@ (|OrderedIntegralDomain|) (|GcdDomain|) (|IntegralDomain|) (|Algebra| $$) (|CharacteristicZero|) - (|LinearlyExplicitRingOver| 11) + (|LinearlyExplicitRingOver| 17) (|DifferentialRing|) (|OrderedRing|) (|CommutativeRing|) (|EntireRing|) (|Module| $$) (|BiModule| $$ $$) @@ -650,66 +653,68 @@ (|CancellationAbelianMonoid|) (|OrderedAbelianSemiGroup|) (|AbelianMonoid|) (|Monoid|) - (|StepThrough|) (|PatternMatchable| 11) + (|StepThrough|) (|PatternMatchable| 17) (|OrderedSet|) (|AbelianSemiGroup|) (|SemiGroup|) (|RealConstant|) - (|RetractableTo| 11) (|SetCategory|) - (|OpenMath|) (|ConvertibleTo| 9) - (|ConvertibleTo| 45) - (|ConvertibleTo| 48) + (|RetractableTo| 17) (|SetCategory|) + (|OpenMath|) (|ConvertibleTo| 14) + (|ConvertibleTo| 55) + (|ConvertibleTo| 58) (|CombinatorialFunctionCategory|) - (|ConvertibleTo| 123) - (|ConvertibleTo| 50) - (|ConvertibleTo| 11) + (|ConvertibleTo| 129) + (|ConvertibleTo| 61) + (|ConvertibleTo| 17) (|CoercibleFrom| $$) - (|CoercibleFrom| 11) (|BasicType|) - (|CoercibleTo| 36)) - (|makeByteWordVec2| 131 - '(1 7 6 0 8 3 7 6 0 9 9 10 2 7 6 0 11 - 12 1 7 6 0 13 0 14 0 15 2 7 0 9 14 16 - 1 7 6 0 17 1 7 6 0 18 1 7 6 0 19 1 36 - 0 11 37 1 45 0 11 46 1 50 0 11 51 2 - 92 91 90 89 93 1 96 95 94 97 1 94 0 0 - 98 1 94 2 0 99 1 100 95 94 101 1 94 0 - 2 102 2 0 83 0 0 103 1 0 104 0 105 2 - 108 95 106 107 109 2 110 95 95 95 111 - 1 100 95 94 112 1 94 21 0 113 1 94 0 - 0 114 1 116 94 115 117 2 0 21 0 0 1 1 - 0 21 0 25 1 0 86 0 87 1 0 0 0 88 1 0 - 21 0 1 2 0 0 0 0 1 2 0 83 0 0 1 3 0 0 - 0 0 0 43 1 0 0 0 1 1 0 104 0 1 2 0 21 - 0 0 1 1 0 11 0 1 2 0 0 0 0 82 0 0 0 1 - 1 0 124 0 1 1 0 11 0 1 2 0 0 0 0 81 2 - 0 60 57 61 62 1 0 56 57 58 1 0 83 0 - 84 1 0 121 0 1 1 0 21 0 1 1 0 120 0 1 - 0 0 0 64 1 0 0 0 65 2 0 0 0 0 80 1 0 - 126 125 1 1 0 21 0 1 3 0 0 0 0 0 1 2 - 0 0 0 0 55 1 0 21 0 1 2 0 0 0 0 1 3 0 - 122 0 123 122 1 1 0 21 0 26 1 0 21 0 - 75 1 0 83 0 1 1 0 21 0 35 2 0 127 125 - 0 1 3 0 0 0 0 0 44 2 0 0 0 0 77 2 0 0 - 0 0 76 1 0 0 0 1 1 0 0 0 41 2 0 0 0 0 - 1 1 0 0 125 1 1 0 9 0 54 2 0 0 0 0 1 - 0 0 0 1 1 0 0 0 31 1 0 33 0 34 2 0 - 118 118 118 119 2 0 0 0 0 85 1 0 0 - 125 1 1 0 0 0 1 1 0 104 0 105 2 0 128 - 0 0 1 3 0 130 0 0 0 1 2 0 83 0 0 103 - 2 0 127 125 0 1 1 0 21 0 1 1 0 73 0 1 - 2 0 78 0 0 79 1 0 0 0 1 2 0 0 0 73 1 - 1 0 0 0 32 1 0 0 0 30 1 0 9 0 53 1 0 - 48 0 49 1 0 45 0 47 1 0 50 0 52 1 0 - 123 0 1 1 0 11 0 40 1 0 0 11 39 1 0 0 - 0 1 1 0 0 11 39 1 0 36 0 38 0 0 73 1 - 2 0 21 0 0 1 2 0 0 0 0 1 0 0 0 29 2 0 - 21 0 0 1 3 0 0 0 0 0 42 1 0 0 0 63 0 - 0 0 27 0 0 0 28 3 0 6 7 0 21 24 2 0 9 - 0 21 22 2 0 6 7 0 23 1 0 9 0 20 1 0 0 - 0 1 2 0 0 0 73 1 2 0 21 0 0 1 2 0 21 - 0 0 1 2 0 21 0 0 66 2 0 21 0 0 1 2 0 - 21 0 0 67 2 0 0 0 0 70 1 0 0 0 68 2 0 - 0 0 0 69 2 0 0 0 73 74 2 0 0 0 131 1 - 2 0 0 0 0 71 2 0 0 11 0 72 2 0 0 73 0 - 1 2 0 0 131 0 1))))) + (|CoercibleFrom| 17) (|BasicType|) + (|CoercibleTo| 44)) + (|makeByteWordVec2| 137 + '(0 7 0 8 1 12 11 0 13 3 12 11 0 14 14 + 15 2 12 11 0 17 18 1 12 11 0 19 0 20 + 0 21 2 12 0 14 20 22 1 12 11 0 23 1 + 12 11 0 24 1 12 11 0 25 0 7 0 32 1 44 + 0 17 45 1 55 0 17 56 1 58 0 17 59 1 + 61 0 17 62 1 14 0 17 64 2 17 9 0 0 66 + 2 14 0 0 0 67 2 98 97 96 95 99 1 102 + 101 100 103 1 100 0 0 104 1 100 2 0 + 105 1 106 101 100 107 1 100 0 2 108 2 + 0 89 0 0 109 1 0 110 0 111 2 114 101 + 112 113 115 2 116 101 101 101 117 1 + 106 101 100 118 1 100 9 0 119 1 100 0 + 0 120 1 122 100 121 123 2 0 9 0 0 1 1 + 0 9 0 30 1 0 92 0 93 1 0 0 0 94 1 0 9 + 0 1 2 0 0 0 0 1 2 0 89 0 0 1 3 0 0 0 + 0 0 51 1 0 0 0 1 1 0 110 0 1 2 0 9 0 + 0 1 1 0 17 0 1 2 0 0 0 0 88 0 0 0 1 1 + 0 130 0 1 1 0 17 0 1 2 0 0 0 0 53 2 0 + 74 71 75 76 1 0 70 71 72 1 0 89 0 90 + 1 0 127 0 1 1 0 9 0 1 1 0 126 0 1 0 0 + 0 78 1 0 0 0 79 2 0 0 0 0 87 1 0 132 + 131 1 1 0 9 0 1 3 0 0 0 0 0 1 2 0 0 0 + 0 69 1 0 9 0 1 2 0 0 0 0 1 3 0 128 0 + 129 128 1 1 0 9 0 34 1 0 9 0 82 1 0 + 89 0 1 1 0 9 0 43 2 0 133 131 0 1 3 0 + 0 0 0 0 54 2 0 0 0 0 84 2 0 0 0 0 83 + 1 0 0 0 1 1 0 0 0 49 2 0 0 0 0 1 1 0 + 0 131 1 1 0 14 0 68 2 0 0 0 0 1 0 0 0 + 1 1 0 0 0 38 1 0 41 0 42 2 0 124 124 + 124 125 2 0 0 0 0 91 1 0 0 131 1 1 0 + 0 0 1 1 0 110 0 111 2 0 134 0 0 1 3 0 + 136 0 0 0 1 2 0 89 0 0 109 2 0 133 + 131 0 1 1 0 9 0 1 1 0 7 0 1 2 0 85 0 + 0 86 1 0 0 0 1 2 0 0 0 7 1 1 0 0 0 40 + 1 0 0 0 36 1 0 14 0 65 1 0 58 0 60 1 + 0 55 0 57 1 0 61 0 63 1 0 129 0 1 1 0 + 17 0 48 1 0 0 17 47 1 0 0 0 1 1 0 0 + 17 47 1 0 44 0 46 0 0 7 1 2 0 9 0 0 1 + 2 0 0 0 0 1 0 0 0 35 2 0 9 0 0 1 3 0 + 0 0 0 0 50 1 0 0 0 77 0 0 0 6 0 0 0 + 31 3 0 11 12 0 9 29 2 0 14 0 9 27 2 0 + 11 12 0 28 1 0 14 0 26 1 0 0 0 1 2 0 + 0 0 7 1 2 0 9 0 0 1 2 0 9 0 0 1 2 0 9 + 0 0 33 2 0 9 0 0 1 2 0 9 0 0 10 2 0 0 + 0 0 39 1 0 0 0 16 2 0 0 0 0 37 2 0 0 + 0 7 81 2 0 0 0 137 1 2 0 0 0 0 52 2 0 + 0 17 0 80 2 0 0 7 0 1 2 0 0 137 0 1))))) '|lookupComplete|)) (MAKEPROP '|Integer| 'NILADIC T) diff --git a/src/algebra/strap/INTDOM-.lsp b/src/algebra/strap/INTDOM-.lsp index b44a7d0d..9cdf7fb7 100644 --- a/src/algebra/strap/INTDOM-.lsp +++ b/src/algebra/strap/INTDOM-.lsp @@ -38,7 +38,7 @@ (DEFUN |INTDOM-;associates?;2SB;5| (|x| |y| $) (SPADCALL (QVELT (SPADCALL |x| (|getShellEntry| $ 10)) 1) (QVELT (SPADCALL |y| (|getShellEntry| $ 10)) 1) - (|getShellEntry| $ 19))) + (|getShellEntry| $ 21))) (DEFUN |INTDOM-;associates?;2SB;6| (|x| |y| $) (COND @@ -56,7 +56,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|IntegralDomain&|)) (LETT |dv$| (LIST '|IntegralDomain&| |dv$1|) . #0#) - (LETT $ (|newShell| 21) . #0#) + (LETT $ (|newShell| 23) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -69,11 +69,11 @@ (CONS (|dispatchFunction| |INTDOM-;unitNormal;SR;1|) $)))) (COND ((|HasAttribute| |#1| '|canonicalUnitNormal|) - (|setShellEntry| $ 20 + (|setShellEntry| $ 22 (CONS (|dispatchFunction| |INTDOM-;associates?;2SB;5|) $))) ('T - (|setShellEntry| $ 20 + (|setShellEntry| $ 22 (CONS (|dispatchFunction| |INTDOM-;associates?;2SB;6|) $)))) $)))) @@ -85,18 +85,18 @@ (4 . |unitNormal|) (9 . |unitNormal|) |INTDOM-;unitCanonical;2S;2| (|Boolean|) (14 . |zero?|) (|Union| $ '"failed") (19 . |exquo|) |INTDOM-;recip;SU;3| - (25 . |recip|) |INTDOM-;unit?;SB;4| (30 . =) - (36 . |associates?|)) - '#(|unitNormal| 42 |unitCanonical| 47 |unit?| 52 |recip| 57 - |associates?| 62) + (25 . |recip|) (30 . |false|) (34 . |true|) + |INTDOM-;unit?;SB;4| (38 . =) (44 . |associates?|)) + '#(|unitNormal| 50 |unitCanonical| 55 |unit?| 60 |recip| 65 + |associates?| 70) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 20 + (|makeByteWordVec2| 22 '(0 6 0 7 1 0 8 0 9 1 6 8 0 10 1 6 12 0 - 13 2 6 14 0 0 15 1 6 14 0 17 2 6 12 0 - 0 19 2 0 12 0 0 20 1 0 8 0 9 1 0 0 0 - 11 1 0 12 0 18 1 0 14 0 16 2 0 12 0 0 - 20))))) + 13 2 6 14 0 0 15 1 6 14 0 17 0 12 0 + 18 0 12 0 19 2 6 12 0 0 21 2 0 12 0 0 + 22 1 0 8 0 9 1 0 0 0 11 1 0 12 0 20 1 + 0 14 0 16 2 0 12 0 0 22))))) '|lookupComplete|)) diff --git a/src/algebra/strap/ISTRING.lsp b/src/algebra/strap/ISTRING.lsp index a7ba5fa0..33d4cd6d 100644 --- a/src/algebra/strap/ISTRING.lsp +++ b/src/algebra/strap/ISTRING.lsp @@ -160,22 +160,22 @@ (DEFUN |ISTRING;insert;2$I$;9| (|s| |t| |i| $) (STRCONC (STRCONC (|ISTRING;elt;$Us$;31| |s| (SPADCALL (|getShellEntry| $ 6) (- |i| 1) - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) |t|) (|ISTRING;elt;$Us$;31| |s| - (SPADCALL |i| (|getShellEntry| $ 22)) $))) + (SPADCALL |i| (|getShellEntry| $ 26)) $))) (DEFUN |ISTRING;coerce;$Of;10| (|s| $) - (SPADCALL |s| (|getShellEntry| $ 26))) + (SPADCALL |s| (|getShellEntry| $ 30))) (DEFUN |ISTRING;minIndex;$I;11| (|s| $) (|getShellEntry| $ 6)) (DEFUN |ISTRING;upperCase!;2$;12| (|s| $) - (SPADCALL (ELT $ 31) |s| (|getShellEntry| $ 33))) + (SPADCALL (ELT $ 35) |s| (|getShellEntry| $ 37))) (DEFUN |ISTRING;lowerCase!;2$;13| (|s| $) - (SPADCALL (ELT $ 36) |s| (|getShellEntry| $ 33))) + (SPADCALL (ELT $ 40) |s| (|getShellEntry| $ 37))) (DEFUN |ISTRING;latex;$S;14| (|s| $) (STRCONC "\\mbox{``" (STRCONC |s| "''}"))) @@ -185,18 +185,18 @@ #3=#:G1539 |k|) (RETURN (SEQ (LETT |l| - (- (SPADCALL |sg| (|getShellEntry| $ 39)) + (- (SPADCALL |sg| (|getShellEntry| $ 44)) (|getShellEntry| $ 6)) |ISTRING;replace;$Us2$;15|) (LETT |m| (QCSIZE |s|) |ISTRING;replace;$Us2$;15|) (LETT |n| (QCSIZE |t|) |ISTRING;replace;$Us2$;15|) (LETT |h| (COND - ((SPADCALL |sg| (|getShellEntry| $ 40)) - (- (SPADCALL |sg| (|getShellEntry| $ 41)) + ((SPADCALL |sg| (|getShellEntry| $ 45)) + (- (SPADCALL |sg| (|getShellEntry| $ 46)) (|getShellEntry| $ 6))) ('T - (- (SPADCALL |s| (|getShellEntry| $ 42)) + (- (SPADCALL |s| (|getShellEntry| $ 47)) (|getShellEntry| $ 6)))) |ISTRING;replace;$Us2$;15|) (COND @@ -208,7 +208,7 @@ |ISTRING;replace;$Us2$;15|) (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (SPADCALL (|getShellEntry| $ 43))) + (SPADCALL (|getShellEntry| $ 52))) |ISTRING;replace;$Us2$;15|) (SEQ (LETT |i| 0 |ISTRING;replace;$Us2$;15|) (LETT #1# (- |l| 1) |ISTRING;replace;$Us2$;15|) @@ -247,7 +247,7 @@ (DEFUN |ISTRING;setelt;$I2C;16| (|s| |i| |c| $) (SEQ (COND ((OR (< |i| (|getShellEntry| $ 6)) - (< (SPADCALL |s| (|getShellEntry| $ 42)) |i|)) + (< (SPADCALL |s| (|getShellEntry| $ 47)) |i|)) (|error| "index out of range")) ('T (SEQ (QESET |s| (- |i| (|getShellEntry| $ 6)) |c|) @@ -382,7 +382,7 @@ (EXIT (COND ((SPADCALL (CHAR |t| |r|) |cc| - (|getShellEntry| $ 49)) + (|getShellEntry| $ 64)) (PROGN (LETT #1# (+ |r| @@ -398,9 +398,9 @@ (DEFUN |ISTRING;suffix?;2$B;21| (|s| |t| $) (PROG (|n| |m|) (RETURN - (SEQ (LETT |n| (SPADCALL |t| (|getShellEntry| $ 42)) + (SEQ (LETT |n| (SPADCALL |t| (|getShellEntry| $ 47)) |ISTRING;suffix?;2$B;21|) - (LETT |m| (SPADCALL |s| (|getShellEntry| $ 42)) + (LETT |m| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;suffix?;2$B;21|) (EXIT (COND ((< |n| |m|) 'NIL) @@ -411,19 +411,19 @@ (DEFUN |ISTRING;split;$CL;22| (|s| |c| $) (PROG (|n| |j| |i| |l|) (RETURN - (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;split;$CL;22|) (SEQ (LETT |i| (|getShellEntry| $ 6) |ISTRING;split;$CL;22|) G190 (COND ((OR (> |i| |n|) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 53)))) + |c| (|getShellEntry| $ 68)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) |ISTRING;split;$CL;22|) (GO G190) G191 (EXIT NIL)) - (LETT |l| (SPADCALL (|getShellEntry| $ 55)) + (LETT |l| (SPADCALL (|getShellEntry| $ 70)) |ISTRING;split;$CL;22|) (SEQ G190 (COND @@ -440,9 +440,9 @@ (SPADCALL (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| (- |j| 1) - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 56)) + |l| (|getShellEntry| $ 71)) |ISTRING;split;$CL;22|) (EXIT (SEQ (LETT |i| |j| |ISTRING;split;$CL;22|) G190 @@ -451,7 +451,7 @@ (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 53)))) + |c| (|getShellEntry| $ 68)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) @@ -463,16 +463,16 @@ (LETT |l| (SPADCALL (|ISTRING;elt;$Us$;31| |s| - (SPADCALL |i| |n| (|getShellEntry| $ 20)) + (SPADCALL |i| |n| (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 56)) + |l| (|getShellEntry| $ 71)) |ISTRING;split;$CL;22|))) - (EXIT (SPADCALL |l| (|getShellEntry| $ 57))))))) + (EXIT (SPADCALL |l| (|getShellEntry| $ 72))))))) (DEFUN |ISTRING;split;$CcL;23| (|s| |cc| $) (PROG (|n| |j| |i| |l|) (RETURN - (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;split;$CcL;23|) (SEQ (LETT |i| (|getShellEntry| $ 6) |ISTRING;split;$CcL;23|) @@ -480,12 +480,12 @@ (COND ((OR (> |i| |n|) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 49)))) + |cc| (|getShellEntry| $ 64)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) |ISTRING;split;$CcL;23|) (GO G190) G191 (EXIT NIL)) - (LETT |l| (SPADCALL (|getShellEntry| $ 55)) + (LETT |l| (SPADCALL (|getShellEntry| $ 70)) |ISTRING;split;$CcL;23|) (SEQ G190 (COND @@ -502,9 +502,9 @@ (SPADCALL (|ISTRING;elt;$Us$;31| |s| (SPADCALL |i| (- |j| 1) - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 56)) + |l| (|getShellEntry| $ 71)) |ISTRING;split;$CcL;23|) (EXIT (SEQ (LETT |i| |j| |ISTRING;split;$CcL;23|) G190 @@ -513,7 +513,7 @@ (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 49)))) + |cc| (|getShellEntry| $ 64)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) @@ -525,16 +525,16 @@ (LETT |l| (SPADCALL (|ISTRING;elt;$Us$;31| |s| - (SPADCALL |i| |n| (|getShellEntry| $ 20)) + (SPADCALL |i| |n| (|getShellEntry| $ 24)) $) - |l| (|getShellEntry| $ 56)) + |l| (|getShellEntry| $ 71)) |ISTRING;split;$CcL;23|))) - (EXIT (SPADCALL |l| (|getShellEntry| $ 57))))))) + (EXIT (SPADCALL |l| (|getShellEntry| $ 72))))))) (DEFUN |ISTRING;leftTrim;$C$;24| (|s| |c| $) (PROG (|n| |i|) (RETURN - (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;leftTrim;$C$;24|) (SEQ (LETT |i| (|getShellEntry| $ 6) |ISTRING;leftTrim;$C$;24|) @@ -542,18 +542,18 @@ (COND ((OR (> |i| |n|) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |c| (|getShellEntry| $ 53)))) + |c| (|getShellEntry| $ 68)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) |ISTRING;leftTrim;$C$;24|) (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| - (SPADCALL |i| |n| (|getShellEntry| $ 20)) $)))))) + (SPADCALL |i| |n| (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;leftTrim;$Cc$;25| (|s| |cc| $) (PROG (|n| |i|) (RETURN - (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (LETT |n| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;leftTrim;$Cc$;25|) (SEQ (LETT |i| (|getShellEntry| $ 6) |ISTRING;leftTrim;$Cc$;25|) @@ -561,18 +561,18 @@ (COND ((OR (> |i| |n|) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |i| $) - |cc| (|getShellEntry| $ 49)))) + |cc| (|getShellEntry| $ 64)))) (GO G191))) (SEQ (EXIT 0)) (LETT |i| (+ |i| 1) |ISTRING;leftTrim;$Cc$;25|) (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| - (SPADCALL |i| |n| (|getShellEntry| $ 20)) $)))))) + (SPADCALL |i| |n| (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;rightTrim;$C$;26| (|s| |c| $) (PROG (|j| #0=#:G1543) (RETURN - (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;rightTrim;$C$;26|) (LETT #0# (|getShellEntry| $ 6) |ISTRING;rightTrim;$C$;26|) @@ -580,20 +580,20 @@ (COND ((OR (< |j| #0#) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) - |c| (|getShellEntry| $ 53)))) + |c| (|getShellEntry| $ 68)))) (GO G191))) (SEQ (EXIT 0)) (LETT |j| (+ |j| -1) |ISTRING;rightTrim;$C$;26|) (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL (|ISTRING;minIndex;$I;11| |s| $) |j| - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;rightTrim;$Cc$;27| (|s| |cc| $) (PROG (|j| #0=#:G1544) (RETURN - (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 42)) + (SEQ (SEQ (LETT |j| (SPADCALL |s| (|getShellEntry| $ 47)) |ISTRING;rightTrim;$Cc$;27|) (LETT #0# (|getShellEntry| $ 6) |ISTRING;rightTrim;$Cc$;27|) @@ -601,14 +601,14 @@ (COND ((OR (< |j| #0#) (NULL (SPADCALL (|ISTRING;elt;$IC;30| |s| |j| $) - |cc| (|getShellEntry| $ 49)))) + |cc| (|getShellEntry| $ 64)))) (GO G191))) (SEQ (EXIT 0)) (LETT |j| (+ |j| -1) |ISTRING;rightTrim;$Cc$;27|) (GO G190) G191 (EXIT NIL)) (EXIT (|ISTRING;elt;$Us$;31| |s| (SPADCALL (|ISTRING;minIndex;$I;11| |s| $) |j| - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $)))))) (DEFUN |ISTRING;concat;L$;28| (|l| $) @@ -644,7 +644,7 @@ (LETT #0# (CDR #0#) |ISTRING;concat;L$;28|) (GO G190) G191 (EXIT NIL)) (COND (#3# #2#) ('T 0))) - (SPADCALL (|getShellEntry| $ 43))) + (SPADCALL (|getShellEntry| $ 52))) |ISTRING;concat;L$;28|) (LETT |i| (|getShellEntry| $ 6) |ISTRING;concat;L$;28|) (SEQ (LETT |s| NIL |ISTRING;concat;L$;28|) @@ -677,7 +677,7 @@ (DEFUN |ISTRING;elt;$IC;30| (|s| |i| $) (COND ((OR (< |i| (|getShellEntry| $ 6)) - (< (SPADCALL |s| (|getShellEntry| $ 42)) |i|)) + (< (SPADCALL |s| (|getShellEntry| $ 47)) |i|)) (|error| "index out of range")) ('T (CHAR |s| (- |i| (|getShellEntry| $ 6)))))) @@ -685,16 +685,16 @@ (PROG (|l| |h|) (RETURN (SEQ (LETT |l| - (- (SPADCALL |sg| (|getShellEntry| $ 39)) + (- (SPADCALL |sg| (|getShellEntry| $ 44)) (|getShellEntry| $ 6)) |ISTRING;elt;$Us$;31|) (LETT |h| (COND - ((SPADCALL |sg| (|getShellEntry| $ 40)) - (- (SPADCALL |sg| (|getShellEntry| $ 41)) + ((SPADCALL |sg| (|getShellEntry| $ 45)) + (- (SPADCALL |sg| (|getShellEntry| $ 46)) (|getShellEntry| $ 6))) ('T - (- (SPADCALL |s| (|getShellEntry| $ 42)) + (- (SPADCALL |s| (|getShellEntry| $ 47)) (|getShellEntry| $ 6)))) |ISTRING;elt;$Us$;31|) (COND @@ -712,23 +712,23 @@ (SPADCALL (|ISTRING;elt;$IC;30| |s| (|getShellEntry| $ 6) $) - (|getShellEntry| $ 67))) + (|getShellEntry| $ 87))) ('T (* (* (SPADCALL (|ISTRING;elt;$IC;30| |s| (|getShellEntry| $ 6) $) - (|getShellEntry| $ 67)) + (|getShellEntry| $ 87)) (SPADCALL (|ISTRING;elt;$IC;30| |s| (- (+ (|getShellEntry| $ 6) |n|) 1) $) - (|getShellEntry| $ 67))) + (|getShellEntry| $ 87))) (SPADCALL (|ISTRING;elt;$IC;30| |s| (+ (|getShellEntry| $ 6) (QUOTIENT2 |n| 2)) $) - (|getShellEntry| $ 67)))))))))) + (|getShellEntry| $ 87)))))))))) (DEFUN |ISTRING;match;2$CNni;33| (|pattern| |target| |wildcard| $) (|stringMatch| |pattern| |target| (CHARACTER |wildcard|))) @@ -738,7 +738,7 @@ |p| #4=#:G1522 |q|) (RETURN (SEQ (EXIT (SEQ (LETT |n| - (SPADCALL |pattern| (|getShellEntry| $ 42)) + (SPADCALL |pattern| (|getShellEntry| $ 47)) |ISTRING;match?;2$CB;34|) (LETT |p| (PROG1 (LETT #0# @@ -760,17 +760,17 @@ ('T (SEQ (COND ((SPADCALL |p| |m| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 92)) (COND ((NULL (SPADCALL (|ISTRING;elt;$Us$;31| |pattern| (SPADCALL |m| (- |p| 1) - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) |target| - (|getShellEntry| $ 71))) + (|getShellEntry| $ 93))) (EXIT 'NIL))))) (LETT |i| |p| |ISTRING;match?;2$CB;34|) @@ -791,13 +791,13 @@ (COND ((NULL (SPADCALL |q| (- |m| 1) - (|getShellEntry| $ 70))) + (|getShellEntry| $ 92))) (GO G191))) (SEQ (LETT |s| (|ISTRING;elt;$Us$;31| |pattern| (SPADCALL (+ |p| 1) (- |q| 1) - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) |ISTRING;match?;2$CB;34|) (LETT |i| @@ -844,14 +844,14 @@ NIL (GO G190) G191 (EXIT NIL)) (COND ((SPADCALL |p| |n| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 92)) (COND ((NULL (|ISTRING;suffix?;2$B;21| (|ISTRING;elt;$Us$;31| |pattern| (SPADCALL (+ |p| 1) |n| - (|getShellEntry| $ 20)) + (|getShellEntry| $ 24)) $) |target| $)) (EXIT 'NIL))))) @@ -884,7 +884,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|IndexedString|)) (LETT |dv$| (LIST '|IndexedString| |dv$1|) . #0#) - (LETT $ (|newShell| 84) . #0#) + (LETT $ (|newShell| 105) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -929,52 +929,58 @@ (MAKEPROP '|IndexedString| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|NonNegativeInteger|) (|Character|) |ISTRING;new;NniC$;1| - |ISTRING;empty;$;2| (|Boolean|) |ISTRING;empty?;$B;3| - |ISTRING;#;$Nni;4| |ISTRING;=;2$B;5| |ISTRING;<;2$B;6| - |ISTRING;concat;3$;7| |ISTRING;copy;2$;8| (|Integer|) - (|UniversalSegment| 18) (0 . SEGMENT) - |ISTRING;elt;$Us$;31| (6 . SEGMENT) + |ISTRING;empty;$;2| (|Integer|) (0 . |Zero|) (|Boolean|) + (4 . =) |ISTRING;empty?;$B;3| |ISTRING;#;$Nni;4| + |ISTRING;=;2$B;5| |ISTRING;<;2$B;6| |ISTRING;concat;3$;7| + |ISTRING;copy;2$;8| (10 . |One|) (14 . -) + (|UniversalSegment| 11) (20 . SEGMENT) + |ISTRING;elt;$Us$;31| (26 . SEGMENT) |ISTRING;insert;2$I$;9| (|String|) (|OutputForm|) - (11 . |outputForm|) |ISTRING;coerce;$Of;10| + (31 . |outputForm|) |ISTRING;coerce;$Of;10| |ISTRING;minIndex;$I;11| (|CharacterClass|) - (16 . |upperCase|) (20 . |upperCase|) (|Mapping| 8 8) - (25 . |map!|) |ISTRING;upperCase!;2$;12| - (31 . |lowerCase|) (35 . |lowerCase|) - |ISTRING;lowerCase!;2$;13| |ISTRING;latex;$S;14| - (40 . |lo|) (45 . |hasHi|) (50 . |hi|) (55 . |maxIndex|) - (60 . |space|) |ISTRING;replace;$Us2$;15| - |ISTRING;setelt;$I2C;16| |ISTRING;substring?;2$IB;17| - |ISTRING;position;2$2I;18| |ISTRING;position;C$2I;19| - (64 . |member?|) |ISTRING;position;Cc$2I;20| - |ISTRING;suffix?;2$B;21| |ISTRING;elt;$IC;30| (70 . =) - (|List| $$) (76 . |empty|) (80 . |concat|) - (86 . |reverse!|) (|List| $) |ISTRING;split;$CL;22| - |ISTRING;split;$CcL;23| |ISTRING;leftTrim;$C$;24| - |ISTRING;leftTrim;$Cc$;25| |ISTRING;rightTrim;$C$;26| - |ISTRING;rightTrim;$Cc$;27| |ISTRING;copyInto!;2$I$;29| - |ISTRING;concat;L$;28| (91 . |ord|) |ISTRING;hash;$I;32| - |ISTRING;match;2$CNni;33| (96 . ~=) (102 . |prefix?|) + (36 . |upperCase|) (40 . |upperCase|) (|Mapping| 8 8) + (45 . |map!|) |ISTRING;upperCase!;2$;12| + (51 . |lowerCase|) (55 . |lowerCase|) + |ISTRING;lowerCase!;2$;13| (60 . |concat|) + |ISTRING;latex;$S;14| (66 . |lo|) (71 . |hasHi|) + (76 . |hi|) (81 . |maxIndex|) (86 . |Zero|) (90 . <) + (96 . |One|) (100 . +) (106 . |space|) (|SingleInteger|) + (110 . |Zero|) (114 . |One|) |ISTRING;replace;$Us2$;15| + |ISTRING;setelt;$I2C;16| (118 . |false|) (122 . |true|) + |ISTRING;substring?;2$IB;17| |ISTRING;position;2$2I;18| + (126 . -) |ISTRING;position;C$2I;19| (132 . |member?|) + |ISTRING;position;Cc$2I;20| |ISTRING;suffix?;2$B;21| + |ISTRING;elt;$IC;30| (138 . =) (|List| $$) (144 . |empty|) + (148 . |concat|) (154 . |reverse!|) (|List| $) + |ISTRING;split;$CL;22| |ISTRING;split;$CcL;23| + |ISTRING;leftTrim;$C$;24| |ISTRING;leftTrim;$Cc$;25| + (159 . -) |ISTRING;rightTrim;$C$;26| + |ISTRING;rightTrim;$Cc$;27| (164 . +) + |ISTRING;copyInto!;2$I$;29| |ISTRING;concat;L$;28| + (170 . |max|) (176 . |zero?|) (181 . |one?|) (186 . |ord|) + (191 . *) (197 . |quo|) |ISTRING;hash;$I;32| + |ISTRING;match;2$CNni;33| (203 . ~=) (209 . |prefix?|) |ISTRING;match?;2$CB;34| (|List| 8) (|Equation| 8) - (|List| 74) (|Mapping| 8 8 8) (|InputForm|) - (|SingleInteger|) (|Mapping| 11 8) (|Mapping| 11 8 8) - (|Void|) (|Union| 8 '"failed") (|List| 18)) - '#(~= 108 |upperCase!| 114 |upperCase| 119 |trim| 124 |swap!| - 136 |suffix?| 143 |substring?| 149 |split| 156 |sorted?| - 168 |sort!| 179 |sort| 190 |size?| 201 |setelt| 207 - |select| 221 |sample| 227 |rightTrim| 231 |reverse!| 243 - |reverse| 248 |replace| 253 |removeDuplicates| 260 - |remove| 265 |reduce| 277 |qsetelt!| 298 |qelt| 305 - |prefix?| 311 |position| 317 |parts| 350 |new| 355 |more?| - 361 |minIndex| 367 |min| 372 |merge| 378 |members| 391 - |member?| 396 |maxIndex| 402 |max| 407 |match?| 413 - |match| 420 |map!| 427 |map| 433 |lowerCase!| 446 - |lowerCase| 451 |less?| 456 |leftTrim| 462 |latex| 474 - |insert| 479 |indices| 493 |index?| 498 |hash| 504 |first| - 514 |find| 519 |fill!| 525 |every?| 531 |eval| 537 |eq?| - 563 |entry?| 569 |entries| 575 |empty?| 580 |empty| 585 - |elt| 589 |delete| 614 |count| 626 |copyInto!| 638 |copy| - 645 |convert| 650 |construct| 655 |concat| 660 |coerce| - 683 |any?| 693 >= 699 > 705 = 711 <= 717 < 723 |#| 729) + (|List| 96) (|Mapping| 8 8 8) (|InputForm|) + (|Mapping| 13 8) (|Mapping| 13 8 8) (|Void|) + (|Union| 8 '"failed") (|List| 11)) + '#(~= 215 |upperCase!| 221 |upperCase| 226 |trim| 231 |swap!| + 243 |suffix?| 250 |substring?| 256 |split| 263 |sorted?| + 275 |sort!| 286 |sort| 297 |size?| 308 |setelt| 314 + |select| 328 |sample| 334 |rightTrim| 338 |reverse!| 350 + |reverse| 355 |replace| 360 |removeDuplicates| 367 + |remove| 372 |reduce| 384 |qsetelt!| 405 |qelt| 412 + |prefix?| 418 |position| 424 |parts| 457 |new| 462 |more?| + 468 |minIndex| 474 |min| 479 |merge| 485 |members| 498 + |member?| 503 |maxIndex| 509 |max| 514 |match?| 520 + |match| 527 |map!| 534 |map| 540 |lowerCase!| 553 + |lowerCase| 558 |less?| 563 |leftTrim| 569 |latex| 581 + |insert| 586 |indices| 600 |index?| 605 |hash| 611 |first| + 621 |find| 626 |fill!| 632 |every?| 638 |eval| 644 |eq?| + 670 |entry?| 676 |entries| 682 |empty?| 687 |empty| 692 + |elt| 696 |delete| 721 |count| 733 |copyInto!| 745 |copy| + 752 |convert| 757 |construct| 762 |concat| 767 |coerce| + 790 |any?| 800 >= 806 > 812 = 818 <= 824 < 830 |#| 836) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 5 '(0 0 0 0 0 0 0 5 0 0 1 4 0 0 1 2 3 4)) @@ -990,58 +996,66 @@ (|OneDimensionalArrayAggregate| 8) (|FiniteLinearAggregate| 8) (|LinearAggregate| 8) - (|IndexedAggregate| 18 8) + (|IndexedAggregate| 11 8) (|Collection| 8) (|HomogeneousAggregate| 8) (|OrderedSet|) (|Aggregate|) - (|EltableAggregate| 18 8) (|Evalable| 8) + (|EltableAggregate| 11 8) (|Evalable| 8) (|SetCategory|) (|Type|) - (|Eltable| 18 8) (|InnerEvalable| 8 8) - (|CoercibleTo| 25) (|ConvertibleTo| 77) + (|Eltable| 11 8) (|InnerEvalable| 8 8) + (|CoercibleTo| 29) (|ConvertibleTo| 99) (|BasicType|)) - (|makeByteWordVec2| 83 - '(2 19 0 18 18 20 1 19 0 18 22 1 25 0 - 24 26 0 29 0 30 1 8 0 0 31 2 0 0 32 0 - 33 0 29 0 35 1 8 0 0 36 1 19 18 0 39 - 1 19 11 0 40 1 19 18 0 41 1 0 18 0 42 - 0 8 0 43 2 29 11 8 0 49 2 8 11 0 0 53 - 0 54 0 55 2 54 0 2 0 56 1 54 0 0 57 1 - 8 7 0 67 2 18 11 0 0 70 2 0 11 0 0 71 - 2 7 11 0 0 1 1 0 0 0 34 1 0 0 0 1 2 0 - 0 0 8 1 2 0 0 0 29 1 3 0 81 0 18 18 1 - 2 0 11 0 0 51 3 0 11 0 0 18 46 2 0 58 - 0 29 60 2 0 58 0 8 59 1 5 11 0 1 2 0 - 11 80 0 1 1 5 0 0 1 2 0 0 80 0 1 1 5 - 0 0 1 2 0 0 80 0 1 2 0 11 0 7 1 3 0 8 - 0 19 8 1 3 0 8 0 18 8 45 2 0 0 79 0 1 - 0 0 0 1 2 0 0 0 8 63 2 0 0 0 29 64 1 - 0 0 0 1 1 0 0 0 1 3 0 0 0 19 0 44 1 7 - 0 0 1 2 7 0 8 0 1 2 0 0 79 0 1 4 7 8 - 76 0 8 8 1 3 0 8 76 0 8 1 2 0 8 76 0 - 1 3 0 8 0 18 8 1 2 0 8 0 18 1 2 0 11 - 0 0 71 3 7 18 8 0 18 48 2 7 18 8 0 1 - 3 0 18 29 0 18 50 3 0 18 0 0 18 47 2 - 0 18 79 0 1 1 0 73 0 1 2 0 0 7 8 9 2 - 0 11 0 7 1 1 6 18 0 28 2 5 0 0 0 1 2 - 5 0 0 0 1 3 0 0 80 0 0 1 1 0 73 0 1 2 - 7 11 8 0 1 1 6 18 0 42 2 5 0 0 0 1 3 - 0 11 0 0 8 72 3 0 7 0 0 8 69 2 0 0 32 - 0 33 3 0 0 76 0 0 1 2 0 0 32 0 1 1 0 - 0 0 37 1 0 0 0 1 2 0 11 0 7 1 2 0 0 0 - 8 61 2 0 0 0 29 62 1 7 24 0 38 3 0 0 - 8 0 18 1 3 0 0 0 0 18 23 1 0 83 0 1 2 - 0 11 18 0 1 1 7 78 0 1 1 0 18 0 68 1 - 6 8 0 1 2 0 82 79 0 1 2 0 0 0 8 1 2 0 - 11 79 0 1 3 9 0 0 73 73 1 3 9 0 0 8 8 - 1 2 9 0 0 75 1 2 9 0 0 74 1 2 0 11 0 - 0 1 2 7 11 8 0 1 1 0 73 0 1 1 0 11 0 - 12 0 0 0 10 2 0 0 0 0 1 2 0 0 0 19 21 - 2 0 8 0 18 52 3 0 8 0 18 8 1 2 0 0 0 - 18 1 2 0 0 0 19 1 2 7 7 8 0 1 2 0 7 - 79 0 1 3 0 0 0 0 18 65 1 0 0 0 17 1 3 - 77 0 1 1 0 0 73 1 1 0 0 58 66 2 0 0 0 - 0 16 2 0 0 0 8 1 2 0 0 8 0 1 1 8 25 0 - 27 1 0 0 8 1 2 0 11 79 0 1 2 5 11 0 0 - 1 2 5 11 0 0 1 2 7 11 0 0 14 2 5 11 0 - 0 1 2 5 11 0 0 15 1 0 7 0 13))))) + (|makeByteWordVec2| 104 + '(0 11 0 12 2 11 13 0 0 14 0 11 0 21 2 + 11 0 0 0 22 2 23 0 11 11 24 1 23 0 11 + 26 1 29 0 28 30 0 33 0 34 1 8 0 0 35 + 2 0 0 36 0 37 0 33 0 39 1 8 0 0 40 2 + 28 0 0 0 42 1 23 11 0 44 1 23 13 0 45 + 1 23 11 0 46 1 0 11 0 47 0 7 0 48 2 + 11 13 0 0 49 0 7 0 50 2 11 0 0 0 51 0 + 8 0 52 0 53 0 54 0 53 0 55 0 13 0 58 + 0 13 0 59 2 53 0 0 0 62 2 33 13 8 0 + 64 2 8 13 0 0 68 0 69 0 70 2 69 0 2 0 + 71 1 69 0 0 72 1 53 0 0 78 2 7 0 0 0 + 81 2 11 0 0 0 84 1 11 13 0 85 1 11 13 + 0 86 1 8 7 0 87 2 11 0 11 0 88 2 11 0 + 0 0 89 2 11 13 0 0 92 2 0 13 0 0 93 2 + 7 13 0 0 1 1 0 0 0 38 1 0 0 0 1 2 0 0 + 0 8 1 2 0 0 0 33 1 3 0 102 0 11 11 1 + 2 0 13 0 0 66 3 0 13 0 0 11 60 2 0 73 + 0 33 75 2 0 73 0 8 74 1 5 13 0 1 2 0 + 13 101 0 1 1 5 0 0 1 2 0 0 101 0 1 1 + 5 0 0 1 2 0 0 101 0 1 2 0 13 0 7 1 3 + 0 8 0 23 8 1 3 0 8 0 11 8 57 2 0 0 + 100 0 1 0 0 0 1 2 0 0 0 8 79 2 0 0 0 + 33 80 1 0 0 0 1 1 0 0 0 1 3 0 0 0 23 + 0 56 1 7 0 0 1 2 7 0 8 0 1 2 0 0 100 + 0 1 4 7 8 98 0 8 8 1 3 0 8 98 0 8 1 2 + 0 8 98 0 1 3 0 8 0 11 8 1 2 0 8 0 11 + 1 2 0 13 0 0 93 3 7 11 8 0 11 63 2 7 + 11 8 0 1 3 0 11 33 0 11 65 3 0 11 0 0 + 11 61 2 0 11 100 0 1 1 0 95 0 1 2 0 0 + 7 8 9 2 0 13 0 7 1 1 6 11 0 32 2 5 0 + 0 0 1 2 5 0 0 0 1 3 0 0 101 0 0 1 1 0 + 95 0 1 2 7 13 8 0 1 1 6 11 0 47 2 5 0 + 0 0 1 3 0 13 0 0 8 94 3 0 7 0 0 8 91 + 2 0 0 36 0 37 3 0 0 98 0 0 1 2 0 0 36 + 0 1 1 0 0 0 41 1 0 0 0 1 2 0 13 0 7 1 + 2 0 0 0 8 76 2 0 0 0 33 77 1 7 28 0 + 43 3 0 0 8 0 11 1 3 0 0 0 0 11 27 1 0 + 104 0 1 2 0 13 11 0 1 1 7 53 0 1 1 0 + 11 0 90 1 6 8 0 1 2 0 103 100 0 1 2 0 + 0 0 8 1 2 0 13 100 0 1 3 9 0 0 95 95 + 1 3 9 0 0 8 8 1 2 9 0 0 97 1 2 9 0 0 + 96 1 2 0 13 0 0 1 2 7 13 8 0 1 1 0 95 + 0 1 1 0 13 0 15 0 0 0 10 2 0 0 0 0 1 + 2 0 0 0 23 25 2 0 8 0 11 67 3 0 8 0 + 11 8 1 2 0 0 0 11 1 2 0 0 0 23 1 2 7 + 7 8 0 1 2 0 7 100 0 1 3 0 0 0 0 11 82 + 1 0 0 0 20 1 3 99 0 1 1 0 0 95 1 1 0 + 0 73 83 2 0 0 0 0 19 2 0 0 0 8 1 2 0 + 0 8 0 1 1 8 29 0 31 1 0 0 8 1 2 0 13 + 100 0 1 2 5 13 0 0 1 2 5 13 0 0 1 2 7 + 13 0 0 17 2 5 13 0 0 1 2 5 13 0 0 18 + 1 0 7 0 16))))) '|lookupComplete|)) diff --git a/src/algebra/strap/LIST.lsp b/src/algebra/strap/LIST.lsp index d4c195af..f49808e5 100644 --- a/src/algebra/strap/LIST.lsp +++ b/src/algebra/strap/LIST.lsp @@ -61,14 +61,14 @@ (APPEND |l| |t|)) (DEFUN |LIST;writeOMList| (|dev| |x| $) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 14)) - (SPADCALL |dev| "list1" "list" (|getShellEntry| $ 16)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 16)) + (SPADCALL |dev| "list1" "list" (|getShellEntry| $ 18)) (SEQ G190 (COND ((NULL (NOT (NULL |x|))) (GO G191))) (SEQ (SPADCALL |dev| (|SPADfirst| |x|) 'NIL - (|getShellEntry| $ 17)) + (|getShellEntry| $ 21)) (EXIT (LETT |x| (CDR |x|) |LIST;writeOMList|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 18))))) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 23))))) (DEFUN |LIST;OMwrite;$S;6| (|x| $) (PROG (|sp| |dev| |s|) @@ -76,13 +76,13 @@ (SEQ (LETT |s| "" |LIST;OMwrite;$S;6|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |LIST;OMwrite;$S;6|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 20)) - (|getShellEntry| $ 21)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) |LIST;OMwrite;$S;6|) - (SPADCALL |dev| (|getShellEntry| $ 22)) + (SPADCALL |dev| (|getShellEntry| $ 27)) (|LIST;writeOMList| |dev| |x| $) - (SPADCALL |dev| (|getShellEntry| $ 23)) - (SPADCALL |dev| (|getShellEntry| $ 24)) + (SPADCALL |dev| (|getShellEntry| $ 28)) + (SPADCALL |dev| (|getShellEntry| $ 29)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |LIST;OMwrite;$S;6|) (EXIT |s|))))) @@ -92,41 +92,41 @@ (SEQ (LETT |s| "" |LIST;OMwrite;$BS;7|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |LIST;OMwrite;$BS;7|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 20)) - (|getShellEntry| $ 21)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) |LIST;OMwrite;$BS;7|) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 22)))) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 27)))) (|LIST;writeOMList| |dev| |x| $) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23)))) - (SPADCALL |dev| (|getShellEntry| $ 24)) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 28)))) + (SPADCALL |dev| (|getShellEntry| $ 29)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |LIST;OMwrite;$BS;7|) (EXIT |s|))))) (DEFUN |LIST;OMwrite;Omd$V;8| (|dev| |x| $) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 22)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 27)) (|LIST;writeOMList| |dev| |x| $) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 23))))) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 28))))) (DEFUN |LIST;OMwrite;Omd$BV;9| (|dev| |x| |wholeObj| $) - (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 22)))) + (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 27)))) (|LIST;writeOMList| |dev| |x| $) (EXIT (COND - (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23))))))) + (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 28))))))) (DEFUN |LIST;setUnion;3$;10| (|l1| |l2| $) - (SPADCALL (SPADCALL |l1| |l2| (|getShellEntry| $ 29)) - (|getShellEntry| $ 30))) + (SPADCALL (SPADCALL |l1| |l2| (|getShellEntry| $ 34)) + (|getShellEntry| $ 35))) (DEFUN |LIST;setIntersection;3$;11| (|l1| |l2| $) (PROG (|u|) (RETURN (SEQ (LETT |u| NIL |LIST;setIntersection;3$;11|) - (LETT |l1| (SPADCALL |l1| (|getShellEntry| $ 30)) + (LETT |l1| (SPADCALL |l1| (|getShellEntry| $ 35)) |LIST;setIntersection;3$;11|) (SEQ G190 (COND ((NULL (NOT (NULL |l1|))) (GO G191))) (SEQ (COND ((SPADCALL (|SPADfirst| |l1|) |l2| - (|getShellEntry| $ 32)) + (|getShellEntry| $ 39)) (LETT |u| (CONS (|SPADfirst| |l1|) |u|) |LIST;setIntersection;3$;11|))) (EXIT (LETT |l1| (CDR |l1|) @@ -137,16 +137,16 @@ (DEFUN |LIST;setDifference;3$;12| (|l1| |l2| $) (PROG (|l11| |lu|) (RETURN - (SEQ (LETT |l1| (SPADCALL |l1| (|getShellEntry| $ 30)) + (SEQ (LETT |l1| (SPADCALL |l1| (|getShellEntry| $ 35)) |LIST;setDifference;3$;12|) (LETT |lu| NIL |LIST;setDifference;3$;12|) (SEQ G190 (COND ((NULL (NOT (NULL |l1|))) (GO G191))) (SEQ (LETT |l11| - (SPADCALL |l1| 1 (|getShellEntry| $ 35)) + (SPADCALL |l1| 1 (|getShellEntry| $ 41)) |LIST;setDifference;3$;12|) (COND ((NULL (SPADCALL |l11| |l2| - (|getShellEntry| $ 32))) + (|getShellEntry| $ 39))) (LETT |lu| (CONS |l11| |lu|) |LIST;setDifference;3$;12|))) (EXIT (LETT |l1| (CDR |l1|) @@ -158,7 +158,7 @@ (PROG (#0=#:G1444 |a| #1=#:G1445) (RETURN (SEQ (SPADCALL - (CONS (SPADCALL '|construct| (|getShellEntry| $ 39)) + (CONS (SPADCALL '|construct| (|getShellEntry| $ 46)) (PROGN (LETT #0# NIL |LIST;convert;$If;13|) (SEQ (LETT |a| NIL |LIST;convert;$If;13|) @@ -173,12 +173,12 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |a| - (|getShellEntry| $ 40)) + (|getShellEntry| $ 47)) #0#) |LIST;convert;$If;13|))) (LETT #1# (CDR #1#) |LIST;convert;$If;13|) (GO G190) G191 (EXIT (NREVERSE0 #0#))))) - (|getShellEntry| $ 42)))))) + (|getShellEntry| $ 51)))))) (DEFUN |List| (#0=#:G1446) (PROG () @@ -203,7 +203,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|List|)) (LETT |dv$| (LIST '|List| |dv$1|) . #0#) - (LETT $ (|newShell| 61) . #0#) + (LETT $ (|newShell| 70) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -246,57 +246,60 @@ (COND ((|testBitVector| |pv$| 6) (PROGN - (|setShellEntry| $ 25 + (|setShellEntry| $ 30 (CONS (|dispatchFunction| |LIST;OMwrite;$S;6|) $)) - (|setShellEntry| $ 26 + (|setShellEntry| $ 31 (CONS (|dispatchFunction| |LIST;OMwrite;$BS;7|) $)) - (|setShellEntry| $ 27 + (|setShellEntry| $ 32 (CONS (|dispatchFunction| |LIST;OMwrite;Omd$V;8|) $)) - (|setShellEntry| $ 28 + (|setShellEntry| $ 33 (CONS (|dispatchFunction| |LIST;OMwrite;Omd$BV;9|) $))))) (COND ((|testBitVector| |pv$| 8) (PROGN - (|setShellEntry| $ 31 + (|setShellEntry| $ 36 (CONS (|dispatchFunction| |LIST;setUnion;3$;10|) $)) - (|setShellEntry| $ 33 + (|setShellEntry| $ 40 (CONS (|dispatchFunction| |LIST;setIntersection;3$;11|) $)) - (|setShellEntry| $ 36 + (|setShellEntry| $ 43 (CONS (|dispatchFunction| |LIST;setDifference;3$;12|) $))))) (COND ((|testBitVector| |pv$| 3) - (|setShellEntry| $ 43 + (|setShellEntry| $ 52 (CONS (|dispatchFunction| |LIST;convert;$If;13|) $)))) $)))) (MAKEPROP '|List| '|infovec| (LIST '#(NIL NIL NIL NIL NIL (|IndexedList| 6 (NRTEVAL 1)) - (|local| |#1|) |LIST;nil;$;1| (|Boolean|) |LIST;null;$B;2| - |LIST;cons;S2$;3| |LIST;append;3$;4| (|Void|) - (|OpenMathDevice|) (0 . |OMputApp|) (|String|) - (5 . |OMputSymbol|) (12 . |OMwrite|) (19 . |OMputEndApp|) - (|OpenMathEncoding|) (24 . |OMencodingXML|) - (28 . |OMopenString|) (34 . |OMputObject|) - (39 . |OMputEndObject|) (44 . |OMclose|) (49 . |OMwrite|) - (54 . |OMwrite|) (60 . |OMwrite|) (66 . |OMwrite|) - (73 . |concat|) (79 . |removeDuplicates|) - (84 . |setUnion|) (90 . |member?|) - (96 . |setIntersection|) (|Integer|) (102 . |elt|) - (108 . |setDifference|) (|Symbol|) (|InputForm|) - (114 . |convert|) (119 . |convert|) (|List| $) - (124 . |convert|) (129 . |convert|) (|Mapping| 6 6 6) - (|NonNegativeInteger|) (|List| 6) (|Equation| 6) - (|List| 47) (|Mapping| 8 6) (|Mapping| 8 6 6) - (|UniversalSegment| 34) '"last" '"rest" '"first" '"value" - (|Mapping| 6 6) (|OutputForm|) (|SingleInteger|) - (|List| 34) (|Union| 6 '"failed")) - '#(|setUnion| 134 |setIntersection| 140 |setDifference| 146 - |removeDuplicates| 152 |null| 157 |nil| 162 |member?| 166 - |elt| 172 |convert| 178 |cons| 183 |concat| 189 |append| - 195 |OMwrite| 201) + (|local| |#1|) (|Integer|) (0 . |One|) |LIST;nil;$;1| + (|Boolean|) |LIST;null;$B;2| |LIST;cons;S2$;3| + |LIST;append;3$;4| (|Void|) (|OpenMathDevice|) + (4 . |OMputApp|) (|String|) (9 . |OMputSymbol|) + (16 . |first|) (21 . |false|) (25 . |OMwrite|) + (32 . |rest|) (37 . |OMputEndApp|) (|OpenMathEncoding|) + (42 . |OMencodingXML|) (46 . |OMopenString|) + (52 . |OMputObject|) (57 . |OMputEndObject|) + (62 . |OMclose|) (67 . |OMwrite|) (72 . |OMwrite|) + (78 . |OMwrite|) (84 . |OMwrite|) (91 . |concat|) + (97 . |removeDuplicates|) (102 . |setUnion|) + (108 . |empty|) (112 . |empty?|) (117 . |member?|) + (123 . |setIntersection|) (129 . |elt|) (135 . |concat|) + (141 . |setDifference|) (|Symbol|) (|InputForm|) + (147 . |convert|) (152 . |convert|) (|List| 45) + (157 . |concat|) (|List| $) (163 . |convert|) + (168 . |convert|) (|Mapping| 6 6 6) (|NonNegativeInteger|) + (|List| 6) (|Equation| 6) (|List| 56) (|Mapping| 10 6) + (|Mapping| 10 6 6) (|UniversalSegment| 7) '"last" '"rest" + '"first" '"value" (|Mapping| 6 6) (|OutputForm|) + (|SingleInteger|) (|List| 7) (|Union| 6 '"failed")) + '#(|setUnion| 173 |setIntersection| 179 |setDifference| 185 + |rest| 191 |removeDuplicates| 196 |null| 201 |nil| 206 + |member?| 210 |first| 216 |empty?| 221 |empty| 226 |elt| + 230 |convert| 236 |cons| 241 |concat| 247 |append| 259 + |OMwrite| 265) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 6 '(0 0 0 0 0 0 0 0 0 0 5 0 0 1 4 0 0 1 2 3 4 6)) @@ -316,29 +319,33 @@ (|UnaryRecursiveAggregate| 6) (|LinearAggregate| 6) (|RecursiveAggregate| 6) - (|IndexedAggregate| 34 6) + (|IndexedAggregate| 7 6) (|Collection| 6) (|HomogeneousAggregate| 6) (|OrderedSet|) (|Aggregate|) - (|EltableAggregate| 34 6) (|Evalable| 6) - (|SetCategory|) (|Type|) - (|Eltable| 34 6) (|InnerEvalable| 6 6) - (|CoercibleTo| 57) (|ConvertibleTo| 38) - (|BasicType|) (|OpenMath|)) - (|makeByteWordVec2| 43 - '(1 13 12 0 14 3 13 12 0 15 15 16 3 6 - 12 13 0 8 17 1 13 12 0 18 0 19 0 20 2 - 13 0 15 19 21 1 13 12 0 22 1 13 12 0 - 23 1 13 12 0 24 1 0 15 0 25 2 0 15 0 - 8 26 2 0 12 13 0 27 3 0 12 13 0 8 28 - 2 0 0 0 0 29 1 0 0 0 30 2 0 0 0 0 31 - 2 0 8 6 0 32 2 0 0 0 0 33 2 0 6 0 34 - 35 2 0 0 0 0 36 1 38 0 37 39 1 6 38 0 - 40 1 38 0 41 42 1 0 38 0 43 2 8 0 0 0 - 31 2 8 0 0 0 33 2 8 0 0 0 36 1 8 0 0 - 30 1 0 8 0 9 0 0 0 7 2 8 8 6 0 32 2 0 - 6 0 34 35 1 3 38 0 43 2 0 0 6 0 10 2 - 0 0 0 0 29 2 0 0 0 0 11 3 6 12 13 0 8 - 28 2 6 12 13 0 27 1 6 15 0 25 2 6 15 - 0 8 26))))) + (|EltableAggregate| 7 6) (|Evalable| 6) + (|SetCategory|) (|Type|) (|Eltable| 7 6) + (|InnerEvalable| 6 6) (|CoercibleTo| 66) + (|ConvertibleTo| 45) (|BasicType|) + (|OpenMath|)) + (|makeByteWordVec2| 52 + '(0 7 0 8 1 15 14 0 16 3 15 14 0 17 17 + 18 1 0 6 0 19 0 10 0 20 3 6 14 15 0 + 10 21 1 0 0 0 22 1 15 14 0 23 0 24 0 + 25 2 15 0 17 24 26 1 15 14 0 27 1 15 + 14 0 28 1 15 14 0 29 1 0 17 0 30 2 0 + 17 0 10 31 2 0 14 15 0 32 3 0 14 15 0 + 10 33 2 0 0 0 0 34 1 0 0 0 35 2 0 0 0 + 0 36 0 0 0 37 1 0 10 0 38 2 0 10 6 0 + 39 2 0 0 0 0 40 2 0 6 0 7 41 2 0 0 6 + 0 42 2 0 0 0 0 43 1 45 0 44 46 1 6 45 + 0 47 2 48 0 45 0 49 1 45 0 50 51 1 0 + 45 0 52 2 8 0 0 0 36 2 8 0 0 0 40 2 8 + 0 0 0 43 1 0 0 0 22 1 8 0 0 35 1 0 10 + 0 11 0 0 0 9 2 8 10 6 0 39 1 0 6 0 19 + 1 0 10 0 38 0 0 0 37 2 0 6 0 7 41 1 3 + 45 0 52 2 0 0 6 0 12 2 0 0 6 0 42 2 0 + 0 0 0 34 2 0 0 0 0 13 3 6 14 15 0 10 + 33 2 6 14 15 0 32 1 6 17 0 30 2 6 17 + 0 10 31))))) '|lookupIncomplete|)) diff --git a/src/algebra/strap/LNAGG-.lsp b/src/algebra/strap/LNAGG-.lsp index 6f6d374f..d140a5dc 100644 --- a/src/algebra/strap/LNAGG-.lsp +++ b/src/algebra/strap/LNAGG-.lsp @@ -41,19 +41,19 @@ ('T (NOT (< (SPADCALL |a| (|getShellEntry| $ 10)) |i|))))) (DEFUN |LNAGG-;concat;ASA;3| (|a| |x| $) - (SPADCALL |a| (SPADCALL 1 |x| (|getShellEntry| $ 16)) - (|getShellEntry| $ 17))) + (SPADCALL |a| (SPADCALL 1 |x| (|getShellEntry| $ 20)) + (|getShellEntry| $ 21))) (DEFUN |LNAGG-;concat;S2A;4| (|x| |y| $) - (SPADCALL (SPADCALL 1 |x| (|getShellEntry| $ 16)) |y| - (|getShellEntry| $ 17))) + (SPADCALL (SPADCALL 1 |x| (|getShellEntry| $ 20)) |y| + (|getShellEntry| $ 21))) (DEFUN |LNAGG-;insert;SAIA;5| (|x| |a| |i| $) - (SPADCALL (SPADCALL 1 |x| (|getShellEntry| $ 16)) |a| |i| - (|getShellEntry| $ 20))) + (SPADCALL (SPADCALL 1 |x| (|getShellEntry| $ 20)) |a| |i| + (|getShellEntry| $ 24))) (DEFUN |LNAGG-;maxIndex;AI;6| (|l| $) - (+ (- (SPADCALL |l| (|getShellEntry| $ 22)) 1) + (+ (- (SPADCALL |l| (|getShellEntry| $ 26)) 1) (SPADCALL |l| (|getShellEntry| $ 9)))) (DEFUN |LinearAggregate&| (|#1| |#2|) @@ -63,7 +63,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|LinearAggregate&|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|LinearAggregate&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 25) . #0#) + (LETT $ (|newShell| 31) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -74,28 +74,31 @@ (|setShellEntry| $ 7 |#2|) (COND ((|HasAttribute| |#1| '|finiteAggregate|) - (|setShellEntry| $ 23 + (|setShellEntry| $ 29 (CONS (|dispatchFunction| |LNAGG-;maxIndex;AI;6|) $)))) $)))) (MAKEPROP '|LinearAggregate&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|Integer|) (0 . |minIndex|) (5 . |maxIndex|) (|List| 8) - |LNAGG-;indices;AL;1| (|Boolean|) |LNAGG-;index?;IAB;2| - (|NonNegativeInteger|) (10 . |new|) (16 . |concat|) + |LNAGG-;indices;AL;1| (|Boolean|) (10 . <) (16 . |false|) + |LNAGG-;index?;IAB;2| (|NonNegativeInteger|) (20 . |One|) + (24 . |One|) (28 . |new|) (34 . |concat|) |LNAGG-;concat;ASA;3| |LNAGG-;concat;S2A;4| - (22 . |insert|) |LNAGG-;insert;SAIA;5| (29 . |#|) - (34 . |maxIndex|) (|List| $)) - '#(|maxIndex| 39 |insert| 44 |indices| 51 |index?| 56 - |concat| 62) + (40 . |insert|) |LNAGG-;insert;SAIA;5| (47 . |#|) (52 . -) + (58 . +) (64 . |maxIndex|) (|List| $)) + '#(|maxIndex| 69 |insert| 74 |indices| 81 |index?| 86 + |concat| 92) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 23 - '(1 6 8 0 9 1 6 8 0 10 2 6 0 15 7 16 2 - 6 0 0 0 17 3 6 0 0 0 8 20 1 6 15 0 22 - 1 0 8 0 23 1 0 8 0 23 3 0 0 7 0 8 21 - 1 0 11 0 12 2 0 13 8 0 14 2 0 0 0 7 - 18 2 0 0 7 0 19))))) + (|makeByteWordVec2| 29 + '(1 6 8 0 9 1 6 8 0 10 2 8 13 0 0 14 0 + 13 0 15 0 17 0 18 0 8 0 19 2 6 0 17 7 + 20 2 6 0 0 0 21 3 6 0 0 0 8 24 1 6 17 + 0 26 2 8 0 0 0 27 2 8 0 0 0 28 1 0 8 + 0 29 1 0 8 0 29 3 0 0 7 0 8 25 1 0 11 + 0 12 2 0 13 8 0 16 2 0 0 0 7 22 2 0 0 + 7 0 23))))) '|lookupComplete|)) diff --git a/src/algebra/strap/LSAGG-.lsp b/src/algebra/strap/LSAGG-.lsp index 380c9292..a1ad4e13 100644 --- a/src/algebra/strap/LSAGG-.lsp +++ b/src/algebra/strap/LSAGG-.lsp @@ -159,7 +159,7 @@ |LSAGG-;select!;M2A;5|) (EXIT (SPADCALL |y| |z| - (|getShellEntry| $ 25)))))))) + (|getShellEntry| $ 26)))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |x|))))))))) @@ -169,7 +169,7 @@ (SEQ (COND ((SPADCALL |p| (|getShellEntry| $ 16)) |q|) ((SPADCALL |q| (|getShellEntry| $ 16)) |p|) - ((SPADCALL |p| |q| (|getShellEntry| $ 28)) + ((SPADCALL |p| |q| (|getShellEntry| $ 29)) (|error| "cannot merge a list into itself")) ('T (SEQ (COND @@ -210,7 +210,7 @@ |f|) (SEQ (SPADCALL |t| |p| - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) (LETT |t| |p| |LSAGG-;merge!;M3A;6|) (EXIT @@ -221,7 +221,7 @@ ('T (SEQ (SPADCALL |t| |q| - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) (LETT |t| |q| |LSAGG-;merge!;M3A;6|) (EXIT @@ -234,13 +234,13 @@ (COND ((SPADCALL |p| (|getShellEntry| $ 16)) |q|) ('T |p|)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) (EXIT |r|)))))))) (DEFUN |LSAGG-;insert!;SAIA;7| (|s| |x| |i| $) (PROG (|m| #0=#:G1465 |y| |z|) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 31)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;insert!;SAIA;7|) (EXIT (COND ((< |i| |m|) (|error| "index out of range")) @@ -255,25 +255,25 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;insert!;SAIA;7|) (LETT |z| (SPADCALL |y| (|getShellEntry| $ 17)) |LSAGG-;insert!;SAIA;7|) (SPADCALL |y| (SPADCALL |s| |z| (|getShellEntry| $ 14)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) (EXIT |x|))))))))) (DEFUN |LSAGG-;insert!;2AIA;8| (|w| |x| |i| $) (PROG (|m| #0=#:G1469 |y| |z|) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 31)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;insert!;2AIA;8|) (EXIT (COND ((< |i| |m|) (|error| "index out of range")) ((EQL |i| |m|) - (SPADCALL |w| |x| (|getShellEntry| $ 34))) + (SPADCALL |w| |x| (|getShellEntry| $ 40))) ('T (SEQ (LETT |y| (SPADCALL |x| @@ -283,13 +283,13 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;insert!;2AIA;8|) (LETT |z| (SPADCALL |y| (|getShellEntry| $ 17)) |LSAGG-;insert!;2AIA;8|) - (SPADCALL |y| |w| (|getShellEntry| $ 25)) - (SPADCALL |y| |z| (|getShellEntry| $ 34)) + (SPADCALL |y| |w| (|getShellEntry| $ 26)) + (SPADCALL |y| |z| (|getShellEntry| $ 40)) (EXIT |x|))))))))) (DEFUN |LSAGG-;remove!;M2A;9| (|f| |x| $) @@ -331,7 +331,7 @@ (SPADCALL |p| (SPADCALL |q| (|getShellEntry| $ 17)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) |LSAGG-;remove!;M2A;9|)) ('T (SEQ @@ -348,7 +348,7 @@ (DEFUN |LSAGG-;delete!;AIA;10| (|x| |i| $) (PROG (|m| #0=#:G1481 |y|) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 31)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;delete!;AIA;10|) (EXIT (COND ((< |i| |m|) (|error| "index out of range")) @@ -363,29 +363,29 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;delete!;AIA;10|) (SPADCALL |y| - (SPADCALL |y| 2 (|getShellEntry| $ 32)) - (|getShellEntry| $ 25)) + (SPADCALL |y| 2 (|getShellEntry| $ 38)) + (|getShellEntry| $ 26)) (EXIT |x|))))))))) (DEFUN |LSAGG-;delete!;AUsA;11| (|x| |i| $) (PROG (|l| |m| |h| #0=#:G1486 #1=#:G1487 |t| #2=#:G1488) (RETURN - (SEQ (LETT |l| (SPADCALL |i| (|getShellEntry| $ 39)) + (SEQ (LETT |l| (SPADCALL |i| (|getShellEntry| $ 45)) |LSAGG-;delete!;AUsA;11|) - (LETT |m| (SPADCALL |x| (|getShellEntry| $ 31)) + (LETT |m| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;delete!;AUsA;11|) (EXIT (COND ((< |l| |m|) (|error| "index out of range")) ('T (SEQ (LETT |h| (COND - ((SPADCALL |i| (|getShellEntry| $ 40)) - (SPADCALL |i| (|getShellEntry| $ 41))) + ((SPADCALL |i| (|getShellEntry| $ 46)) + (SPADCALL |i| (|getShellEntry| $ 47))) ('T - (SPADCALL |x| (|getShellEntry| $ 42)))) + (SPADCALL |x| (|getShellEntry| $ 48)))) |LSAGG-;delete!;AUsA;11|) (EXIT (COND ((< |h| |l|) |x|) @@ -399,7 +399,7 @@ ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32))) + (|getShellEntry| $ 38))) ('T (SEQ (LETT |t| (SPADCALL |x| @@ -412,7 +412,7 @@ ('T 'T)) '(|NonNegativeInteger|) #1#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;delete!;AUsA;11|) (SPADCALL |t| (SPADCALL |t| @@ -425,8 +425,8 @@ ('T 'T)) '(|NonNegativeInteger|) #2#)) - (|getShellEntry| $ 32)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 38)) + (|getShellEntry| $ 26)) (EXIT |x|))))))))))))) (DEFUN |LSAGG-;find;MAU;12| (|f| |x| $) @@ -450,7 +450,7 @@ (DEFUN |LSAGG-;position;MAI;13| (|f| |x| $) (PROG (|k|) (RETURN - (SEQ (SEQ (LETT |k| (SPADCALL |x| (|getShellEntry| $ 31)) + (SEQ (SEQ (LETT |k| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;position;MAI;13|) G190 (COND @@ -469,7 +469,7 @@ G191 (EXIT NIL)) (EXIT (COND ((SPADCALL |x| (|getShellEntry| $ 16)) - (- (SPADCALL |x| (|getShellEntry| $ 31)) 1)) + (- (SPADCALL |x| (|getShellEntry| $ 32)) 1)) ('T |k|))))))) (DEFUN |LSAGG-;mergeSort| (|f| |p| |n| $) @@ -482,7 +482,7 @@ (SPADCALL (SPADCALL |p| (|getShellEntry| $ 17)) (|getShellEntry| $ 18)) (SPADCALL |p| (|getShellEntry| $ 18)) |f|) - (LETT |p| (SPADCALL |p| (|getShellEntry| $ 47)) + (LETT |p| (SPADCALL |p| (|getShellEntry| $ 56)) |LSAGG-;mergeSort|))))) (EXIT (COND ((< |n| 3) |p|) @@ -496,7 +496,7 @@ |LSAGG-;mergeSort|) (LETT |q| (SPADCALL |p| |l| - (|getShellEntry| $ 48)) + (|getShellEntry| $ 58)) |LSAGG-;mergeSort|) (LETT |p| (|LSAGG-;mergeSort| |f| |p| |l| $) |LSAGG-;mergeSort|) @@ -574,7 +574,7 @@ ((NULL (COND ((SPADCALL |x| (|getShellEntry| $ 16)) 'NIL) ('T - (SPADCALL |r| |a| (|getShellEntry| $ 51))))) + (SPADCALL |r| |a| (|getShellEntry| $ 62))))) (GO G191))) (SEQ (LETT |r| (SPADCALL |r| @@ -630,7 +630,7 @@ (SPADCALL |y| (|getShellEntry| $ 17)) |LSAGG-;map;M3A;19|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |z| (|getShellEntry| $ 47))))))) + (EXIT (SPADCALL |z| (|getShellEntry| $ 56))))))) (DEFUN |LSAGG-;reverse!;2A;20| (|x| $) (PROG (|z| |y|) @@ -644,7 +644,7 @@ |x|) ('T (SEQ (SPADCALL |x| (SPADCALL (|getShellEntry| $ 13)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 26)) (SEQ G190 (COND ((NULL (NOT (SPADCALL |y| @@ -654,7 +654,7 @@ (SPADCALL |y| (|getShellEntry| $ 17)) |LSAGG-;reverse!;2A;20|) - (SPADCALL |y| |x| (|getShellEntry| $ 25)) + (SPADCALL |y| |x| (|getShellEntry| $ 26)) (LETT |x| |y| |LSAGG-;reverse!;2A;20|) (EXIT (LETT |y| |z| |LSAGG-;reverse!;2A;20|))) @@ -673,7 +673,7 @@ (SEQ (COND ((EQL |k| 1000) (COND - ((SPADCALL |x| (|getShellEntry| $ 56)) + ((SPADCALL |x| (|getShellEntry| $ 70)) (EXIT (|error| "cyclic list")))))) (LETT |y| (SPADCALL @@ -685,12 +685,12 @@ |LSAGG-;copy;2A;21|))) (LETT |k| (QSADD1 |k|) |LSAGG-;copy;2A;21|) (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |y| (|getShellEntry| $ 47))))))) + (EXIT (SPADCALL |y| (|getShellEntry| $ 56))))))) (DEFUN |LSAGG-;copyInto!;2AIA;22| (|y| |x| |s| $) (PROG (|m| #0=#:G1546 |z|) (RETURN - (SEQ (LETT |m| (SPADCALL |y| (|getShellEntry| $ 31)) + (SEQ (LETT |m| (SPADCALL |y| (|getShellEntry| $ 32)) |LSAGG-;copyInto!;2AIA;22|) (EXIT (COND ((< |s| |m|) (|error| "index out of range")) @@ -703,7 +703,7 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;copyInto!;2AIA;22|) (SEQ G190 (COND @@ -719,7 +719,7 @@ (SEQ (SPADCALL |z| (SPADCALL |x| (|getShellEntry| $ 18)) - (|getShellEntry| $ 58)) + (|getShellEntry| $ 72)) (LETT |x| (SPADCALL |x| (|getShellEntry| $ 17)) @@ -735,7 +735,7 @@ (DEFUN |LSAGG-;position;SA2I;23| (|w| |x| |s| $) (PROG (|m| #0=#:G1553 |k|) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 31)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 32)) |LSAGG-;position;SA2I;23|) (EXIT (COND ((< |s| |m|) (|error| "index out of range")) @@ -748,7 +748,7 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 32)) + (|getShellEntry| $ 38)) |LSAGG-;position;SA2I;23|) (SEQ (LETT |k| |s| |LSAGG-;position;SA2I;23|) G190 @@ -761,7 +761,7 @@ (SPADCALL |w| (SPADCALL |x| (|getShellEntry| $ 18)) - (|getShellEntry| $ 51))))) + (|getShellEntry| $ 62))))) (GO G191))) (SEQ (EXIT (LETT |x| @@ -774,7 +774,7 @@ (EXIT (COND ((SPADCALL |x| (|getShellEntry| $ 16)) (- (SPADCALL |x| - (|getShellEntry| $ 31)) + (|getShellEntry| $ 32)) 1)) ('T |k|))))))))))) @@ -794,8 +794,8 @@ (VECTOR $ |p|)) (SPADCALL |p| (|getShellEntry| $ 17)) - (|getShellEntry| $ 62)) - (|getShellEntry| $ 25)) + (|getShellEntry| $ 76)) + (|getShellEntry| $ 26)) |LSAGG-;removeDuplicates!;2A;24|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |l|))))) @@ -807,7 +807,7 @@ (PROGN (SPADCALL |#1| (SPADCALL (|getShellEntry| $$ 1) (|getShellEntry| $ 18)) - (|getShellEntry| $ 61)))))) + (|getShellEntry| $ 75)))))) (DEFUN |LSAGG-;<;2AB;25| (|x| |y| $) (PROG (#0=#:G1567) @@ -829,7 +829,7 @@ (|getShellEntry| $ 18)) (SPADCALL |y| (|getShellEntry| $ 18)) - (|getShellEntry| $ 51)) + (|getShellEntry| $ 62)) (PROGN (LETT #0# (SPADCALL @@ -837,7 +837,7 @@ (|getShellEntry| $ 18)) (SPADCALL |y| (|getShellEntry| $ 18)) - (|getShellEntry| $ 64)) + (|getShellEntry| $ 78)) |LSAGG-;<;2AB;25|) (GO #0#))) ('T @@ -866,7 +866,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|ListAggregate&|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|ListAggregate&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 67) . #0#) + (LETT $ (|newShell| 81) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -875,21 +875,21 @@ (|setShellEntry| $ 7 |#2|) (COND ((|HasCategory| |#2| '(|SetCategory|)) - (|setShellEntry| $ 52 + (|setShellEntry| $ 63 (CONS (|dispatchFunction| |LSAGG-;reduce;MA3S;17|) $)))) (COND ((|HasCategory| |#2| '(|SetCategory|)) (PROGN - (|setShellEntry| $ 60 + (|setShellEntry| $ 74 (CONS (|dispatchFunction| |LSAGG-;position;SA2I;23|) $)) - (|setShellEntry| $ 63 + (|setShellEntry| $ 77 (CONS (|dispatchFunction| |LSAGG-;removeDuplicates!;2A;24|) $))))) (COND ((|HasCategory| |#2| '(|OrderedSet|)) - (|setShellEntry| $ 65 + (|setShellEntry| $ 79 (CONS (|dispatchFunction| |LSAGG-;<;2AB;25|) $)))) $)))) @@ -900,51 +900,60 @@ (9 . |concat|) |LSAGG-;list;SA;2| (15 . |empty?|) (20 . |rest|) (25 . |first|) (|Mapping| 7 7 7) (30 . |reduce|) |LSAGG-;reduce;MAS;3| (37 . |copy|) - (42 . |merge!|) |LSAGG-;merge;M3A;4| (49 . |setrest!|) - (|Mapping| 10 7) |LSAGG-;select!;M2A;5| (55 . |eq?|) - |LSAGG-;merge!;M3A;6| (|Integer|) (61 . |minIndex|) - (66 . |rest|) |LSAGG-;insert!;SAIA;7| (72 . |concat!|) + (42 . |merge!|) |LSAGG-;merge;M3A;4| (49 . |false|) + (53 . |setrest!|) (|Mapping| 10 7) |LSAGG-;select!;M2A;5| + (59 . |eq?|) |LSAGG-;merge!;M3A;6| (|Integer|) + (65 . |minIndex|) (70 . <) (76 . =) (82 . |One|) + (86 . |One|) (90 . -) (96 . |rest|) + |LSAGG-;insert!;SAIA;7| (102 . |concat!|) |LSAGG-;insert!;2AIA;8| |LSAGG-;remove!;M2A;9| - |LSAGG-;delete!;AIA;10| (|UniversalSegment| 30) - (78 . |lo|) (83 . |hasHi|) (88 . |hi|) (93 . |maxIndex|) - |LSAGG-;delete!;AUsA;11| (|Union| 7 '"failed") - |LSAGG-;find;MAU;12| |LSAGG-;position;MAI;13| - (98 . |reverse!|) (103 . |split!|) |LSAGG-;sorted?;MAB;15| - |LSAGG-;reduce;MA2S;16| (109 . ~=) (115 . |reduce|) + |LSAGG-;delete!;AIA;10| (|UniversalSegment| 31) + (108 . |lo|) (113 . |hasHi|) (118 . |hi|) + (123 . |maxIndex|) (128 . +) |LSAGG-;delete!;AUsA;11| + (|Union| 7 '"failed") |LSAGG-;find;MAU;12| + (|SingleInteger|) (134 . |One|) |LSAGG-;position;MAI;13| + (138 . |reverse!|) (143 . |quo|) (149 . |split!|) + (155 . |true|) |LSAGG-;sorted?;MAB;15| + |LSAGG-;reduce;MA2S;16| (159 . ~=) (165 . |reduce|) |LSAGG-;new;NniSA;18| |LSAGG-;map;M3A;19| - |LSAGG-;reverse!;2A;20| (123 . |cyclic?|) - |LSAGG-;copy;2A;21| (128 . |setfirst!|) - |LSAGG-;copyInto!;2AIA;22| (134 . |position|) (141 . =) - (147 . |remove!|) (153 . |removeDuplicates!|) (158 . <) - (164 . <) (|Mapping| 7 7)) - '#(|sorted?| 170 |sort!| 176 |select!| 182 |reverse!| 188 - |removeDuplicates!| 193 |remove!| 198 |reduce| 204 - |position| 225 |new| 238 |merge!| 244 |merge| 251 |map| - 258 |list| 265 |insert!| 270 |find| 284 |delete!| 290 - |copyInto!| 302 |copy| 309 < 314) + |LSAGG-;reverse!;2A;20| (173 . |Zero|) (177 . |Zero|) + (181 . =) (187 . |cyclic?|) |LSAGG-;copy;2A;21| + (192 . |setfirst!|) |LSAGG-;copyInto!;2AIA;22| + (198 . |position|) (205 . =) (211 . |remove!|) + (217 . |removeDuplicates!|) (222 . <) (228 . <) + (|Mapping| 7 7)) + '#(|sorted?| 234 |sort!| 240 |select!| 246 |reverse!| 252 + |removeDuplicates!| 257 |remove!| 262 |reduce| 268 + |position| 289 |new| 302 |merge!| 308 |merge| 315 |map| + 322 |list| 329 |insert!| 334 |find| 348 |delete!| 354 + |copyInto!| 366 |copy| 373 < 378) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 65 + (|makeByteWordVec2| 79 '(1 6 8 0 9 0 6 0 13 2 6 0 7 0 14 1 6 10 0 16 1 6 0 0 17 1 6 7 0 18 3 6 7 19 0 7 20 1 6 0 0 22 3 6 0 11 0 0 23 - 2 6 0 0 0 25 2 6 10 0 0 28 1 6 30 0 - 31 2 6 0 0 8 32 2 6 0 0 0 34 1 38 30 - 0 39 1 38 10 0 40 1 38 30 0 41 1 6 30 - 0 42 1 6 0 0 47 2 6 0 0 30 48 2 7 10 - 0 0 51 4 0 7 19 0 7 7 52 1 6 10 0 56 - 2 6 7 0 7 58 3 0 30 7 0 30 60 2 7 10 - 0 0 61 2 6 0 26 0 62 1 0 0 0 63 2 7 - 10 0 0 64 2 0 10 0 0 65 2 0 10 11 0 - 49 2 0 0 11 0 12 2 0 0 26 0 27 1 0 0 - 0 55 1 0 0 0 63 2 0 0 26 0 36 3 0 7 - 19 0 7 50 4 0 7 19 0 7 7 52 2 0 7 19 - 0 21 2 0 30 26 0 46 3 0 30 7 0 30 60 - 2 0 0 8 7 53 3 0 0 11 0 0 29 3 0 0 11 - 0 0 24 3 0 0 19 0 0 54 1 0 0 7 15 3 0 - 0 7 0 30 33 3 0 0 0 0 30 35 2 0 44 26 - 0 45 2 0 0 0 38 43 2 0 0 0 30 37 3 0 - 0 0 0 30 59 1 0 0 0 57 2 0 10 0 0 65))))) + 0 10 0 25 2 6 0 0 0 26 2 6 10 0 0 29 + 1 6 31 0 32 2 31 10 0 0 33 2 31 10 0 + 0 34 0 8 0 35 0 31 0 36 2 31 0 0 0 37 + 2 6 0 0 8 38 2 6 0 0 0 40 1 44 31 0 + 45 1 44 10 0 46 1 44 31 0 47 1 6 31 0 + 48 2 31 0 0 0 49 0 53 0 54 1 6 0 0 56 + 2 31 0 0 0 57 2 6 0 0 31 58 0 10 0 59 + 2 7 10 0 0 62 4 0 7 19 0 7 7 63 0 53 + 0 67 0 8 0 68 2 8 10 0 0 69 1 6 10 0 + 70 2 6 7 0 7 72 3 0 31 7 0 31 74 2 7 + 10 0 0 75 2 6 0 27 0 76 1 0 0 0 77 2 + 7 10 0 0 78 2 0 10 0 0 79 2 0 10 11 0 + 60 2 0 0 11 0 12 2 0 0 27 0 28 1 0 0 + 0 66 1 0 0 0 77 2 0 0 27 0 42 3 0 7 + 19 0 7 61 4 0 7 19 0 7 7 63 2 0 7 19 + 0 21 2 0 31 27 0 55 3 0 31 7 0 31 74 + 2 0 0 8 7 64 3 0 0 11 0 0 30 3 0 0 11 + 0 0 24 3 0 0 19 0 0 65 1 0 0 7 15 3 0 + 0 7 0 31 39 3 0 0 0 0 31 41 2 0 51 27 + 0 52 2 0 0 0 44 50 2 0 0 0 31 43 3 0 + 0 0 0 31 73 1 0 0 0 71 2 0 10 0 0 79))))) '|lookupComplete|)) diff --git a/src/algebra/strap/MONOID-.lsp b/src/algebra/strap/MONOID-.lsp index b4c3de53..3e5853ed 100644 --- a/src/algebra/strap/MONOID-.lsp +++ b/src/algebra/strap/MONOID-.lsp @@ -26,7 +26,7 @@ (DEFUN |MONOID-;**;SNniS;4| (|x| |n| $) (COND ((ZEROP |n|) (|spadConstant| $ 7)) - ('T (SPADCALL |x| |n| (|getShellEntry| $ 17))))) + ('T (SPADCALL |x| |n| (|getShellEntry| $ 19))))) (DEFUN |Monoid&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -34,7 +34,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|Monoid&|)) (LETT |dv$| (LIST '|Monoid&| |dv$1|) . #0#) - (LETT $ (|newShell| 20) . #0#) + (LETT $ (|newShell| 21) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -46,15 +46,15 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |One|) (|Boolean|) (4 . =) |MONOID-;one?;SB;1| |MONOID-;sample;S;2| (10 . |one?|) (|Union| $ '"failed") - |MONOID-;recip;SU;3| (|PositiveInteger|) - (|RepeatedSquaring| 6) (15 . |expt|) - (|NonNegativeInteger|) |MONOID-;**;SNniS;4|) - '#(|sample| 21 |recip| 25 |one?| 30 ** 35) 'NIL + |MONOID-;recip;SU;3| (|NonNegativeInteger|) (15 . |zero?|) + (|PositiveInteger|) (|RepeatedSquaring| 6) (20 . |expt|) + |MONOID-;**;SNniS;4|) + '#(|sample| 26 |recip| 30 |one?| 35 ** 40) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 19 - '(0 6 0 7 2 6 8 0 0 9 1 6 8 0 12 2 16 6 - 6 15 17 0 0 0 11 1 0 13 0 14 1 0 8 0 - 10 2 0 0 0 18 19))))) + (|makeByteWordVec2| 20 + '(0 6 0 7 2 6 8 0 0 9 1 6 8 0 12 1 15 8 + 0 16 2 18 6 6 17 19 0 0 0 11 1 0 13 0 + 14 1 0 8 0 10 2 0 0 0 15 20))))) '|lookupComplete|)) diff --git a/src/algebra/strap/NNI.lsp b/src/algebra/strap/NNI.lsp index 34ec379e..bd82e49c 100644 --- a/src/algebra/strap/NNI.lsp +++ b/src/algebra/strap/NNI.lsp @@ -70,7 +70,7 @@ (PROGN (LETT |dv$| '(|NonNegativeInteger|) . #0=(|NonNegativeInteger|)) - (LETT $ (|newShell| 17) . #0#) + (LETT $ (|newShell| 23) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -80,17 +80,18 @@ $)))) (MAKEPROP '|NonNegativeInteger| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL (|Integer|) |NNI;sup;3$;1| - |NNI;shift;$I$;2| (|Union| $ '"failed") - |NNI;subtractIfCan;2$U;3| + (LIST '#(NIL NIL NIL NIL NIL (|Integer|) (0 . |Zero|) (4 . |Zero|) + (|Boolean|) (8 . <) (14 . |false|) (18 . |true|) + |NNI;sup;3$;1| |NNI;shift;$I$;2| (22 . -) + (|Union| $ '"failed") |NNI;subtractIfCan;2$U;3| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - (|PositiveInteger|) (|NonNegativeInteger|) (|Boolean|) - (|String|) (|OutputForm|) (|SingleInteger|)) - '#(~= 0 |zero?| 6 |sup| 11 |subtractIfCan| 17 |shift| 23 - |sample| 29 |rem| 33 |recip| 39 |random| 44 |quo| 49 - |one?| 55 |min| 60 |max| 66 |latex| 72 |hash| 77 |gcd| 82 - |exquo| 88 |divide| 94 |coerce| 100 |Zero| 105 |One| 109 - >= 113 > 119 = 125 <= 131 < 137 + 143 ** 149 * 161) + (|PositiveInteger|) (|NonNegativeInteger|) (|String|) + (|OutputForm|) (|SingleInteger|)) + '#(~= 28 |zero?| 34 |sup| 39 |subtractIfCan| 45 |shift| 51 + |sample| 57 |rem| 61 |recip| 67 |random| 72 |quo| 77 + |one?| 83 |min| 88 |max| 94 |latex| 100 |hash| 105 |gcd| + 110 |exquo| 116 |divide| 122 |coerce| 128 |Zero| 133 |One| + 137 >= 141 > 147 = 153 <= 159 < 165 + 171 ** 177 * 189) '(((|commutative| "*") . 0)) (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0 0)) (CONS '#(NIL NIL NIL NIL NIL |Monoid&| |AbelianMonoid&| @@ -104,18 +105,20 @@ (|AbelianMonoid|) (|OrderedSet|) (|SemiGroup|) (|AbelianSemiGroup|) (|SetCategory|) (|BasicType|) - (|CoercibleTo| 15)) - (|makeByteWordVec2| 16 - '(2 0 13 0 0 1 1 0 13 0 1 2 0 0 0 0 6 2 - 0 8 0 0 9 2 0 0 0 5 7 0 0 0 1 2 0 0 0 - 0 1 1 0 8 0 1 1 0 0 0 1 2 0 0 0 0 1 1 - 0 13 0 1 2 0 0 0 0 1 2 0 0 0 0 1 1 0 - 14 0 1 1 0 16 0 1 2 0 0 0 0 1 2 0 8 0 - 0 1 2 0 10 0 0 1 1 0 15 0 1 0 0 0 1 0 - 0 0 1 2 0 13 0 0 1 2 0 13 0 0 1 2 0 - 13 0 0 1 2 0 13 0 0 1 2 0 13 0 0 1 2 - 0 0 0 0 1 2 0 0 0 11 1 2 0 0 0 12 1 2 - 0 0 0 0 1 2 0 0 12 0 1 2 0 0 11 0 1))))) + (|CoercibleTo| 21)) + (|makeByteWordVec2| 22 + '(0 0 0 6 0 5 0 7 2 5 8 0 0 9 0 8 0 10 + 0 8 0 11 2 5 0 0 0 14 2 0 8 0 0 1 1 0 + 8 0 1 2 0 0 0 0 12 2 0 15 0 0 16 2 0 + 0 0 5 13 0 0 0 1 2 0 0 0 0 1 1 0 15 0 + 1 1 0 0 0 1 2 0 0 0 0 1 1 0 8 0 1 2 0 + 0 0 0 1 2 0 0 0 0 1 1 0 20 0 1 1 0 22 + 0 1 2 0 0 0 0 1 2 0 15 0 0 1 2 0 17 0 + 0 1 1 0 21 0 1 0 0 0 6 0 0 0 1 2 0 8 + 0 0 1 2 0 8 0 0 1 2 0 8 0 0 1 2 0 8 0 + 0 1 2 0 8 0 0 1 2 0 0 0 0 1 2 0 0 0 + 18 1 2 0 0 0 19 1 2 0 0 0 0 1 2 0 0 + 19 0 1 2 0 0 18 0 1))))) '|lookupComplete|)) (MAKEPROP '|NonNegativeInteger| 'NILADIC T) diff --git a/src/algebra/strap/ORDRING-.lsp b/src/algebra/strap/ORDRING-.lsp index c5eb9558..5a7d725e 100644 --- a/src/algebra/strap/ORDRING-.lsp +++ b/src/algebra/strap/ORDRING-.lsp @@ -22,16 +22,16 @@ (DEFUN |ORDRING-;sign;SI;3| (|x| $) (COND ((SPADCALL |x| (|getShellEntry| $ 12)) 1) - ((SPADCALL |x| (|getShellEntry| $ 13)) -1) - ((SPADCALL |x| (|getShellEntry| $ 15)) 0) + ((SPADCALL |x| (|getShellEntry| $ 15)) -1) + ((SPADCALL |x| (|getShellEntry| $ 18)) 0) ('T (|error| "x satisfies neither positive?, negative? or zero?")))) (DEFUN |ORDRING-;abs;2S;4| (|x| $) (COND ((SPADCALL |x| (|getShellEntry| $ 12)) |x|) - ((SPADCALL |x| (|getShellEntry| $ 13)) - (SPADCALL |x| (|getShellEntry| $ 18))) - ((SPADCALL |x| (|getShellEntry| $ 15)) (|spadConstant| $ 7)) + ((SPADCALL |x| (|getShellEntry| $ 15)) + (SPADCALL |x| (|getShellEntry| $ 21))) + ((SPADCALL |x| (|getShellEntry| $ 18)) (|spadConstant| $ 7)) ('T (|error| "x satisfies neither positive?, negative? or zero?")))) (DEFUN |OrderedRing&| (|#1|) @@ -40,7 +40,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|OrderedRing&|)) (LETT |dv$| (LIST '|OrderedRing&| |dv$1|) . #0#) - (LETT $ (|newShell| 20) . #0#) + (LETT $ (|newShell| 23) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -51,16 +51,18 @@ (MAKEPROP '|OrderedRing&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |Zero|) (|Boolean|) (4 . <) |ORDRING-;positive?;SB;1| - |ORDRING-;negative?;SB;2| (10 . |positive?|) - (15 . |negative?|) (20 . |One|) (24 . |zero?|) (|Integer|) - |ORDRING-;sign;SI;3| (29 . -) |ORDRING-;abs;2S;4|) - '#(|sign| 34 |positive?| 39 |negative?| 44 |abs| 49) 'NIL + |ORDRING-;negative?;SB;2| (10 . |positive?|) (|Integer|) + (15 . |One|) (19 . |negative?|) (24 . |One|) (28 . -) + (33 . |zero?|) (38 . |Zero|) |ORDRING-;sign;SI;3| (42 . -) + |ORDRING-;abs;2S;4|) + '#(|sign| 47 |positive?| 52 |negative?| 57 |abs| 62) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 19 - '(0 6 0 7 2 6 8 0 0 9 1 6 8 0 12 1 6 8 - 0 13 0 6 0 14 1 6 8 0 15 1 6 0 0 18 1 - 0 16 0 17 1 0 8 0 10 1 0 8 0 11 1 0 0 - 0 19))))) + (|makeByteWordVec2| 22 + '(0 6 0 7 2 6 8 0 0 9 1 6 8 0 12 0 13 0 + 14 1 6 8 0 15 0 6 0 16 1 13 0 0 17 1 + 6 8 0 18 0 13 0 19 1 6 0 0 21 1 0 13 + 0 20 1 0 8 0 10 1 0 8 0 11 1 0 0 0 + 22))))) '|lookupComplete|)) diff --git a/src/algebra/strap/OUTFORM.lsp b/src/algebra/strap/OUTFORM.lsp index 964b4b9a..33f67b44 100644 --- a/src/algebra/strap/OUTFORM.lsp +++ b/src/algebra/strap/OUTFORM.lsp @@ -556,7 +556,7 @@ (SEQ (LETT |c| 'CONCATB |OUTFORM;blankSeparate;L$;35|) (LETT |l1| NIL |OUTFORM;blankSeparate;L$;35|) (SEQ (LETT |u| NIL |OUTFORM;blankSeparate;L$;35|) - (LETT #0# (SPADCALL |l| (|getShellEntry| $ 55)) + (LETT #0# (SPADCALL |l| (|getShellEntry| $ 64)) |OUTFORM;blankSeparate;L$;35|) G190 (COND @@ -570,7 +570,7 @@ ((EQCAR |u| |c|) (LETT |l1| (SPADCALL (CDR |u|) |l1| - (|getShellEntry| $ 56)) + (|getShellEntry| $ 65)) |OUTFORM;blankSeparate;L$;35|)) ('T (LETT |l1| (CONS |u| |l1|) @@ -606,18 +606,18 @@ (DEFUN |OUTFORM;scripts;$L$;46| (|a| |l| $) (COND - ((SPADCALL |l| (|getShellEntry| $ 68)) |a|) - ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 69)) - (|getShellEntry| $ 68)) - (|OUTFORM;sub;3$;42| |a| (SPADCALL |l| (|getShellEntry| $ 70)) $)) + ((SPADCALL |l| (|getShellEntry| $ 77)) |a|) + ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 78)) + (|getShellEntry| $ 77)) + (|OUTFORM;sub;3$;42| |a| (SPADCALL |l| (|getShellEntry| $ 79)) $)) ('T (CONS 'SUPERSUB (CONS |a| |l|))))) (DEFUN |OUTFORM;supersub;$L$;47| (|a| |l| $) (SEQ (COND - ((ODDP (SPADCALL |l| (|getShellEntry| $ 73))) + ((ODDP (SPADCALL |l| (|getShellEntry| $ 81))) (LETT |l| (SPADCALL |l| (LIST (|OUTFORM;empty;$;73| $)) - (|getShellEntry| $ 56)) + (|getShellEntry| $ 65)) |OUTFORM;supersub;$L$;47|))) (EXIT (CONS 'ALTSUPERSUB (CONS |a| |l|))))) @@ -737,16 +737,16 @@ (DEFUN |OUTFORM;infix;$L$;77| (|a| |l| $) (COND - ((SPADCALL |l| (|getShellEntry| $ 68)) (|OUTFORM;empty;$;73| $)) - ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 69)) - (|getShellEntry| $ 68)) - (SPADCALL |l| (|getShellEntry| $ 70))) + ((SPADCALL |l| (|getShellEntry| $ 77)) (|OUTFORM;empty;$;73| $)) + ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 78)) + (|getShellEntry| $ 77)) + (SPADCALL |l| (|getShellEntry| $ 79))) ((|OUTFORM;infix?;$B;74| |a| $) (CONS |a| |l|)) ('T (|OUTFORM;hconcat;L$;49| - (LIST (SPADCALL |l| (|getShellEntry| $ 70)) |a| + (LIST (SPADCALL |l| (|getShellEntry| $ 79)) |a| (|OUTFORM;infix;$L$;77| |a| - (SPADCALL |l| (|getShellEntry| $ 69)) $)) + (SPADCALL |l| (|getShellEntry| $ 78)) $)) $)))) (DEFUN |OUTFORM;infix;4$;78| (|a| |b| |c| $) @@ -773,7 +773,7 @@ (RETURN (SEQ (LETT |s| (MAKE-FULL-CVEC |nn| - (SPADCALL "." (|getShellEntry| $ 109))) + (SPADCALL "." (|getShellEntry| $ 120))) |OUTFORM;dot;$Nni$;85|) (EXIT (|OUTFORM;super;3$;43| |a| |s| $)))))) @@ -782,7 +782,7 @@ (RETURN (SEQ (LETT |s| (MAKE-FULL-CVEC |nn| - (SPADCALL "," (|getShellEntry| $ 109))) + (SPADCALL "," (|getShellEntry| $ 120))) |OUTFORM;prime;$Nni$;86|) (EXIT (|OUTFORM;super;3$;43| |a| |s| $)))))) @@ -819,9 +819,9 @@ (PROG1 |nn| (|check-subtype| (< 0 |nn|) '(|PositiveInteger|) |nn|)) - (|getShellEntry| $ 124)) + (|getShellEntry| $ 138)) |OUTFORM;differentiate;$Nni$;97|) - (LETT |s| (SPADCALL |r| (|getShellEntry| $ 125)) + (LETT |s| (SPADCALL |r| (|getShellEntry| $ 139)) |OUTFORM;differentiate;$Nni$;97|) (EXIT (|OUTFORM;super;3$;43| |a| (|OUTFORM;paren;2$;40| |s| $) $))))))))) @@ -873,7 +873,7 @@ (RETURN (PROGN (LETT |dv$| '(|OutputForm|) . #0=(|OutputForm|)) - (LETT $ (|newShell| 137) . #0#) + (LETT $ (|newShell| 151) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -895,118 +895,127 @@ (9 . |concat|) (15 . |concat|) |OUTFORM;outputForm;S$;15| |OUTFORM;width;$I;16| |OUTFORM;height;$I;17| |OUTFORM;subHeight;$I;18| |OUTFORM;superHeight;$I;19| - |OUTFORM;height;I;20| |OUTFORM;width;I;21| - |OUTFORM;hspace;I$;29| |OUTFORM;hconcat;3$;48| - |OUTFORM;center;$I$;22| |OUTFORM;left;$I$;23| - |OUTFORM;right;$I$;24| |OUTFORM;center;2$;25| - |OUTFORM;left;2$;26| |OUTFORM;right;2$;27| - |OUTFORM;vspace;I$;28| |OUTFORM;vconcat;3$;50| - |OUTFORM;rspace;2I$;30| (|List| $) (|List| 48) - |OUTFORM;matrix;L$;31| |OUTFORM;pile;L$;32| + |OUTFORM;height;I;20| |OUTFORM;width;I;21| (21 . -) + (27 . |quo|) |OUTFORM;hspace;I$;29| + |OUTFORM;hconcat;3$;48| |OUTFORM;center;$I$;22| + |OUTFORM;left;$I$;23| |OUTFORM;right;$I$;24| + |OUTFORM;center;2$;25| |OUTFORM;left;2$;26| + |OUTFORM;right;2$;27| (|NonNegativeInteger|) (33 . |Zero|) + (37 . |Zero|) (41 . |Zero|) (45 . <) (51 . |One|) + (55 . |One|) |OUTFORM;vspace;I$;28| + |OUTFORM;vconcat;3$;50| |OUTFORM;rspace;2I$;30| (|List| $) + (|List| 57) |OUTFORM;matrix;L$;31| |OUTFORM;pile;L$;32| |OUTFORM;commaSeparate;L$;33| |OUTFORM;semicolonSeparate;L$;34| (|List| $$) - (21 . |reverse|) (26 . |append|) + (59 . |reverse|) (64 . |append|) |OUTFORM;blankSeparate;L$;35| |OUTFORM;brace;2$;36| |OUTFORM;brace;L$;37| |OUTFORM;bracket;2$;38| |OUTFORM;bracket;L$;39| |OUTFORM;paren;2$;40| |OUTFORM;paren;L$;41| |OUTFORM;sub;3$;42| |OUTFORM;super;3$;43| |OUTFORM;presub;3$;44| - |OUTFORM;presuper;3$;45| (32 . |null|) (37 . |rest|) - (42 . |first|) |OUTFORM;scripts;$L$;46| - (|NonNegativeInteger|) (47 . |#|) - |OUTFORM;supersub;$L$;47| |OUTFORM;hconcat;L$;49| - |OUTFORM;vconcat;L$;51| |OUTFORM;~=;3$;52| - |OUTFORM;<;3$;53| |OUTFORM;>;3$;54| |OUTFORM;<=;3$;55| - |OUTFORM;>=;3$;56| |OUTFORM;+;3$;57| |OUTFORM;-;3$;58| - |OUTFORM;-;2$;59| |OUTFORM;*;3$;60| |OUTFORM;/;3$;61| - |OUTFORM;**;3$;62| |OUTFORM;div;3$;63| |OUTFORM;rem;3$;64| - |OUTFORM;quo;3$;65| |OUTFORM;exquo;3$;66| - |OUTFORM;and;3$;67| |OUTFORM;or;3$;68| |OUTFORM;not;2$;69| + |OUTFORM;presuper;3$;45| (70 . |null|) (75 . |rest|) + (80 . |first|) |OUTFORM;scripts;$L$;46| (85 . |#|) + (90 . |odd?|) |OUTFORM;supersub;$L$;47| + |OUTFORM;hconcat;L$;49| |OUTFORM;vconcat;L$;51| + |OUTFORM;~=;3$;52| |OUTFORM;<;3$;53| |OUTFORM;>;3$;54| + |OUTFORM;<=;3$;55| |OUTFORM;>=;3$;56| |OUTFORM;+;3$;57| + |OUTFORM;-;3$;58| |OUTFORM;-;2$;59| |OUTFORM;*;3$;60| + |OUTFORM;/;3$;61| |OUTFORM;**;3$;62| |OUTFORM;div;3$;63| + |OUTFORM;rem;3$;64| |OUTFORM;quo;3$;65| + |OUTFORM;exquo;3$;66| |OUTFORM;and;3$;67| + |OUTFORM;or;3$;68| |OUTFORM;not;2$;69| |OUTFORM;SEGMENT;3$;70| |OUTFORM;SEGMENT;2$;71| - |OUTFORM;binomial;3$;72| |OUTFORM;infix?;$B;74| - |OUTFORM;elt;$L$;75| |OUTFORM;prefix;$L$;76| - |OUTFORM;infix;$L$;77| |OUTFORM;infix;4$;78| - |OUTFORM;postfix;3$;79| |OUTFORM;string;2$;80| - |OUTFORM;quote;2$;81| |OUTFORM;overbar;2$;82| - |OUTFORM;dot;2$;83| |OUTFORM;prime;2$;84| (52 . |char|) + |OUTFORM;binomial;3$;72| (95 . |false|) (99 . |true|) + |OUTFORM;infix?;$B;74| |OUTFORM;elt;$L$;75| + |OUTFORM;prefix;$L$;76| |OUTFORM;infix;$L$;77| + |OUTFORM;infix;4$;78| |OUTFORM;postfix;3$;79| + |OUTFORM;string;2$;80| |OUTFORM;quote;2$;81| + |OUTFORM;overbar;2$;82| |OUTFORM;dot;2$;83| + |OUTFORM;prime;2$;84| (103 . |char|) (108 . |new|) |OUTFORM;dot;$Nni$;85| |OUTFORM;prime;$Nni$;86| |OUTFORM;overlabel;3$;87| |OUTFORM;box;2$;88| |OUTFORM;zag;3$;89| |OUTFORM;root;2$;90| |OUTFORM;root;3$;91| |OUTFORM;over;3$;92| |OUTFORM;slash;3$;93| |OUTFORM;assign;3$;94| |OUTFORM;label;3$;95| |OUTFORM;rarrow;3$;96| - (|PositiveInteger|) (|NumberFormats|) (57 . |FormatRoman|) - (62 . |lowerCase|) |OUTFORM;differentiate;$Nni$;97| + (114 . |zero?|) (119 . <) (|PositiveInteger|) + (|NumberFormats|) (125 . |FormatRoman|) + (130 . |lowerCase|) |OUTFORM;differentiate;$Nni$;97| |OUTFORM;sum;2$;98| |OUTFORM;sum;3$;99| |OUTFORM;sum;4$;100| |OUTFORM;prod;2$;101| |OUTFORM;prod;3$;102| |OUTFORM;prod;4$;103| |OUTFORM;int;2$;104| |OUTFORM;int;3$;105| |OUTFORM;int;4$;106| (|SingleInteger|)) - '#(~= 67 |zag| 79 |width| 85 |vspace| 94 |vconcat| 99 - |supersub| 110 |superHeight| 116 |super| 121 |sum| 127 - |subHeight| 145 |sub| 150 |string| 156 |slash| 161 - |semicolonSeparate| 167 |scripts| 172 |rspace| 178 |root| - 184 |right| 195 |rem| 206 |rarrow| 212 |quote| 218 |quo| - 223 |prod| 229 |print| 247 |prime| 252 |presuper| 263 - |presub| 269 |prefix| 275 |postfix| 281 |pile| 287 |paren| - 292 |overlabel| 302 |overbar| 308 |over| 313 |outputForm| - 319 |or| 339 |not| 345 |messagePrint| 350 |message| 355 - |matrix| 360 |left| 365 |latex| 376 |label| 381 |int| 387 - |infix?| 405 |infix| 410 |hspace| 423 |height| 428 - |hconcat| 437 |hash| 448 |exquo| 453 |empty| 459 |elt| 463 - |doubleFloatFormat| 469 |dot| 474 |div| 485 - |differentiate| 491 |commaSeparate| 497 |coerce| 502 - |center| 507 |bracket| 518 |brace| 528 |box| 538 - |blankSeparate| 543 |binomial| 548 |assign| 554 |and| 560 - SEGMENT 566 >= 577 > 583 = 589 <= 601 < 607 / 613 - 619 + - 630 ** 636 * 642) + '#(~= 135 |zag| 147 |width| 153 |vspace| 162 |vconcat| 167 + |supersub| 178 |superHeight| 184 |super| 189 |sum| 195 + |subHeight| 213 |sub| 218 |string| 224 |slash| 229 + |semicolonSeparate| 235 |scripts| 240 |rspace| 246 |root| + 252 |right| 263 |rem| 274 |rarrow| 280 |quote| 286 |quo| + 291 |prod| 297 |print| 315 |prime| 320 |presuper| 331 + |presub| 337 |prefix| 343 |postfix| 349 |pile| 355 |paren| + 360 |overlabel| 370 |overbar| 376 |over| 381 |outputForm| + 387 |or| 407 |not| 413 |messagePrint| 418 |message| 423 + |matrix| 428 |left| 433 |latex| 444 |label| 449 |int| 455 + |infix?| 473 |infix| 478 |hspace| 491 |height| 496 + |hconcat| 505 |hash| 516 |exquo| 521 |empty| 527 |elt| 531 + |doubleFloatFormat| 537 |dot| 542 |div| 553 + |differentiate| 559 |commaSeparate| 565 |coerce| 570 + |center| 575 |bracket| 586 |brace| 596 |box| 606 + |blankSeparate| 611 |binomial| 616 |assign| 622 |and| 628 + SEGMENT 634 >= 645 > 651 = 657 <= 669 < 675 / 681 - 687 + + 698 ** 704 * 710) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0)) (CONS '#(|SetCategory&| |BasicType&| NIL) (CONS '#((|SetCategory|) (|BasicType|) (|CoercibleTo| 18)) - (|makeByteWordVec2| 136 + (|makeByteWordVec2| 150 '(1 7 11 0 12 0 26 0 27 2 7 0 0 26 28 2 - 7 0 26 0 29 1 54 0 0 55 2 54 0 0 0 56 - 1 54 11 0 68 1 54 0 0 69 1 54 2 0 70 - 1 54 72 0 73 1 26 0 7 109 1 123 7 122 - 124 1 7 0 0 125 2 0 0 0 0 77 2 0 11 0 - 0 1 2 0 0 0 0 114 0 0 20 36 1 0 20 0 - 31 1 0 0 20 45 1 0 0 48 76 2 0 0 0 0 - 46 2 0 0 0 48 74 1 0 20 0 34 2 0 0 0 - 0 65 2 0 0 0 0 128 3 0 0 0 0 0 129 1 - 0 0 0 127 1 0 20 0 33 2 0 0 0 0 64 1 - 0 0 0 104 2 0 0 0 0 118 1 0 0 48 53 2 - 0 0 0 48 71 2 0 0 20 20 47 1 0 0 0 - 115 2 0 0 0 0 116 1 0 0 0 44 2 0 0 0 - 20 41 2 0 0 0 0 89 2 0 0 0 0 121 1 0 - 0 0 105 2 0 0 0 0 90 3 0 0 0 0 0 132 - 1 0 0 0 130 2 0 0 0 0 131 1 0 9 0 10 - 2 0 0 0 72 111 1 0 0 0 108 2 0 0 0 0 - 67 2 0 0 0 0 66 2 0 0 0 48 100 2 0 0 - 0 0 103 1 0 0 48 51 1 0 0 48 63 1 0 0 - 0 62 2 0 0 0 0 112 1 0 0 0 106 2 0 0 - 0 0 117 1 0 0 24 25 1 0 0 22 23 1 0 0 - 7 30 1 0 0 20 21 2 0 0 0 0 93 1 0 0 0 - 94 1 0 9 7 15 1 0 0 7 14 1 0 0 49 50 - 1 0 0 0 43 2 0 0 0 20 40 1 0 7 0 1 2 - 0 0 0 0 120 3 0 0 0 0 0 135 2 0 0 0 0 - 134 1 0 0 0 133 1 0 11 0 98 2 0 0 0 - 48 101 3 0 0 0 0 0 102 1 0 0 20 37 0 - 0 20 35 1 0 20 0 32 1 0 0 48 75 2 0 0 - 0 0 38 1 0 136 0 1 2 0 0 0 0 91 0 0 0 - 13 2 0 0 0 48 99 1 0 7 7 8 2 0 0 0 72 - 110 1 0 0 0 107 2 0 0 0 0 88 2 0 0 0 - 72 126 1 0 0 48 52 1 0 18 0 19 1 0 0 - 0 42 2 0 0 0 20 39 1 0 0 0 60 1 0 0 - 48 61 1 0 0 48 59 1 0 0 0 58 1 0 0 0 - 113 1 0 0 48 57 2 0 0 0 0 97 2 0 0 0 - 0 119 2 0 0 0 0 92 1 0 0 0 96 2 0 0 0 - 0 95 2 0 0 0 0 81 2 0 0 0 0 79 2 0 0 - 0 0 17 2 0 11 0 0 16 2 0 0 0 0 80 2 0 - 0 0 0 78 2 0 0 0 0 86 1 0 0 0 84 2 0 - 0 0 0 83 2 0 0 0 0 82 2 0 0 0 0 87 2 - 0 0 0 0 85))))) + 7 0 26 0 29 2 20 0 0 0 37 2 20 0 0 0 + 38 0 47 0 48 0 20 0 49 0 24 0 50 2 20 + 11 0 0 51 0 47 0 52 0 20 0 53 1 63 0 + 0 64 2 63 0 0 0 65 1 63 11 0 77 1 63 + 0 0 78 1 63 2 0 79 1 63 47 0 81 1 20 + 11 0 82 0 11 0 107 0 11 0 108 1 26 0 + 7 120 2 7 0 47 26 121 1 47 11 0 134 2 + 47 11 0 0 135 1 137 7 136 138 1 7 0 0 + 139 2 0 0 0 0 86 2 0 11 0 0 1 2 0 0 0 + 0 126 0 0 20 36 1 0 20 0 31 1 0 0 20 + 54 1 0 0 57 85 2 0 0 0 0 55 2 0 0 0 + 57 83 1 0 20 0 34 2 0 0 0 0 74 2 0 0 + 0 0 142 3 0 0 0 0 0 143 1 0 0 0 141 1 + 0 20 0 33 2 0 0 0 0 73 1 0 0 0 115 2 + 0 0 0 0 130 1 0 0 57 62 2 0 0 0 57 80 + 2 0 0 20 20 56 1 0 0 0 127 2 0 0 0 0 + 128 1 0 0 0 46 2 0 0 0 20 43 2 0 0 0 + 0 98 2 0 0 0 0 133 1 0 0 0 116 2 0 0 + 0 0 99 3 0 0 0 0 0 146 1 0 0 0 144 2 + 0 0 0 0 145 1 0 9 0 10 2 0 0 0 47 123 + 1 0 0 0 119 2 0 0 0 0 76 2 0 0 0 0 75 + 2 0 0 0 57 111 2 0 0 0 0 114 1 0 0 57 + 60 1 0 0 57 72 1 0 0 0 71 2 0 0 0 0 + 124 1 0 0 0 117 2 0 0 0 0 129 1 0 0 + 24 25 1 0 0 22 23 1 0 0 7 30 1 0 0 20 + 21 2 0 0 0 0 102 1 0 0 0 103 1 0 9 7 + 15 1 0 0 7 14 1 0 0 58 59 1 0 0 0 45 + 2 0 0 0 20 42 1 0 7 0 1 2 0 0 0 0 132 + 3 0 0 0 0 0 149 2 0 0 0 0 148 1 0 0 0 + 147 1 0 11 0 109 2 0 0 0 57 112 3 0 0 + 0 0 0 113 1 0 0 20 39 0 0 20 35 1 0 + 20 0 32 1 0 0 57 84 2 0 0 0 0 40 1 0 + 150 0 1 2 0 0 0 0 100 0 0 0 13 2 0 0 + 0 57 110 1 0 7 7 8 2 0 0 0 47 122 1 0 + 0 0 118 2 0 0 0 0 97 2 0 0 0 47 140 1 + 0 0 57 61 1 0 18 0 19 1 0 0 0 44 2 0 + 0 0 20 41 1 0 0 0 69 1 0 0 57 70 1 0 + 0 57 68 1 0 0 0 67 1 0 0 0 125 1 0 0 + 57 66 2 0 0 0 0 106 2 0 0 0 0 131 2 0 + 0 0 0 101 1 0 0 0 105 2 0 0 0 0 104 2 + 0 0 0 0 90 2 0 0 0 0 88 2 0 0 0 0 17 + 2 0 11 0 0 16 2 0 0 0 0 89 2 0 0 0 0 + 87 2 0 0 0 0 95 1 0 0 0 93 2 0 0 0 0 + 92 2 0 0 0 0 91 2 0 0 0 0 96 2 0 0 0 + 0 94))))) '|lookupComplete|)) (MAKEPROP '|OutputForm| 'NILADIC T) diff --git a/src/algebra/strap/PI.lsp b/src/algebra/strap/PI.lsp index 6845dd67..4dc3184c 100644 --- a/src/algebra/strap/PI.lsp +++ b/src/algebra/strap/PI.lsp @@ -30,7 +30,7 @@ (RETURN (PROGN (LETT |dv$| '(|PositiveInteger|) . #0=(|PositiveInteger|)) - (LETT $ (|newShell| 12) . #0#) + (LETT $ (|newShell| 16) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -40,12 +40,13 @@ $)))) (MAKEPROP '|PositiveInteger| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL (|NonNegativeInteger|) - (|PositiveInteger|) (|Boolean|) (|Union| $ '"failed") + (LIST '#(NIL NIL NIL NIL NIL (|NonNegativeInteger|) (0 . |Zero|) + (|Integer|) (4 . |Zero|) (|Boolean|) (8 . <) + (|PositiveInteger|) (|Union| $ '"failed") (|SingleInteger|) (|String|) (|OutputForm|)) - '#(~= 0 |sample| 6 |recip| 10 |one?| 15 |min| 20 |max| 26 - |latex| 32 |hash| 37 |gcd| 42 |coerce| 48 |One| 53 >= 57 > - 63 = 69 <= 75 < 81 + 87 ** 93 * 105) + '#(~= 14 |sample| 20 |recip| 24 |one?| 29 |min| 34 |max| 40 + |latex| 46 |hash| 51 |gcd| 56 |coerce| 62 |One| 67 >= 71 > + 77 = 83 <= 89 < 95 + 101 ** 107 * 119) '(((|commutative| "*") . 0)) (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0)) (CONS '#(NIL |Monoid&| |OrderedSet&| |SemiGroup&| @@ -54,15 +55,16 @@ (CONS '#((|OrderedAbelianSemiGroup|) (|Monoid|) (|OrderedSet|) (|SemiGroup|) (|AbelianSemiGroup|) (|SetCategory|) - (|BasicType|) (|CoercibleTo| 11)) - (|makeByteWordVec2| 11 - '(2 0 7 0 0 1 0 0 0 1 1 0 8 0 1 1 0 7 0 - 1 2 0 0 0 0 1 2 0 0 0 0 1 1 0 10 0 1 - 1 0 9 0 1 2 0 0 0 0 1 1 0 11 0 1 0 0 - 0 1 2 0 7 0 0 1 2 0 7 0 0 1 2 0 7 0 0 - 1 2 0 7 0 0 1 2 0 7 0 0 1 2 0 0 0 0 1 - 2 0 0 0 6 1 2 0 0 0 5 1 2 0 0 0 0 1 2 - 0 0 6 0 1))))) + (|BasicType|) (|CoercibleTo| 15)) + (|makeByteWordVec2| 15 + '(0 5 0 6 0 7 0 8 2 5 9 0 0 10 2 0 9 0 + 0 1 0 0 0 1 1 0 12 0 1 1 0 9 0 1 2 0 + 0 0 0 1 2 0 0 0 0 1 1 0 14 0 1 1 0 13 + 0 1 2 0 0 0 0 1 1 0 15 0 1 0 0 0 1 2 + 0 9 0 0 1 2 0 9 0 0 1 2 0 9 0 0 1 2 0 + 9 0 0 1 2 0 9 0 0 1 2 0 0 0 0 1 2 0 0 + 0 11 1 2 0 0 0 5 1 2 0 0 0 0 1 2 0 0 + 11 0 1))))) '|lookupComplete|)) (MAKEPROP '|PositiveInteger| 'NILADIC T) diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp index d196bca2..c8d88782 100644 --- a/src/algebra/strap/POLYCAT-.lsp +++ b/src/algebra/strap/POLYCAT-.lsp @@ -164,8 +164,8 @@ ((QEQCAR (SPADCALL (SPADCALL |e| - (|getShellEntry| $ 11)) - (|getShellEntry| $ 13)) + (|getShellEntry| $ 14)) + (|getShellEntry| $ 16)) 1) (PROGN (LETT #1# @@ -195,8 +195,8 @@ (CONS (SPADCALL (SPADCALL |e| - (|getShellEntry| $ 11)) - (|getShellEntry| $ 14)) + (|getShellEntry| $ 14)) + (|getShellEntry| $ 17)) #2#) |POLYCAT-;eval;SLS;1|))) (LETT #3# (CDR #3#) @@ -223,14 +223,14 @@ (LETT #4# (CONS (SPADCALL |e| - (|getShellEntry| $ 15)) + (|getShellEntry| $ 18)) #4#) |POLYCAT-;eval;SLS;1|))) (LETT #5# (CDR #5#) |POLYCAT-;eval;SLS;1|) (GO G190) G191 (EXIT (NREVERSE0 #4#)))) - (|getShellEntry| $ 18)))))))))) + (|getShellEntry| $ 21)))))))))) (DEFUN |POLYCAT-;monomials;SL;2| (|p| $) (PROG (|ml|) @@ -238,15 +238,15 @@ (SEQ (LETT |ml| NIL |POLYCAT-;monomials;SL;2|) (SEQ G190 (COND - ((NULL (SPADCALL |p| (|spadConstant| $ 22) - (|getShellEntry| $ 25))) + ((NULL (SPADCALL |p| (|spadConstant| $ 27) + (|getShellEntry| $ 29))) (GO G191))) (SEQ (LETT |ml| - (CONS (SPADCALL |p| (|getShellEntry| $ 26)) + (CONS (SPADCALL |p| (|getShellEntry| $ 30)) |ml|) |POLYCAT-;monomials;SL;2|) (EXIT (LETT |p| - (SPADCALL |p| (|getShellEntry| $ 27)) + (SPADCALL |p| (|getShellEntry| $ 32)) |POLYCAT-;monomials;SL;2|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (REVERSE |ml|)))))) @@ -255,7 +255,7 @@ (PROG (|l|) (RETURN (COND - ((NULL (CDR (LETT |l| (SPADCALL |p| (|getShellEntry| $ 29)) + ((NULL (CDR (LETT |l| (SPADCALL |p| (|getShellEntry| $ 35)) |POLYCAT-;isPlus;SU;3|))) (CONS 1 "failed")) ('T (CONS 0 |l|)))))) @@ -265,9 +265,9 @@ (RETURN (SEQ (COND ((OR (NULL (LETT |lv| - (SPADCALL |p| (|getShellEntry| $ 32)) + (SPADCALL |p| (|getShellEntry| $ 40)) |POLYCAT-;isTimes;SU;4|)) - (NULL (SPADCALL |p| (|getShellEntry| $ 33)))) + (NULL (SPADCALL |p| (|getShellEntry| $ 42)))) (CONS 1 "failed")) ('T (SEQ (LETT |l| @@ -286,11 +286,11 @@ (SEQ (EXIT (LETT #0# (CONS - (SPADCALL (|spadConstant| $ 34) + (SPADCALL (|spadConstant| $ 43) |v| (SPADCALL |p| |v| - (|getShellEntry| $ 37)) - (|getShellEntry| $ 38)) + (|getShellEntry| $ 46)) + (|getShellEntry| $ 47)) #0#) |POLYCAT-;isTimes;SU;4|))) (LETT #1# (CDR #1#) @@ -301,40 +301,40 @@ ((SPADCALL (LETT |r| (SPADCALL |p| - (|getShellEntry| $ 39)) + (|getShellEntry| $ 48)) |POLYCAT-;isTimes;SU;4|) - (|getShellEntry| $ 40)) + (|getShellEntry| $ 49)) (COND ((NULL (CDR |lv|)) (CONS 1 "failed")) ('T (CONS 0 |l|)))) ('T (CONS 0 (CONS (SPADCALL |r| - (|getShellEntry| $ 41)) + (|getShellEntry| $ 51)) |l|)))))))))))) (DEFUN |POLYCAT-;isExpt;SU;5| (|p| $) (PROG (|u| |d|) (RETURN - (SEQ (LETT |u| (SPADCALL |p| (|getShellEntry| $ 43)) + (SEQ (LETT |u| (SPADCALL |p| (|getShellEntry| $ 53)) |POLYCAT-;isExpt;SU;5|) (EXIT (COND ((OR (QEQCAR |u| 1) (NULL (SPADCALL |p| - (SPADCALL (|spadConstant| $ 34) + (SPADCALL (|spadConstant| $ 43) (QCDR |u|) (LETT |d| (SPADCALL |p| (QCDR |u|) - (|getShellEntry| $ 37)) + (|getShellEntry| $ 46)) |POLYCAT-;isExpt;SU;5|) - (|getShellEntry| $ 38)) - (|getShellEntry| $ 44)))) + (|getShellEntry| $ 47)) + (|getShellEntry| $ 54)))) (CONS 1 "failed")) ('T (CONS 0 (CONS (QCDR |u|) |d|))))))))) (DEFUN |POLYCAT-;coefficient;SVarSetNniS;6| (|p| |v| |n| $) - (SPADCALL (SPADCALL |p| |v| (|getShellEntry| $ 49)) |n| - (|getShellEntry| $ 51))) + (SPADCALL (SPADCALL |p| |v| (|getShellEntry| $ 59)) |n| + (|getShellEntry| $ 61))) (DEFUN |POLYCAT-;coefficient;SLLS;7| (|p| |lv| |ln| $) (COND @@ -346,9 +346,9 @@ ('T (SPADCALL (SPADCALL - (SPADCALL |p| (|SPADfirst| |lv|) (|getShellEntry| $ 49)) - (|SPADfirst| |ln|) (|getShellEntry| $ 51)) - (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 54))))) + (SPADCALL |p| (|SPADfirst| |lv|) (|getShellEntry| $ 59)) + (|SPADfirst| |ln|) (|getShellEntry| $ 61)) + (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 68))))) (DEFUN |POLYCAT-;monomial;SLLS;8| (|p| |lv| |ln| $) (COND @@ -360,22 +360,22 @@ ('T (SPADCALL (SPADCALL |p| (|SPADfirst| |lv|) (|SPADfirst| |ln|) - (|getShellEntry| $ 38)) - (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 56))))) + (|getShellEntry| $ 47)) + (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 70))))) (DEFUN |POLYCAT-;retract;SVarSet;9| (|p| $) (PROG (#0=#:G1479 |q|) (RETURN (SEQ (LETT |q| - (PROG2 (LETT #0# (SPADCALL |p| (|getShellEntry| $ 43)) + (PROG2 (LETT #0# (SPADCALL |p| (|getShellEntry| $ 53)) |POLYCAT-;retract;SVarSet;9|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 9) #0#)) |POLYCAT-;retract;SVarSet;9|) (EXIT (COND - ((SPADCALL (SPADCALL |q| (|getShellEntry| $ 58)) |p| - (|getShellEntry| $ 44)) + ((SPADCALL (SPADCALL |q| (|getShellEntry| $ 72)) |p| + (|getShellEntry| $ 54)) |q|) ('T (|error| "Polynomial is not a single variable")))))))) @@ -383,15 +383,15 @@ (PROG (|q| #0=#:G1487) (RETURN (SEQ (EXIT (SEQ (SEQ (LETT |q| - (SPADCALL |p| (|getShellEntry| $ 43)) + (SPADCALL |p| (|getShellEntry| $ 53)) |POLYCAT-;retractIfCan;SU;10|) (EXIT (COND ((QEQCAR |q| 0) (COND ((SPADCALL (SPADCALL (QCDR |q|) - (|getShellEntry| $ 58)) - |p| (|getShellEntry| $ 44)) + (|getShellEntry| $ 72)) + |p| (|getShellEntry| $ 54)) (PROGN (LETT #0# |q| |POLYCAT-;retractIfCan;SU;10|) @@ -400,8 +400,8 @@ #0# (EXIT #0#))))) (DEFUN |POLYCAT-;mkPrim| (|p| $) - (SPADCALL (|spadConstant| $ 35) (SPADCALL |p| (|getShellEntry| $ 61)) - (|getShellEntry| $ 62))) + (SPADCALL (|spadConstant| $ 44) (SPADCALL |p| (|getShellEntry| $ 75)) + (|getShellEntry| $ 76))) (DEFUN |POLYCAT-;primitiveMonomials;SL;12| (|p| $) (PROG (#0=#:G1697 |q| #1=#:G1698) @@ -409,7 +409,7 @@ (SEQ (PROGN (LETT #0# NIL |POLYCAT-;primitiveMonomials;SL;12|) (SEQ (LETT |q| NIL |POLYCAT-;primitiveMonomials;SL;12|) - (LETT #1# (SPADCALL |p| (|getShellEntry| $ 29)) + (LETT #1# (SPADCALL |p| (|getShellEntry| $ 35)) |POLYCAT-;primitiveMonomials;SL;12|) G190 (COND @@ -430,38 +430,38 @@ (PROG (#0=#:G1493 |d| |u|) (RETURN (SEQ (COND - ((SPADCALL |p| (|getShellEntry| $ 64)) 0) + ((SPADCALL |p| (|getShellEntry| $ 78)) 0) ('T (SEQ (LETT |u| (SPADCALL |p| (PROG2 (LETT #0# (SPADCALL |p| - (|getShellEntry| $ 43)) + (|getShellEntry| $ 53)) |POLYCAT-;totalDegree;SNni;13|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 9) #0#)) - (|getShellEntry| $ 49)) + (|getShellEntry| $ 59)) |POLYCAT-;totalDegree;SNni;13|) (LETT |d| 0 |POLYCAT-;totalDegree;SNni;13|) (SEQ G190 (COND - ((NULL (SPADCALL |u| (|spadConstant| $ 65) - (|getShellEntry| $ 66))) + ((NULL (SPADCALL |u| (|spadConstant| $ 80) + (|getShellEntry| $ 81))) (GO G191))) (SEQ (LETT |d| (MAX |d| (+ (SPADCALL |u| - (|getShellEntry| $ 67)) + (|getShellEntry| $ 82)) (SPADCALL (SPADCALL |u| - (|getShellEntry| $ 68)) - (|getShellEntry| $ 69)))) + (|getShellEntry| $ 83)) + (|getShellEntry| $ 84)))) |POLYCAT-;totalDegree;SNni;13|) (EXIT (LETT |u| (SPADCALL |u| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 87)) |POLYCAT-;totalDegree;SNni;13|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |d|)))))))) @@ -470,7 +470,7 @@ (PROG (#0=#:G1501 |v| |w| |d| |u|) (RETURN (SEQ (COND - ((SPADCALL |p| (|getShellEntry| $ 64)) 0) + ((SPADCALL |p| (|getShellEntry| $ 78)) 0) ('T (SEQ (LETT |u| (SPADCALL |p| @@ -478,50 +478,50 @@ (PROG2 (LETT #0# (SPADCALL |p| - (|getShellEntry| $ 43)) + (|getShellEntry| $ 53)) |POLYCAT-;totalDegree;SLNni;14|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 9) #0#)) |POLYCAT-;totalDegree;SLNni;14|) - (|getShellEntry| $ 49)) + (|getShellEntry| $ 59)) |POLYCAT-;totalDegree;SLNni;14|) (LETT |d| 0 |POLYCAT-;totalDegree;SLNni;14|) (LETT |w| 0 |POLYCAT-;totalDegree;SLNni;14|) (COND - ((SPADCALL |v| |lv| (|getShellEntry| $ 72)) + ((SPADCALL |v| |lv| (|getShellEntry| $ 89)) (LETT |w| 1 |POLYCAT-;totalDegree;SLNni;14|))) (SEQ G190 (COND - ((NULL (SPADCALL |u| (|spadConstant| $ 65) - (|getShellEntry| $ 66))) + ((NULL (SPADCALL |u| (|spadConstant| $ 80) + (|getShellEntry| $ 81))) (GO G191))) (SEQ (LETT |d| (MAX |d| (+ (* |w| (SPADCALL |u| - (|getShellEntry| $ 67))) + (|getShellEntry| $ 82))) (SPADCALL (SPADCALL |u| - (|getShellEntry| $ 68)) - |lv| (|getShellEntry| $ 73)))) + (|getShellEntry| $ 83)) + |lv| (|getShellEntry| $ 92)))) |POLYCAT-;totalDegree;SLNni;14|) (EXIT (LETT |u| (SPADCALL |u| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 87)) |POLYCAT-;totalDegree;SLNni;14|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |d|)))))))) (DEFUN |POLYCAT-;resultant;2SVarSetS;15| (|p1| |p2| |mvar| $) - (SPADCALL (SPADCALL |p1| |mvar| (|getShellEntry| $ 49)) - (SPADCALL |p2| |mvar| (|getShellEntry| $ 49)) - (|getShellEntry| $ 75))) + (SPADCALL (SPADCALL |p1| |mvar| (|getShellEntry| $ 59)) + (SPADCALL |p2| |mvar| (|getShellEntry| $ 59)) + (|getShellEntry| $ 94))) (DEFUN |POLYCAT-;discriminant;SVarSetS;16| (|p| |var| $) - (SPADCALL (SPADCALL |p| |var| (|getShellEntry| $ 49)) - (|getShellEntry| $ 77))) + (SPADCALL (SPADCALL |p| |var| (|getShellEntry| $ 59)) + (|getShellEntry| $ 96))) (DEFUN |POLYCAT-;allMonoms| (|l| $) (PROG (#0=#:G1699 |p| #1=#:G1700) @@ -542,24 +542,24 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |p| - (|getShellEntry| $ 79)) + (|getShellEntry| $ 98)) #0#) |POLYCAT-;allMonoms|))) (LETT #1# (CDR #1#) |POLYCAT-;allMonoms|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 81)) - (|getShellEntry| $ 82)))))) + (|getShellEntry| $ 99)) + (|getShellEntry| $ 100)))))) (DEFUN |POLYCAT-;P2R| (|p| |b| |n| $) (PROG (|w| |bj| #0=#:G1702 |i| #1=#:G1701) (RETURN (SEQ (LETT |w| - (SPADCALL |n| (|spadConstant| $ 23) - (|getShellEntry| $ 84)) + (SPADCALL |n| (|spadConstant| $ 28) + (|getShellEntry| $ 102)) |POLYCAT-;P2R|) (SEQ (LETT |bj| NIL |POLYCAT-;P2R|) (LETT #0# |b| |POLYCAT-;P2R|) - (LETT |i| (SPADCALL |w| (|getShellEntry| $ 86)) + (LETT |i| (SPADCALL |w| (|getShellEntry| $ 104)) |POLYCAT-;P2R|) (LETT #1# (QVSIZE |w|) |POLYCAT-;P2R|) G190 (COND @@ -570,8 +570,8 @@ (GO G191))) (SEQ (EXIT (SPADCALL |w| |i| (SPADCALL |p| |bj| - (|getShellEntry| $ 87)) - (|getShellEntry| $ 88)))) + (|getShellEntry| $ 106)) + (|getShellEntry| $ 107)))) (LETT |i| (PROG1 (+ |i| 1) (LETT #0# (CDR #0#) |POLYCAT-;P2R|)) @@ -616,7 +616,7 @@ (LETT #2# (CONS (SPADCALL |p| |bj| - (|getShellEntry| $ 87)) + (|getShellEntry| $ 106)) #2#) |POLYCAT-;eq2R|))) (LETT #3# (CDR #3#) @@ -627,13 +627,13 @@ |POLYCAT-;eq2R|))) (LETT #1# (CDR #1#) |POLYCAT-;eq2R|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 92)))))) + (|getShellEntry| $ 111)))))) (DEFUN |POLYCAT-;reducedSystem;MM;20| (|m| $) (PROG (#0=#:G1707 |r| #1=#:G1708 |b| #2=#:G1709 |bj| #3=#:G1710 |d| |mm| |l|) (RETURN - (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 95)) + (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 114)) |POLYCAT-;reducedSystem;MM;20|) (LETT |b| (SPADCALL @@ -662,8 +662,8 @@ (LETT #1# (CDR #1#) |POLYCAT-;reducedSystem;MM;20|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 81)) - (|getShellEntry| $ 82)) + (|getShellEntry| $ 99)) + (|getShellEntry| $ 100)) |POLYCAT-;reducedSystem;MM;20|) (LETT |d| (PROGN @@ -681,7 +681,7 @@ (SEQ (EXIT (LETT #2# (CONS (SPADCALL |bj| - (|getShellEntry| $ 61)) + (|getShellEntry| $ 75)) #2#) |POLYCAT-;reducedSystem;MM;20|))) (LETT #3# (CDR #3#) @@ -696,7 +696,7 @@ (SPADCALL |mm| (|POLYCAT-;eq2R| (|SPADfirst| |l|) |d| $) - (|getShellEntry| $ 96)) + (|getShellEntry| $ 118)) |POLYCAT-;reducedSystem;MM;20|) (EXIT (LETT |l| (CDR |l|) |POLYCAT-;reducedSystem;MM;20|))) @@ -707,9 +707,9 @@ (PROG (#0=#:G1711 |s| #1=#:G1712 |b| #2=#:G1713 |bj| #3=#:G1714 |d| |n| |mm| |w| |l| |r|) (RETURN - (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 95)) + (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 114)) |POLYCAT-;reducedSystem;MVR;21|) - (LETT |r| (SPADCALL |v| (|getShellEntry| $ 100)) + (LETT |r| (SPADCALL |v| (|getShellEntry| $ 122)) |POLYCAT-;reducedSystem;MVR;21|) (LETT |b| (SPADCALL @@ -741,9 +741,9 @@ |POLYCAT-;reducedSystem;MVR;21|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 81)) - (|getShellEntry| $ 101)) - (|getShellEntry| $ 82)) + (|getShellEntry| $ 99)) + (|getShellEntry| $ 123)) + (|getShellEntry| $ 100)) |POLYCAT-;reducedSystem;MVR;21|) (LETT |d| (PROGN @@ -761,7 +761,7 @@ (SEQ (EXIT (LETT #2# (CONS (SPADCALL |bj| - (|getShellEntry| $ 61)) + (|getShellEntry| $ 75)) #2#) |POLYCAT-;reducedSystem;MVR;21|))) (LETT #3# (CDR #3#) @@ -780,13 +780,13 @@ (SPADCALL |mm| (|POLYCAT-;eq2R| (|SPADfirst| |l|) |d| $) - (|getShellEntry| $ 96)) + (|getShellEntry| $ 118)) |POLYCAT-;reducedSystem;MVR;21|) (LETT |w| (SPADCALL |w| (|POLYCAT-;P2R| (|SPADfirst| |r|) |d| |n| $) - (|getShellEntry| $ 102)) + (|getShellEntry| $ 127)) |POLYCAT-;reducedSystem;MVR;21|) (LETT |l| (CDR |l|) |POLYCAT-;reducedSystem;MVR;21|) @@ -796,36 +796,36 @@ (EXIT (CONS |mm| |w|)))))) (DEFUN |POLYCAT-;gcdPolynomial;3Sup;22| (|pp| |qq| $) - (SPADCALL |pp| |qq| (|getShellEntry| $ 107))) + (SPADCALL |pp| |qq| (|getShellEntry| $ 132))) (DEFUN |POLYCAT-;solveLinearPolynomialEquation;LSupU;23| (|lpp| |pp| $) - (SPADCALL |lpp| |pp| (|getShellEntry| $ 112))) + (SPADCALL |lpp| |pp| (|getShellEntry| $ 137))) (DEFUN |POLYCAT-;factorPolynomial;SupF;24| (|pp| $) - (SPADCALL |pp| (|getShellEntry| $ 117))) + (SPADCALL |pp| (|getShellEntry| $ 142))) (DEFUN |POLYCAT-;factorSquareFreePolynomial;SupF;25| (|pp| $) - (SPADCALL |pp| (|getShellEntry| $ 120))) + (SPADCALL |pp| (|getShellEntry| $ 145))) (DEFUN |POLYCAT-;factor;SF;26| (|p| $) (PROG (|v| |ansR| #0=#:G1715 |w| #1=#:G1716 |up| |ansSUP| #2=#:G1717 |ww| #3=#:G1718) (RETURN - (SEQ (LETT |v| (SPADCALL |p| (|getShellEntry| $ 43)) + (SEQ (LETT |v| (SPADCALL |p| (|getShellEntry| $ 53)) |POLYCAT-;factor;SF;26|) (EXIT (COND ((QEQCAR |v| 1) (SEQ (LETT |ansR| (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 39)) - (|getShellEntry| $ 123)) + (|getShellEntry| $ 48)) + (|getShellEntry| $ 148)) |POLYCAT-;factor;SF;26|) (EXIT (SPADCALL (SPADCALL (SPADCALL |ansR| - (|getShellEntry| $ 125)) - (|getShellEntry| $ 41)) + (|getShellEntry| $ 150)) + (|getShellEntry| $ 51)) (PROGN (LETT #0# NIL |POLYCAT-;factor;SF;26|) @@ -834,7 +834,7 @@ |POLYCAT-;factor;SF;26|) (LETT #1# (SPADCALL |ansR| - (|getShellEntry| $ 129)) + (|getShellEntry| $ 154)) |POLYCAT-;factor;SF;26|) G190 (COND @@ -850,7 +850,7 @@ (CONS (VECTOR (QVELT |w| 0) (SPADCALL (QVELT |w| 1) - (|getShellEntry| $ 41)) + (|getShellEntry| $ 51)) (QVELT |w| 2)) #0#) |POLYCAT-;factor;SF;26|))) @@ -858,20 +858,20 @@ |POLYCAT-;factor;SF;26|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 133))))) + (|getShellEntry| $ 158))))) ('T (SEQ (LETT |up| (SPADCALL |p| (QCDR |v|) - (|getShellEntry| $ 49)) + (|getShellEntry| $ 59)) |POLYCAT-;factor;SF;26|) (LETT |ansSUP| - (SPADCALL |up| (|getShellEntry| $ 117)) + (SPADCALL |up| (|getShellEntry| $ 142)) |POLYCAT-;factor;SF;26|) (EXIT (SPADCALL (SPADCALL (SPADCALL |ansSUP| - (|getShellEntry| $ 134)) - (QCDR |v|) (|getShellEntry| $ 135)) + (|getShellEntry| $ 159)) + (QCDR |v|) (|getShellEntry| $ 160)) (PROGN (LETT #2# NIL |POLYCAT-;factor;SF;26|) @@ -880,7 +880,7 @@ |POLYCAT-;factor;SF;26|) (LETT #3# (SPADCALL |ansSUP| - (|getShellEntry| $ 138)) + (|getShellEntry| $ 163)) |POLYCAT-;factor;SF;26|) G190 (COND @@ -897,7 +897,7 @@ (VECTOR (QVELT |ww| 0) (SPADCALL (QVELT |ww| 1) (QCDR |v|) - (|getShellEntry| $ 135)) + (|getShellEntry| $ 160)) (QVELT |ww| 2)) #2#) |POLYCAT-;factor;SF;26|))) @@ -905,7 +905,7 @@ |POLYCAT-;factor;SF;26|) (GO G190) G191 (EXIT (NREVERSE0 #2#)))) - (|getShellEntry| $ 133))))))))))) + (|getShellEntry| $ 158))))))))))) (DEFUN |POLYCAT-;conditionP;MU;27| (|mat| $) (PROG (|ll| #0=#:G1719 |z| #1=#:G1720 |ch| |l| #2=#:G1721 #3=#:G1722 @@ -919,8 +919,8 @@ (SEQ (EXIT (SEQ (LETT |ll| (SPADCALL (SPADCALL |mat| - (|getShellEntry| $ 140)) - (|getShellEntry| $ 95)) + (|getShellEntry| $ 165)) + (|getShellEntry| $ 114)) |POLYCAT-;conditionP;MU;27|) (LETT |llR| (PROGN @@ -948,7 +948,7 @@ (EXIT (NREVERSE0 #0#)))) |POLYCAT-;conditionP;MU;27|) (LETT |monslist| NIL |POLYCAT-;conditionP;MU;27|) - (LETT |ch| (SPADCALL (|getShellEntry| $ 141)) + (LETT |ch| (|spadConstant| $ 168) |POLYCAT-;conditionP;MU;27|) (SEQ (LETT |l| NIL |POLYCAT-;conditionP;MU;27|) (LETT #2# |ll| |POLYCAT-;conditionP;MU;27|) @@ -982,14 +982,14 @@ (PROGN (LETT #4# (SPADCALL |u| - (|getShellEntry| $ 79)) + (|getShellEntry| $ 98)) |POLYCAT-;conditionP;MU;27|) (COND (#6# (LETT #5# (SPADCALL #5# #4# (|getShellEntry| $ - 142)) + 169)) |POLYCAT-;conditionP;MU;27|)) ('T (PROGN @@ -1023,11 +1023,11 @@ (SEQ (LETT |vars| (SPADCALL |m| - (|getShellEntry| $ 32)) + (|getShellEntry| $ 40)) |POLYCAT-;conditionP;MU;27|) (LETT |degs| (SPADCALL |m| |vars| - (|getShellEntry| $ 143)) + (|getShellEntry| $ 170)) |POLYCAT-;conditionP;MU;27|) (LETT |deg1| (PROGN @@ -1054,7 +1054,7 @@ (LETT |nd| (SPADCALL |d| |ch| (|getShellEntry| $ - 145)) + 172)) |POLYCAT-;conditionP;MU;27|) (EXIT (COND @@ -1085,9 +1085,9 @@ |POLYCAT-;conditionP;MU;27|) (LETT |redmons| (CONS - (SPADCALL (|spadConstant| $ 34) + (SPADCALL (|spadConstant| $ 43) |vars| |deg1| - (|getShellEntry| $ 56)) + (|getShellEntry| $ 70)) |redmons|) |POLYCAT-;conditionP;MU;27|) (EXIT @@ -1126,9 +1126,9 @@ (SPADCALL |u| |vars| |degs| (|getShellEntry| $ - 54)) + 68)) (|getShellEntry| $ - 146)) + 174)) |v|) #12#) |POLYCAT-;conditionP;MU;27|))) @@ -1153,9 +1153,9 @@ (SPADCALL (SPADCALL (SPADCALL |llR| - (|getShellEntry| $ 92)) - (|getShellEntry| $ 147)) - (|getShellEntry| $ 149)) + (|getShellEntry| $ 111)) + (|getShellEntry| $ 177)) + (|getShellEntry| $ 179)) |POLYCAT-;conditionP;MU;27|) (EXIT (COND ((QEQCAR |ans| 1) (CONS 1 "failed")) @@ -1216,11 +1216,11 @@ (+ |i| 1) |POLYCAT-;conditionP;MU;27|) (|getShellEntry| - $ 150)) + $ 180)) (|getShellEntry| - $ 41)) + $ 51)) (|getShellEntry| - $ 151)) + $ 181)) |POLYCAT-;conditionP;MU;27|) (COND (#21# @@ -1228,7 +1228,7 @@ (SPADCALL #20# #19# (|getShellEntry| - $ 152)) + $ 182)) |POLYCAT-;conditionP;MU;27|)) ('T (PROGN @@ -1244,7 +1244,7 @@ (COND (#21# #20#) ('T - (|spadConstant| $ 22))))))) + (|spadConstant| $ 27))))))) (LETT #17# (PROG1 (CDR #17#) (LETT #16# (QSADD1 #16#) @@ -1257,24 +1257,24 @@ (DEFUN |POLYCAT-;charthRoot;SU;28| (|p| $) (PROG (|vars| |ans| |ch|) (RETURN - (SEQ (LETT |vars| (SPADCALL |p| (|getShellEntry| $ 32)) + (SEQ (LETT |vars| (SPADCALL |p| (|getShellEntry| $ 40)) |POLYCAT-;charthRoot;SU;28|) (EXIT (COND ((NULL |vars|) (SEQ (LETT |ans| (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 146)) - (|getShellEntry| $ 154)) + (|getShellEntry| $ 174)) + (|getShellEntry| $ 184)) |POLYCAT-;charthRoot;SU;28|) (EXIT (COND ((QEQCAR |ans| 1) (CONS 1 "failed")) ('T (CONS 0 (SPADCALL (QCDR |ans|) - (|getShellEntry| $ 41)))))))) + (|getShellEntry| $ 51)))))))) ('T - (SEQ (LETT |ch| (SPADCALL (|getShellEntry| $ 141)) + (SEQ (LETT |ch| (|spadConstant| $ 168) |POLYCAT-;charthRoot;SU;28|) (EXIT (|POLYCAT-;charthRootlv| |p| |vars| |ch| $)))))))))) @@ -1287,15 +1287,15 @@ (SEQ (LETT |ans| (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 146)) - (|getShellEntry| $ 154)) + (|getShellEntry| $ 174)) + (|getShellEntry| $ 184)) |POLYCAT-;charthRootlv|) (EXIT (COND ((QEQCAR |ans| 1) (CONS 1 "failed")) ('T (CONS 0 (SPADCALL (QCDR |ans|) - (|getShellEntry| $ 41)))))))) + (|getShellEntry| $ 51)))))))) ('T (SEQ (LETT |v| (|SPADfirst| |vars|) |POLYCAT-;charthRootlv|) @@ -1303,14 +1303,14 @@ |POLYCAT-;charthRootlv|) (LETT |d| (SPADCALL |p| |v| - (|getShellEntry| $ 37)) + (|getShellEntry| $ 46)) |POLYCAT-;charthRootlv|) - (LETT |ans| (|spadConstant| $ 22) + (LETT |ans| (|spadConstant| $ 27) |POLYCAT-;charthRootlv|) (SEQ G190 (COND ((NULL (< 0 |d|)) (GO G191))) (SEQ (LETT |dd| (SPADCALL |d| |ch| - (|getShellEntry| $ 145)) + (|getShellEntry| $ 172)) |POLYCAT-;charthRootlv|) (EXIT (COND @@ -1323,13 +1323,13 @@ (SEQ (LETT |cp| (SPADCALL |p| |v| |d| - (|getShellEntry| $ 157)) + (|getShellEntry| $ 189)) |POLYCAT-;charthRootlv|) (LETT |p| (SPADCALL |p| (SPADCALL |cp| |v| |d| - (|getShellEntry| $ 38)) - (|getShellEntry| $ 158)) + (|getShellEntry| $ 47)) + (|getShellEntry| $ 190)) |POLYCAT-;charthRootlv|) (LETT |ansx| (|POLYCAT-;charthRootlv| |cp| @@ -1347,7 +1347,7 @@ (SEQ (LETT |d| (SPADCALL |p| |v| - (|getShellEntry| $ 37)) + (|getShellEntry| $ 46)) |POLYCAT-;charthRootlv|) (EXIT (LETT |ans| @@ -1363,8 +1363,8 @@ ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 38)) - (|getShellEntry| $ 152)) + (|getShellEntry| $ 47)) + (|getShellEntry| $ 182)) |POLYCAT-;charthRootlv|))))))))))) NIL (GO G190) G191 (EXIT NIL)) (LETT |ansx| @@ -1382,7 +1382,7 @@ (LETT #1# (CONS 0 (SPADCALL |ans| (QCDR |ansx|) - (|getShellEntry| $ 152))) + (|getShellEntry| $ 182))) |POLYCAT-;charthRootlv|) (GO #1#))))))))) #1# (EXIT #1#))))) @@ -1392,36 +1392,36 @@ (RETURN (SEQ (LETT |result| (SPADCALL - (SPADCALL |p1| |mvar| (|getShellEntry| $ 49)) - (SPADCALL |p2| |mvar| (|getShellEntry| $ 49)) - (|getShellEntry| $ 160)) + (SPADCALL |p1| |mvar| (|getShellEntry| $ 59)) + (SPADCALL |p2| |mvar| (|getShellEntry| $ 59)) + (|getShellEntry| $ 192)) |POLYCAT-;monicDivide;2SVarSetR;30|) (EXIT (CONS (SPADCALL (QCAR |result|) |mvar| - (|getShellEntry| $ 135)) + (|getShellEntry| $ 160)) (SPADCALL (QCDR |result|) |mvar| - (|getShellEntry| $ 135)))))))) + (|getShellEntry| $ 160)))))))) (DEFUN |POLYCAT-;squareFree;SF;31| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 163))) + (SPADCALL |p| (|getShellEntry| $ 195))) (DEFUN |POLYCAT-;squareFree;SF;32| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 166))) + (SPADCALL |p| (|getShellEntry| $ 198))) (DEFUN |POLYCAT-;squareFree;SF;33| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 166))) + (SPADCALL |p| (|getShellEntry| $ 198))) (DEFUN |POLYCAT-;squareFreePart;2S;34| (|p| $) (PROG (|s| |f| #0=#:G1733 #1=#:G1653 #2=#:G1651 #3=#:G1652) (RETURN (SEQ (SPADCALL (SPADCALL - (LETT |s| (SPADCALL |p| (|getShellEntry| $ 167)) + (LETT |s| (SPADCALL |p| (|getShellEntry| $ 199)) |POLYCAT-;squareFreePart;2S;34|) - (|getShellEntry| $ 168)) + (|getShellEntry| $ 200)) (PROGN (LETT #3# NIL |POLYCAT-;squareFreePart;2S;34|) (SEQ (LETT |f| NIL |POLYCAT-;squareFreePart;2S;34|) - (LETT #0# (SPADCALL |s| (|getShellEntry| $ 171)) + (LETT #0# (SPADCALL |s| (|getShellEntry| $ 203)) |POLYCAT-;squareFreePart;2S;34|) G190 (COND @@ -1438,7 +1438,7 @@ (#3# (LETT #2# (SPADCALL #2# #1# - (|getShellEntry| $ 151)) + (|getShellEntry| $ 181)) |POLYCAT-;squareFreePart;2S;34|)) ('T (PROGN @@ -1449,12 +1449,12 @@ (LETT #0# (CDR #0#) |POLYCAT-;squareFreePart;2S;34|) (GO G190) G191 (EXIT NIL)) - (COND (#3# #2#) ('T (|spadConstant| $ 34)))) - (|getShellEntry| $ 151)))))) + (COND (#3# #2#) ('T (|spadConstant| $ 43)))) + (|getShellEntry| $ 181)))))) (DEFUN |POLYCAT-;content;SVarSetS;35| (|p| |v| $) - (SPADCALL (SPADCALL |p| |v| (|getShellEntry| $ 49)) - (|getShellEntry| $ 173))) + (SPADCALL (SPADCALL |p| |v| (|getShellEntry| $ 59)) + (|getShellEntry| $ 205))) (DEFUN |POLYCAT-;primitivePart;2S;36| (|p| $) (PROG (#0=#:G1657) @@ -1463,13 +1463,13 @@ (PROG2 (LETT #0# (SPADCALL |p| (SPADCALL |p| - (|getShellEntry| $ 175)) - (|getShellEntry| $ 176)) + (|getShellEntry| $ 207)) + (|getShellEntry| $ 208)) |POLYCAT-;primitivePart;2S;36|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 6) #0#)) - (|getShellEntry| $ 178)) + (|getShellEntry| $ 210)) 1)))) (DEFUN |POLYCAT-;primitivePart;SVarSetS;37| (|p| |v| $) @@ -1479,51 +1479,51 @@ (PROG2 (LETT #0# (SPADCALL |p| (SPADCALL |p| |v| - (|getShellEntry| $ 180)) - (|getShellEntry| $ 181)) + (|getShellEntry| $ 212)) + (|getShellEntry| $ 213)) |POLYCAT-;primitivePart;SVarSetS;37|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 6) #0#)) - (|getShellEntry| $ 178)) + (|getShellEntry| $ 210)) 1)))) (DEFUN |POLYCAT-;<;2SB;38| (|p| |q| $) (PROG (|dp| |dq|) (RETURN - (SEQ (LETT |dp| (SPADCALL |p| (|getShellEntry| $ 61)) + (SEQ (LETT |dp| (SPADCALL |p| (|getShellEntry| $ 75)) |POLYCAT-;<;2SB;38|) - (LETT |dq| (SPADCALL |q| (|getShellEntry| $ 61)) + (LETT |dq| (SPADCALL |q| (|getShellEntry| $ 75)) |POLYCAT-;<;2SB;38|) (EXIT (COND - ((SPADCALL |dp| |dq| (|getShellEntry| $ 183)) - (SPADCALL (|spadConstant| $ 23) - (SPADCALL |q| (|getShellEntry| $ 39)) - (|getShellEntry| $ 184))) - ((SPADCALL |dq| |dp| (|getShellEntry| $ 183)) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 39)) - (|spadConstant| $ 23) (|getShellEntry| $ 184))) + ((SPADCALL |dp| |dq| (|getShellEntry| $ 215)) + (SPADCALL (|spadConstant| $ 28) + (SPADCALL |q| (|getShellEntry| $ 48)) + (|getShellEntry| $ 216))) + ((SPADCALL |dq| |dp| (|getShellEntry| $ 215)) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 48)) + (|spadConstant| $ 28) (|getShellEntry| $ 216))) ('T (SPADCALL (SPADCALL (SPADCALL |p| |q| - (|getShellEntry| $ 158)) - (|getShellEntry| $ 39)) - (|spadConstant| $ 23) (|getShellEntry| $ 184))))))))) + (|getShellEntry| $ 190)) + (|getShellEntry| $ 48)) + (|spadConstant| $ 28) (|getShellEntry| $ 216))))))))) (DEFUN |POLYCAT-;patternMatch;SP2Pmr;39| (|p| |pat| |l| $) - (SPADCALL |p| |pat| |l| (|getShellEntry| $ 189))) + (SPADCALL |p| |pat| |l| (|getShellEntry| $ 221))) (DEFUN |POLYCAT-;patternMatch;SP2Pmr;40| (|p| |pat| |l| $) - (SPADCALL |p| |pat| |l| (|getShellEntry| $ 196))) + (SPADCALL |p| |pat| |l| (|getShellEntry| $ 228))) (DEFUN |POLYCAT-;convert;SP;41| (|x| $) - (SPADCALL (ELT $ 199) (ELT $ 200) |x| (|getShellEntry| $ 204))) + (SPADCALL (ELT $ 231) (ELT $ 232) |x| (|getShellEntry| $ 236))) (DEFUN |POLYCAT-;convert;SP;42| (|x| $) - (SPADCALL (ELT $ 206) (ELT $ 207) |x| (|getShellEntry| $ 211))) + (SPADCALL (ELT $ 238) (ELT $ 239) |x| (|getShellEntry| $ 243))) (DEFUN |POLYCAT-;convert;SIf;43| (|p| $) - (SPADCALL (ELT $ 214) (ELT $ 215) |p| (|getShellEntry| $ 219))) + (SPADCALL (ELT $ 246) (ELT $ 247) |p| (|getShellEntry| $ 251))) (DEFUN |PolynomialCategory&| (|#1| |#2| |#3| |#4|) (PROG (|dv$1| |dv$2| |dv$3| |dv$4| |dv$| $ |pv$|) @@ -1535,7 +1535,7 @@ (LETT |dv$4| (|devaluate| |#4|) . #0#) (LETT |dv$| (LIST '|PolynomialCategory&| |dv$1| |dv$2| |dv$3| |dv$4|) . #0#) - (LETT $ (|newShell| 228) . #0#) + (LETT $ (|newShell| 260) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -1579,57 +1579,57 @@ (COND ((|testBitVector| |pv$| 4) (PROGN - (|setShellEntry| $ 76 + (|setShellEntry| $ 95 (CONS (|dispatchFunction| |POLYCAT-;resultant;2SVarSetS;15|) $)) - (|setShellEntry| $ 78 + (|setShellEntry| $ 97 (CONS (|dispatchFunction| |POLYCAT-;discriminant;SVarSetS;16|) $))))) (COND ((|HasCategory| |#2| '(|IntegralDomain|)) (PROGN - (|setShellEntry| $ 98 + (|setShellEntry| $ 120 (CONS (|dispatchFunction| |POLYCAT-;reducedSystem;MM;20|) $)) - (|setShellEntry| $ 105 + (|setShellEntry| $ 130 (CONS (|dispatchFunction| |POLYCAT-;reducedSystem;MVR;21|) $))))) (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 108 + (|setShellEntry| $ 133 (CONS (|dispatchFunction| |POLYCAT-;gcdPolynomial;3Sup;22|) $)) - (|setShellEntry| $ 115 + (|setShellEntry| $ 140 (CONS (|dispatchFunction| |POLYCAT-;solveLinearPolynomialEquation;LSupU;23|) $)) - (|setShellEntry| $ 119 + (|setShellEntry| $ 144 (CONS (|dispatchFunction| |POLYCAT-;factorPolynomial;SupF;24|) $)) - (|setShellEntry| $ 121 + (|setShellEntry| $ 146 (CONS (|dispatchFunction| |POLYCAT-;factorSquareFreePolynomial;SupF;25|) $)) - (|setShellEntry| $ 139 + (|setShellEntry| $ 164 (CONS (|dispatchFunction| |POLYCAT-;factor;SF;26|) $)) (COND ((|HasCategory| |#2| '(|CharacteristicNonZero|)) (PROGN - (|setShellEntry| $ 153 + (|setShellEntry| $ 183 (CONS (|dispatchFunction| |POLYCAT-;conditionP;MU;27|) $)))))))) (COND ((|HasCategory| |#2| '(|CharacteristicNonZero|)) (PROGN - (|setShellEntry| $ 155 + (|setShellEntry| $ 185 (CONS (|dispatchFunction| |POLYCAT-;charthRoot;SU;28|) $))))) (COND @@ -1639,46 +1639,46 @@ ((|HasCategory| |#2| '(|EuclideanDomain|)) (COND ((|HasCategory| |#2| '(|CharacteristicZero|)) - (|setShellEntry| $ 164 + (|setShellEntry| $ 196 (CONS (|dispatchFunction| |POLYCAT-;squareFree;SF;31|) $))) ('T - (|setShellEntry| $ 164 + (|setShellEntry| $ 196 (CONS (|dispatchFunction| |POLYCAT-;squareFree;SF;32|) $))))) ('T - (|setShellEntry| $ 164 + (|setShellEntry| $ 196 (CONS (|dispatchFunction| |POLYCAT-;squareFree;SF;33|) $)))) - (|setShellEntry| $ 172 + (|setShellEntry| $ 204 (CONS (|dispatchFunction| |POLYCAT-;squareFreePart;2S;34|) $)) - (|setShellEntry| $ 174 + (|setShellEntry| $ 206 (CONS (|dispatchFunction| |POLYCAT-;content;SVarSetS;35|) $)) - (|setShellEntry| $ 179 + (|setShellEntry| $ 211 (CONS (|dispatchFunction| |POLYCAT-;primitivePart;2S;36|) $)) - (|setShellEntry| $ 182 + (|setShellEntry| $ 214 (CONS (|dispatchFunction| |POLYCAT-;primitivePart;SVarSetS;37|) $))))) (COND ((|testBitVector| |pv$| 15) (PROGN - (|setShellEntry| $ 185 + (|setShellEntry| $ 217 (CONS (|dispatchFunction| |POLYCAT-;<;2SB;38|) $)) (COND ((|testBitVector| |pv$| 8) (COND ((|testBitVector| |pv$| 7) - (|setShellEntry| $ 191 + (|setShellEntry| $ 223 (CONS (|dispatchFunction| |POLYCAT-;patternMatch;SP2Pmr;39|) $)))))) @@ -1686,7 +1686,7 @@ ((|testBitVector| |pv$| 6) (COND ((|testBitVector| |pv$| 5) - (|setShellEntry| $ 198 + (|setShellEntry| $ 230 (CONS (|dispatchFunction| |POLYCAT-;patternMatch;SP2Pmr;40|) $))))))))) @@ -1694,205 +1694,229 @@ ((|testBitVector| |pv$| 12) (COND ((|testBitVector| |pv$| 11) - (|setShellEntry| $ 205 + (|setShellEntry| $ 237 (CONS (|dispatchFunction| |POLYCAT-;convert;SP;41|) $)))))) (COND ((|testBitVector| |pv$| 10) (COND ((|testBitVector| |pv$| 9) - (|setShellEntry| $ 212 + (|setShellEntry| $ 244 (CONS (|dispatchFunction| |POLYCAT-;convert;SP;42|) $)))))) (COND ((|testBitVector| |pv$| 14) (COND ((|testBitVector| |pv$| 13) - (|setShellEntry| $ 220 + (|setShellEntry| $ 252 (CONS (|dispatchFunction| |POLYCAT-;convert;SIf;43|) $)))))) $)))) (MAKEPROP '|PolynomialCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) - (|local| |#3|) (|local| |#4|) (|Equation| 6) (0 . |lhs|) - (|Union| 9 '"failed") (5 . |retractIfCan|) - (10 . |retract|) (15 . |rhs|) (|List| 9) (|List| $) - (20 . |eval|) (|Equation| $) (|List| 19) - |POLYCAT-;eval;SLS;1| (27 . |Zero|) (31 . |Zero|) - (|Boolean|) (35 . ~=) (41 . |leadingMonomial|) - (46 . |reductum|) |POLYCAT-;monomials;SL;2| - (51 . |monomials|) (|Union| 17 '"failed") - |POLYCAT-;isPlus;SU;3| (56 . |variables|) - (61 . |monomial?|) (66 . |One|) (70 . |One|) - (|NonNegativeInteger|) (74 . |degree|) (80 . |monomial|) - (87 . |leadingCoefficient|) (92 . |one?|) (97 . |coerce|) - |POLYCAT-;isTimes;SU;4| (102 . |mainVariable|) (107 . =) - (|Record| (|:| |var| 9) (|:| |exponent| 36)) - (|Union| 45 '"failed") |POLYCAT-;isExpt;SU;5| - (|SparseUnivariatePolynomial| $) (113 . |univariate|) - (|SparseUnivariatePolynomial| 6) (119 . |coefficient|) - |POLYCAT-;coefficient;SVarSetNniS;6| (|List| 36) - (125 . |coefficient|) |POLYCAT-;coefficient;SLLS;7| - (132 . |monomial|) |POLYCAT-;monomial;SLLS;8| - (139 . |coerce|) |POLYCAT-;retract;SVarSet;9| - |POLYCAT-;retractIfCan;SU;10| (144 . |degree|) - (149 . |monomial|) |POLYCAT-;primitiveMonomials;SL;12| - (155 . |ground?|) (160 . |Zero|) (164 . ~=) - (170 . |degree|) (175 . |leadingCoefficient|) - (180 . |totalDegree|) (185 . |reductum|) - |POLYCAT-;totalDegree;SNni;13| (190 . |member?|) - (196 . |totalDegree|) |POLYCAT-;totalDegree;SLNni;14| - (202 . |resultant|) (208 . |resultant|) - (215 . |discriminant|) (220 . |discriminant|) - (226 . |primitiveMonomials|) (|List| 6) (231 . |concat|) - (236 . |removeDuplicates!|) (|Vector| 7) (241 . |new|) - (|Integer|) (247 . |minIndex|) (252 . |coefficient|) - (258 . |qsetelt!|) (|List| 7) (|List| 89) (|Matrix| 7) - (265 . |matrix|) (|List| 80) (|Matrix| 6) - (270 . |listOfLists|) (275 . |vertConcat|) (|Matrix| $) - (281 . |reducedSystem|) (|Vector| 6) (286 . |entries|) - (291 . |concat|) (297 . |concat|) - (|Record| (|:| |mat| 91) (|:| |vec| 83)) (|Vector| $) - (303 . |reducedSystem|) + (|local| |#3|) (|local| |#4|) (|Boolean|) (|Equation| 6) + (|List| 11) (0 . |empty?|) (5 . |lhs|) + (|Union| 9 '"failed") (10 . |retractIfCan|) + (15 . |retract|) (20 . |rhs|) (|List| 9) (|List| $) + (25 . |eval|) (|Equation| $) (|List| 22) + |POLYCAT-;eval;SLS;1| (|List| 6) (32 . |empty|) + (36 . |Zero|) (40 . |Zero|) (44 . ~=) + (50 . |leadingMonomial|) (55 . |concat|) (61 . |reductum|) + (66 . |reverse|) |POLYCAT-;monomials;SL;2| + (71 . |monomials|) (76 . |rest|) (81 . |empty?|) + (|Union| 20 '"failed") |POLYCAT-;isPlus;SU;3| + (86 . |variables|) (91 . |empty?|) (96 . |monomial?|) + (101 . |One|) (105 . |One|) (|NonNegativeInteger|) + (109 . |degree|) (115 . |monomial|) + (122 . |leadingCoefficient|) (127 . |one?|) (132 . |rest|) + (137 . |coerce|) |POLYCAT-;isTimes;SU;4| + (142 . |mainVariable|) (147 . =) + (|Record| (|:| |var| 9) (|:| |exponent| 45)) + (|Union| 55 '"failed") |POLYCAT-;isExpt;SU;5| + (|SparseUnivariatePolynomial| $) (153 . |univariate|) + (|SparseUnivariatePolynomial| 6) (159 . |coefficient|) + |POLYCAT-;coefficient;SVarSetNniS;6| (|List| 45) + (165 . |empty?|) (170 . |first|) (175 . |first|) + (180 . |rest|) (185 . |coefficient|) + |POLYCAT-;coefficient;SLLS;7| (192 . |monomial|) + |POLYCAT-;monomial;SLLS;8| (199 . |coerce|) + |POLYCAT-;retract;SVarSet;9| |POLYCAT-;retractIfCan;SU;10| + (204 . |degree|) (209 . |monomial|) + |POLYCAT-;primitiveMonomials;SL;12| (215 . |ground?|) + (220 . |Zero|) (224 . |Zero|) (228 . ~=) (234 . |degree|) + (239 . |leadingCoefficient|) (244 . |totalDegree|) + (249 . +) (255 . |max|) (261 . |reductum|) + |POLYCAT-;totalDegree;SNni;13| (266 . |member?|) + (272 . |One|) (276 . *) (282 . |totalDegree|) + |POLYCAT-;totalDegree;SLNni;14| (288 . |resultant|) + (294 . |resultant|) (301 . |discriminant|) + (306 . |discriminant|) (312 . |primitiveMonomials|) + (317 . |concat|) (322 . |removeDuplicates!|) (|Vector| 7) + (327 . |new|) (|Integer|) (333 . |minIndex|) + (338 . |maxIndex|) (343 . |coefficient|) + (349 . |qsetelt!|) (|List| 7) (|List| 108) (|Matrix| 7) + (356 . |matrix|) (|List| 25) (|Matrix| 6) + (361 . |listOfLists|) (366 . |first|) (371 . |rest|) + (376 . |empty?|) (381 . |vertConcat|) (|Matrix| $) + (387 . |reducedSystem|) (|Vector| 6) (392 . |entries|) + (397 . |concat|) (|List| 8) (403 . |#|) (408 . |first|) + (413 . |concat|) + (|Record| (|:| |mat| 110) (|:| |vec| 101)) (|Vector| $) + (419 . |reducedSystem|) (|GeneralPolynomialGcdPackage| 8 9 7 6) - (309 . |gcdPolynomial|) (315 . |gcdPolynomial|) - (|List| 50) (|Union| 109 '"failed") + (425 . |gcdPolynomial|) (431 . |gcdPolynomial|) + (|List| 60) (|Union| 134 '"failed") (|PolynomialFactorizationByRecursion| 7 8 9 6) - (321 . |solveLinearPolynomialEquationByRecursion|) - (|List| 48) (|Union| 113 '"failed") - (327 . |solveLinearPolynomialEquation|) (|Factored| 50) - (333 . |factorByRecursion|) (|Factored| 48) - (338 . |factorPolynomial|) - (343 . |factorSquareFreeByRecursion|) - (348 . |factorSquareFreePolynomial|) (|Factored| $) - (353 . |factor|) (|Factored| 7) (358 . |unit|) + (437 . |solveLinearPolynomialEquationByRecursion|) + (|List| 58) (|Union| 138 '"failed") + (443 . |solveLinearPolynomialEquation|) (|Factored| 60) + (449 . |factorByRecursion|) (|Factored| 58) + (454 . |factorPolynomial|) + (459 . |factorSquareFreeByRecursion|) + (464 . |factorSquareFreePolynomial|) (|Factored| $) + (469 . |factor|) (|Factored| 7) (474 . |unit|) (|Union| '"nil" '"sqfr" '"irred" '"prime") - (|Record| (|:| |flg| 126) (|:| |fctr| 7) (|:| |xpnt| 85)) - (|List| 127) (363 . |factorList|) - (|Record| (|:| |flg| 126) (|:| |fctr| 6) (|:| |xpnt| 85)) - (|List| 130) (|Factored| 6) (368 . |makeFR|) - (374 . |unit|) (379 . |multivariate|) - (|Record| (|:| |flg| 126) (|:| |fctr| 50) (|:| |xpnt| 85)) - (|List| 136) (385 . |factorList|) (390 . |factor|) - (395 . |transpose|) (400 . |characteristic|) - (404 . |setUnion|) (410 . |degree|) (|Union| $ '"failed") - (416 . |exquo|) (422 . |ground|) (427 . |transpose|) - (|Union| 104 '"failed") (432 . |conditionP|) (437 . |elt|) - (443 . *) (449 . +) (455 . |conditionP|) - (460 . |charthRoot|) (465 . |charthRoot|) (470 . |Zero|) - (474 . |coefficient|) (481 . -) + (|Record| (|:| |flg| 151) (|:| |fctr| 7) (|:| |xpnt| 103)) + (|List| 152) (479 . |factorList|) + (|Record| (|:| |flg| 151) (|:| |fctr| 6) (|:| |xpnt| 103)) + (|List| 155) (|Factored| 6) (484 . |makeFR|) + (490 . |unit|) (495 . |multivariate|) + (|Record| (|:| |flg| 151) (|:| |fctr| 60) + (|:| |xpnt| 103)) + (|List| 161) (501 . |factorList|) (506 . |factor|) + (511 . |transpose|) (516 . |empty|) (520 . |empty|) + (524 . |characteristic|) (528 . |setUnion|) + (534 . |degree|) (|Union| $ '"failed") (540 . |exquo|) + (546 . |cons|) (552 . |ground|) (557 . |cons|) + (563 . |cons|) (569 . |transpose|) (|Union| 129 '"failed") + (574 . |conditionP|) (579 . |elt|) (585 . *) (591 . +) + (597 . |conditionP|) (602 . |charthRoot|) + (607 . |charthRoot|) (612 . |Zero|) (616 . |Zero|) + (620 . <) (626 . |coefficient|) (633 . -) (|Record| (|:| |quotient| $) (|:| |remainder| $)) - (487 . |monicDivide|) |POLYCAT-;monicDivide;2SVarSetR;30| - (|MultivariateSquareFree| 8 9 7 6) (493 . |squareFree|) - (498 . |squareFree|) (|PolynomialSquareFree| 9 8 7 6) - (503 . |squareFree|) (508 . |squareFree|) (513 . |unit|) - (|Record| (|:| |factor| 6) (|:| |exponent| 85)) - (|List| 169) (518 . |factors|) (523 . |squareFreePart|) - (528 . |content|) (533 . |content|) (539 . |content|) - (544 . |exquo|) + (639 . |monicDivide|) |POLYCAT-;monicDivide;2SVarSetR;30| + (|MultivariateSquareFree| 8 9 7 6) (645 . |squareFree|) + (650 . |squareFree|) (|PolynomialSquareFree| 9 8 7 6) + (655 . |squareFree|) (660 . |squareFree|) (665 . |unit|) + (|Record| (|:| |factor| 6) (|:| |exponent| 103)) + (|List| 201) (670 . |factors|) (675 . |squareFreePart|) + (680 . |content|) (685 . |content|) (691 . |content|) + (696 . |exquo|) (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) - (550 . |unitNormal|) (555 . |primitivePart|) - (560 . |content|) (566 . |exquo|) (572 . |primitivePart|) - (578 . <) (584 . <) (590 . <) (|PatternMatchResult| 85 6) - (|Pattern| 85) - (|PatternMatchPolynomialCategory| 85 8 9 7 6) - (596 . |patternMatch|) (|PatternMatchResult| 85 $) - (603 . |patternMatch|) (|Float|) - (|PatternMatchResult| 192 6) (|Pattern| 192) - (|PatternMatchPolynomialCategory| 192 8 9 7 6) - (610 . |patternMatch|) (|PatternMatchResult| 192 $) - (617 . |patternMatch|) (624 . |convert|) (629 . |convert|) - (|Mapping| 187 9) (|Mapping| 187 7) - (|PolynomialCategoryLifting| 8 9 7 6 187) (634 . |map|) - (641 . |convert|) (646 . |convert|) (651 . |convert|) - (|Mapping| 194 9) (|Mapping| 194 7) - (|PolynomialCategoryLifting| 8 9 7 6 194) (656 . |map|) - (663 . |convert|) (|InputForm|) (668 . |convert|) - (673 . |convert|) (|Mapping| 213 9) (|Mapping| 213 7) - (|PolynomialCategoryLifting| 8 9 7 6 213) (678 . |map|) - (685 . |convert|) (|Matrix| 85) (|Vector| 85) - (|Record| (|:| |mat| 221) (|:| |vec| 222)) - (|Union| 85 '"failed") (|Fraction| 85) - (|Union| 225 '"failed") (|Union| 7 '"failed")) - '#(|totalDegree| 690 |squareFreePart| 701 |squareFree| 706 - |solveLinearPolynomialEquation| 711 |retractIfCan| 717 - |retract| 722 |resultant| 727 |reducedSystem| 734 - |primitivePart| 745 |primitiveMonomials| 756 - |patternMatch| 761 |monomials| 775 |monomial| 780 - |monicDivide| 787 |isTimes| 794 |isPlus| 799 |isExpt| 804 - |gcdPolynomial| 809 |factorSquareFreePolynomial| 815 - |factorPolynomial| 820 |factor| 825 |eval| 830 - |discriminant| 836 |convert| 842 |content| 857 - |conditionP| 863 |coefficient| 868 |charthRoot| 882 < 887) + (702 . |unitNormal|) (707 . |primitivePart|) + (712 . |content|) (718 . |exquo|) (724 . |primitivePart|) + (730 . <) (736 . <) (742 . <) (|PatternMatchResult| 103 6) + (|Pattern| 103) + (|PatternMatchPolynomialCategory| 103 8 9 7 6) + (748 . |patternMatch|) (|PatternMatchResult| 103 $) + (755 . |patternMatch|) (|Float|) + (|PatternMatchResult| 224 6) (|Pattern| 224) + (|PatternMatchPolynomialCategory| 224 8 9 7 6) + (762 . |patternMatch|) (|PatternMatchResult| 224 $) + (769 . |patternMatch|) (776 . |convert|) (781 . |convert|) + (|Mapping| 219 9) (|Mapping| 219 7) + (|PolynomialCategoryLifting| 8 9 7 6 219) (786 . |map|) + (793 . |convert|) (798 . |convert|) (803 . |convert|) + (|Mapping| 226 9) (|Mapping| 226 7) + (|PolynomialCategoryLifting| 8 9 7 6 226) (808 . |map|) + (815 . |convert|) (|InputForm|) (820 . |convert|) + (825 . |convert|) (|Mapping| 245 9) (|Mapping| 245 7) + (|PolynomialCategoryLifting| 8 9 7 6 245) (830 . |map|) + (837 . |convert|) (|Matrix| 103) (|Vector| 103) + (|Record| (|:| |mat| 253) (|:| |vec| 254)) + (|Union| 103 '"failed") (|Fraction| 103) + (|Union| 257 '"failed") (|Union| 7 '"failed")) + '#(|totalDegree| 842 |squareFreePart| 853 |squareFree| 858 + |solveLinearPolynomialEquation| 863 |retractIfCan| 869 + |retract| 874 |resultant| 879 |reducedSystem| 886 + |primitivePart| 897 |primitiveMonomials| 908 + |patternMatch| 913 |monomials| 927 |monomial| 932 + |monicDivide| 939 |isTimes| 946 |isPlus| 951 |isExpt| 956 + |gcdPolynomial| 961 |factorSquareFreePolynomial| 967 + |factorPolynomial| 972 |factor| 977 |eval| 982 + |discriminant| 988 |convert| 994 |content| 1009 + |conditionP| 1015 |coefficient| 1020 |charthRoot| 1034 < + 1039) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 220 - '(1 10 6 0 11 1 6 12 0 13 1 6 9 0 14 1 - 10 6 0 15 3 6 0 0 16 17 18 0 6 0 22 0 - 7 0 23 2 6 24 0 0 25 1 6 0 0 26 1 6 0 - 0 27 1 6 17 0 29 1 6 16 0 32 1 6 24 0 - 33 0 6 0 34 0 7 0 35 2 6 36 0 9 37 3 - 6 0 0 9 36 38 1 6 7 0 39 1 7 24 0 40 - 1 6 0 7 41 1 6 12 0 43 2 6 24 0 0 44 - 2 6 48 0 9 49 2 50 6 0 36 51 3 6 0 0 - 16 53 54 3 6 0 0 16 53 56 1 6 0 9 58 - 1 6 8 0 61 2 6 0 7 8 62 1 6 24 0 64 0 - 50 0 65 2 50 24 0 0 66 1 50 36 0 67 1 - 50 6 0 68 1 6 36 0 69 1 50 0 0 70 2 - 16 24 9 0 72 2 6 36 0 16 73 2 50 6 0 - 0 75 3 0 0 0 0 9 76 1 50 6 0 77 2 0 0 - 0 9 78 1 6 17 0 79 1 80 0 17 81 1 80 - 0 0 82 2 83 0 36 7 84 1 83 85 0 86 2 - 6 7 0 8 87 3 83 7 0 85 7 88 1 91 0 90 - 92 1 94 93 0 95 2 91 0 0 0 96 1 0 91 - 97 98 1 99 80 0 100 2 80 0 0 0 101 2 - 83 0 0 0 102 2 0 103 97 104 105 2 106 - 50 50 50 107 2 0 48 48 48 108 2 111 - 110 109 50 112 2 0 114 113 48 115 1 - 111 116 50 117 1 0 118 48 119 1 111 - 116 50 120 1 0 118 48 121 1 7 122 0 - 123 1 124 7 0 125 1 124 128 0 129 2 - 132 0 6 131 133 1 116 50 0 134 2 6 0 - 48 9 135 1 116 137 0 138 1 0 122 0 - 139 1 94 0 0 140 0 6 36 141 2 80 0 0 - 0 142 2 6 53 0 16 143 2 85 144 0 0 - 145 1 6 7 0 146 1 91 0 0 147 1 7 148 - 97 149 2 83 7 0 85 150 2 6 0 0 0 151 - 2 6 0 0 0 152 1 0 148 97 153 1 7 144 - 0 154 1 0 144 0 155 0 8 0 156 3 6 0 0 - 9 36 157 2 6 0 0 0 158 2 50 159 0 0 - 160 1 162 132 6 163 1 0 122 0 164 1 - 165 132 6 166 1 6 122 0 167 1 132 6 0 - 168 1 132 170 0 171 1 0 0 0 172 1 50 - 6 0 173 2 0 0 0 9 174 1 6 7 0 175 2 6 - 144 0 7 176 1 6 177 0 178 1 0 0 0 179 - 2 6 0 0 9 180 2 6 144 0 0 181 2 0 0 0 - 9 182 2 8 24 0 0 183 2 7 24 0 0 184 2 - 0 24 0 0 185 3 188 186 6 187 186 189 - 3 0 190 0 187 190 191 3 195 193 6 194 - 193 196 3 0 197 0 194 197 198 1 9 187 - 0 199 1 7 187 0 200 3 203 187 201 202 - 6 204 1 0 187 0 205 1 9 194 0 206 1 7 - 194 0 207 3 210 194 208 209 6 211 1 0 - 194 0 212 1 9 213 0 214 1 7 213 0 215 - 3 218 213 216 217 6 219 1 0 213 0 220 - 2 0 36 0 16 74 1 0 36 0 71 1 0 0 0 - 172 1 0 122 0 164 2 0 114 113 48 115 - 1 0 12 0 60 1 0 9 0 59 3 0 0 0 0 9 76 - 1 0 91 97 98 2 0 103 97 104 105 2 0 0 - 0 9 182 1 0 0 0 179 1 0 17 0 63 3 0 - 190 0 187 190 191 3 0 197 0 194 197 - 198 1 0 17 0 28 3 0 0 0 16 53 57 3 0 - 159 0 0 9 161 1 0 30 0 42 1 0 30 0 31 - 1 0 46 0 47 2 0 48 48 48 108 1 0 118 - 48 121 1 0 118 48 119 1 0 122 0 139 2 - 0 0 0 20 21 2 0 0 0 9 78 1 0 213 0 - 220 1 0 187 0 205 1 0 194 0 212 2 0 0 - 0 9 174 1 0 148 97 153 3 0 0 0 16 53 - 55 3 0 0 0 9 36 52 1 0 144 0 155 2 0 - 24 0 0 185))))) + (|makeByteWordVec2| 252 + '(1 12 10 0 13 1 11 6 0 14 1 6 15 0 16 + 1 6 9 0 17 1 11 6 0 18 3 6 0 0 19 20 + 21 0 25 0 26 0 6 0 27 0 7 0 28 2 6 10 + 0 0 29 1 6 0 0 30 2 25 0 6 0 31 1 6 0 + 0 32 1 25 0 0 33 1 6 20 0 35 1 25 0 0 + 36 1 25 10 0 37 1 6 19 0 40 1 19 10 0 + 41 1 6 10 0 42 0 6 0 43 0 7 0 44 2 6 + 45 0 9 46 3 6 0 0 9 45 47 1 6 7 0 48 + 1 7 10 0 49 1 19 0 0 50 1 6 0 7 51 1 + 6 15 0 53 2 6 10 0 0 54 2 6 58 0 9 59 + 2 60 6 0 45 61 1 63 10 0 64 1 19 9 0 + 65 1 63 45 0 66 1 63 0 0 67 3 6 0 0 + 19 63 68 3 6 0 0 19 63 70 1 6 0 9 72 + 1 6 8 0 75 2 6 0 7 8 76 1 6 10 0 78 0 + 45 0 79 0 60 0 80 2 60 10 0 0 81 1 60 + 45 0 82 1 60 6 0 83 1 6 45 0 84 2 45 + 0 0 0 85 2 45 0 0 0 86 1 60 0 0 87 2 + 19 10 9 0 89 0 45 0 90 2 45 0 45 0 91 + 2 6 45 0 19 92 2 60 6 0 0 94 3 0 0 0 + 0 9 95 1 60 6 0 96 2 0 0 0 9 97 1 6 + 20 0 98 1 25 0 20 99 1 25 0 0 100 2 + 101 0 45 7 102 1 101 103 0 104 1 101 + 103 0 105 2 6 7 0 8 106 3 101 7 0 103 + 7 107 1 110 0 109 111 1 113 112 0 114 + 1 112 25 0 115 1 112 0 0 116 1 112 10 + 0 117 2 110 0 0 0 118 1 0 110 119 120 + 1 121 25 0 122 2 25 0 0 0 123 1 124 + 45 0 125 1 25 6 0 126 2 101 0 0 0 127 + 2 0 128 119 129 130 2 131 60 60 60 + 132 2 0 58 58 58 133 2 136 135 134 60 + 137 2 0 139 138 58 140 1 136 141 60 + 142 1 0 143 58 144 1 136 141 60 145 1 + 0 143 58 146 1 7 147 0 148 1 149 7 0 + 150 1 149 153 0 154 2 157 0 6 156 158 + 1 141 60 0 159 2 6 0 58 9 160 1 141 + 162 0 163 1 0 147 0 164 1 113 0 0 165 + 0 108 0 166 0 112 0 167 0 6 45 168 2 + 25 0 0 0 169 2 6 63 0 19 170 2 103 + 171 0 0 172 2 25 0 6 0 173 1 6 7 0 + 174 2 108 0 7 0 175 2 112 0 25 0 176 + 1 110 0 0 177 1 7 178 119 179 2 101 7 + 0 103 180 2 6 0 0 0 181 2 6 0 0 0 182 + 1 0 178 119 183 1 7 171 0 184 1 0 171 + 0 185 0 8 0 186 0 103 0 187 2 45 10 0 + 0 188 3 6 0 0 9 45 189 2 6 0 0 0 190 + 2 60 191 0 0 192 1 194 157 6 195 1 0 + 147 0 196 1 197 157 6 198 1 6 147 0 + 199 1 157 6 0 200 1 157 202 0 203 1 0 + 0 0 204 1 60 6 0 205 2 0 0 0 9 206 1 + 6 7 0 207 2 6 171 0 7 208 1 6 209 0 + 210 1 0 0 0 211 2 6 0 0 9 212 2 6 171 + 0 0 213 2 0 0 0 9 214 2 8 10 0 0 215 + 2 7 10 0 0 216 2 0 10 0 0 217 3 220 + 218 6 219 218 221 3 0 222 0 219 222 + 223 3 227 225 6 226 225 228 3 0 229 0 + 226 229 230 1 9 219 0 231 1 7 219 0 + 232 3 235 219 233 234 6 236 1 0 219 0 + 237 1 9 226 0 238 1 7 226 0 239 3 242 + 226 240 241 6 243 1 0 226 0 244 1 9 + 245 0 246 1 7 245 0 247 3 250 245 248 + 249 6 251 1 0 245 0 252 2 0 45 0 19 + 93 1 0 45 0 88 1 0 0 0 204 1 0 147 0 + 196 2 0 139 138 58 140 1 0 15 0 74 1 + 0 9 0 73 3 0 0 0 0 9 95 1 0 110 119 + 120 2 0 128 119 129 130 2 0 0 0 9 214 + 1 0 0 0 211 1 0 20 0 77 3 0 222 0 219 + 222 223 3 0 229 0 226 229 230 1 0 20 + 0 34 3 0 0 0 19 63 71 3 0 191 0 0 9 + 193 1 0 38 0 52 1 0 38 0 39 1 0 56 0 + 57 2 0 58 58 58 133 1 0 143 58 146 1 + 0 143 58 144 1 0 147 0 164 2 0 0 0 23 + 24 2 0 0 0 9 97 1 0 245 0 252 1 0 219 + 0 237 1 0 226 0 244 2 0 0 0 9 206 1 0 + 178 119 183 3 0 0 0 19 63 69 3 0 0 0 + 9 45 62 1 0 171 0 185 2 0 10 0 0 217))))) '|lookupComplete|)) diff --git a/src/algebra/strap/PRIMARR.lsp b/src/algebra/strap/PRIMARR.lsp index d27b7682..6c5d17a6 100644 --- a/src/algebra/strap/PRIMARR.lsp +++ b/src/algebra/strap/PRIMARR.lsp @@ -115,7 +115,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|PrimitiveArray|)) (LETT |dv$| (LIST '|PrimitiveArray| |dv$1|) . #0#) - (LETT $ (|newShell| 35) . #0#) + (LETT $ (|newShell| 38) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -159,28 +159,28 @@ (MAKEPROP '|PrimitiveArray| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|NonNegativeInteger|) |PRIMARR;#;$Nni;1| (|Integer|) - |PRIMARR;minIndex;$I;2| |PRIMARR;empty;$;3| + (0 . |Zero|) |PRIMARR;minIndex;$I;2| |PRIMARR;empty;$;3| |PRIMARR;new;NniS$;4| |PRIMARR;qelt;$IS;5| |PRIMARR;elt;$IS;6| |PRIMARR;qsetelt!;$I2S;7| - |PRIMARR;setelt;$I2S;8| |PRIMARR;fill!;$S$;9| - (|Mapping| 6 6 6) (|Boolean|) (|List| 6) (|Equation| 6) - (|List| 21) (|Mapping| 19 6) (|Mapping| 19 6 6) - (|UniversalSegment| 9) (|Void|) (|Mapping| 6 6) - (|OutputForm|) (|InputForm|) (|String|) (|SingleInteger|) - (|List| $) (|Union| 6 '"failed") (|List| 9)) - '#(~= 0 |swap!| 6 |sorted?| 13 |sort!| 24 |sort| 35 |size?| - 46 |setelt| 52 |select| 66 |sample| 72 |reverse!| 76 - |reverse| 81 |removeDuplicates| 86 |remove| 91 |reduce| - 103 |qsetelt!| 124 |qelt| 131 |position| 137 |parts| 156 - |new| 161 |more?| 167 |minIndex| 173 |min| 178 |merge| 184 - |members| 197 |member?| 202 |maxIndex| 208 |max| 213 - |map!| 219 |map| 225 |less?| 238 |latex| 244 |insert| 249 - |indices| 263 |index?| 268 |hash| 274 |first| 279 |find| - 284 |fill!| 290 |every?| 296 |eval| 302 |eq?| 328 |entry?| - 334 |entries| 340 |empty?| 345 |empty| 350 |elt| 354 - |delete| 373 |count| 385 |copyInto!| 397 |copy| 404 - |convert| 409 |construct| 414 |concat| 419 |coerce| 442 - |any?| 447 >= 453 > 459 = 465 <= 471 < 477 |#| 483) + |PRIMARR;setelt;$I2S;8| (|SingleInteger|) (4 . |Zero|) + (8 . |Zero|) |PRIMARR;fill!;$S$;9| (|Mapping| 6 6 6) + (|Boolean|) (|List| 6) (|Equation| 6) (|List| 25) + (|Mapping| 23 6) (|Mapping| 23 6 6) (|UniversalSegment| 9) + (|Void|) (|Mapping| 6 6) (|OutputForm|) (|InputForm|) + (|String|) (|List| $) (|Union| 6 '"failed") (|List| 9)) + '#(~= 12 |swap!| 18 |sorted?| 25 |sort!| 36 |sort| 47 |size?| + 58 |setelt| 64 |select| 78 |sample| 84 |reverse!| 88 + |reverse| 93 |removeDuplicates| 98 |remove| 103 |reduce| + 115 |qsetelt!| 136 |qelt| 143 |position| 149 |parts| 168 + |new| 173 |more?| 179 |minIndex| 185 |min| 190 |merge| 196 + |members| 209 |member?| 214 |maxIndex| 220 |max| 225 + |map!| 231 |map| 237 |less?| 250 |latex| 256 |insert| 261 + |indices| 275 |index?| 280 |hash| 286 |first| 291 |find| + 296 |fill!| 302 |every?| 308 |eval| 314 |eq?| 340 |entry?| + 346 |entries| 352 |empty?| 357 |empty| 362 |elt| 366 + |delete| 385 |count| 397 |copyInto!| 409 |copy| 416 + |convert| 421 |construct| 426 |concat| 431 |coerce| 454 + |any?| 459 >= 465 > 471 = 477 <= 483 < 489 |#| 495) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 5 '(0 0 0 0 0 0 5 0 0 1 4 0 0 1 2 3 4)) @@ -200,36 +200,36 @@ (|OrderedSet|) (|Aggregate|) (|EltableAggregate| 9 6) (|Evalable| 6) (|SetCategory|) (|Type|) (|Eltable| 9 6) - (|InnerEvalable| 6 6) (|CoercibleTo| 28) - (|ConvertibleTo| 29) (|BasicType|)) - (|makeByteWordVec2| 34 - '(2 7 19 0 0 1 3 0 26 0 9 9 1 1 5 19 0 - 1 2 0 19 24 0 1 1 5 0 0 1 2 0 0 24 0 - 1 1 5 0 0 1 2 0 0 24 0 1 2 0 19 0 7 1 - 3 0 6 0 25 6 1 3 0 6 0 9 6 16 2 0 0 - 23 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 - 7 0 0 1 2 7 0 6 0 1 2 0 0 23 0 1 4 7 - 6 18 0 6 6 1 3 0 6 18 0 6 1 2 0 6 18 - 0 1 3 0 6 0 9 6 15 2 0 6 0 9 13 2 7 9 - 6 0 1 3 7 9 6 0 9 1 2 0 9 23 0 1 1 0 - 20 0 1 2 0 0 7 6 12 2 0 19 0 7 1 1 6 - 9 0 10 2 5 0 0 0 1 2 5 0 0 0 1 3 0 0 - 24 0 0 1 1 0 20 0 1 2 7 19 6 0 1 1 6 - 9 0 1 2 5 0 0 0 1 2 0 0 27 0 1 3 0 0 - 18 0 0 1 2 0 0 27 0 1 2 0 19 0 7 1 1 - 7 30 0 1 3 0 0 0 0 9 1 3 0 0 6 0 9 1 - 1 0 34 0 1 2 0 19 9 0 1 1 7 31 0 1 1 - 6 6 0 1 2 0 33 23 0 1 2 0 0 0 6 17 2 - 0 19 23 0 1 3 9 0 0 20 20 1 2 9 0 0 - 21 1 3 9 0 0 6 6 1 2 9 0 0 22 1 2 0 - 19 0 0 1 2 7 19 6 0 1 1 0 20 0 1 1 0 - 19 0 1 0 0 0 11 2 0 0 0 25 1 2 0 6 0 - 9 14 3 0 6 0 9 6 1 2 0 0 0 9 1 2 0 0 - 0 25 1 2 7 7 6 0 1 2 0 7 23 0 1 3 0 0 - 0 0 9 1 1 0 0 0 1 1 3 29 0 1 1 0 0 20 - 1 1 0 0 32 1 2 0 0 6 0 1 2 0 0 0 0 1 - 2 0 0 0 6 1 1 8 28 0 1 2 0 19 23 0 1 - 2 5 19 0 0 1 2 5 19 0 0 1 2 7 19 0 0 - 1 2 5 19 0 0 1 2 5 19 0 0 1 1 0 7 0 - 8))))) + (|InnerEvalable| 6 6) (|CoercibleTo| 32) + (|ConvertibleTo| 33) (|BasicType|)) + (|makeByteWordVec2| 37 + '(0 9 0 10 0 18 0 19 0 7 0 20 2 7 23 0 + 0 1 3 0 30 0 9 9 1 1 5 23 0 1 2 0 23 + 28 0 1 1 5 0 0 1 2 0 0 28 0 1 1 5 0 0 + 1 2 0 0 28 0 1 2 0 23 0 7 1 3 0 6 0 + 29 6 1 3 0 6 0 9 6 17 2 0 0 27 0 1 0 + 0 0 1 1 0 0 0 1 1 0 0 0 1 1 7 0 0 1 2 + 7 0 6 0 1 2 0 0 27 0 1 4 7 6 22 0 6 6 + 1 3 0 6 22 0 6 1 2 0 6 22 0 1 3 0 6 0 + 9 6 16 2 0 6 0 9 14 2 7 9 6 0 1 3 7 9 + 6 0 9 1 2 0 9 27 0 1 1 0 24 0 1 2 0 0 + 7 6 13 2 0 23 0 7 1 1 6 9 0 11 2 5 0 + 0 0 1 2 5 0 0 0 1 3 0 0 28 0 0 1 1 0 + 24 0 1 2 7 23 6 0 1 1 6 9 0 1 2 5 0 0 + 0 1 2 0 0 31 0 1 3 0 0 22 0 0 1 2 0 0 + 31 0 1 2 0 23 0 7 1 1 7 34 0 1 3 0 0 + 0 0 9 1 3 0 0 6 0 9 1 1 0 37 0 1 2 0 + 23 9 0 1 1 7 18 0 1 1 6 6 0 1 2 0 36 + 27 0 1 2 0 0 0 6 21 2 0 23 27 0 1 3 9 + 0 0 24 24 1 2 9 0 0 25 1 3 9 0 0 6 6 + 1 2 9 0 0 26 1 2 0 23 0 0 1 2 7 23 6 + 0 1 1 0 24 0 1 1 0 23 0 1 0 0 0 12 2 + 0 0 0 29 1 2 0 6 0 9 15 3 0 6 0 9 6 1 + 2 0 0 0 9 1 2 0 0 0 29 1 2 7 7 6 0 1 + 2 0 7 27 0 1 3 0 0 0 0 9 1 1 0 0 0 1 + 1 3 33 0 1 1 0 0 24 1 1 0 0 35 1 2 0 + 0 6 0 1 2 0 0 0 0 1 2 0 0 0 6 1 1 8 + 32 0 1 2 0 23 27 0 1 2 5 23 0 0 1 2 5 + 23 0 0 1 2 7 23 0 0 1 2 5 23 0 0 1 2 + 5 23 0 0 1 1 0 7 0 8))))) '|lookupComplete|)) diff --git a/src/algebra/strap/PSETCAT-.lsp b/src/algebra/strap/PSETCAT-.lsp index 63efb140..0168ae69 100644 --- a/src/algebra/strap/PSETCAT-.lsp +++ b/src/algebra/strap/PSETCAT-.lsp @@ -173,7 +173,7 @@ (NOT (SPADCALL (SPADCALL (|SPADfirst| |lp|) (|getShellEntry| $ 22)) - |v| (|getShellEntry| $ 28)))))) + |v| (|getShellEntry| $ 31)))))) (GO G191))) (SEQ (EXIT (LETT |lp| (CDR |lp|) |PSETCAT-;mainVariable?;VarSetSB;6|))) @@ -200,7 +200,7 @@ (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collectUnder;SVarSetS;7|))))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |lq| (|getShellEntry| $ 30))))))) + (EXIT (SPADCALL |lq| (|getShellEntry| $ 35))))))) (DEFUN |PSETCAT-;collectUpper;SVarSetS;8| (|ps| |v| $) (PROG (|p| |lp| |lq|) @@ -224,7 +224,7 @@ (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collectUpper;SVarSetS;8|))))))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |lq| (|getShellEntry| $ 30))))))) + (EXIT (SPADCALL |lq| (|getShellEntry| $ 35))))))) (DEFUN |PSETCAT-;collect;SVarSetS;9| (|ps| |v| $) (PROG (|p| |lp| |lq|) @@ -244,11 +244,11 @@ ((SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) - |v| (|getShellEntry| $ 28)) + |v| (|getShellEntry| $ 31)) (LETT |lq| (CONS |p| |lq|) |PSETCAT-;collect;SVarSetS;9|))))))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |lq| (|getShellEntry| $ 30))))))) + (EXIT (SPADCALL |lq| (|getShellEntry| $ 35))))))) (DEFUN |PSETCAT-;sort;SVarSetR;10| (|ps| |v| $) (PROG (|p| |lp| |us| |vs| |ws|) @@ -272,16 +272,16 @@ |PSETCAT-;sort;SVarSetR;10|)) ((SPADCALL (SPADCALL |p| (|getShellEntry| $ 22)) - |v| (|getShellEntry| $ 28)) + |v| (|getShellEntry| $ 31)) (LETT |vs| (CONS |p| |vs|) |PSETCAT-;sort;SVarSetR;10|)) ('T (LETT |ws| (CONS |p| |ws|) |PSETCAT-;sort;SVarSetR;10|))))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (VECTOR (SPADCALL |us| (|getShellEntry| $ 30)) - (SPADCALL |vs| (|getShellEntry| $ 30)) - (SPADCALL |ws| (|getShellEntry| $ 30)))))))) + (EXIT (VECTOR (SPADCALL |us| (|getShellEntry| $ 35)) + (SPADCALL |vs| (|getShellEntry| $ 35)) + (SPADCALL |ws| (|getShellEntry| $ 35)))))))) (DEFUN |PSETCAT-;=;2SB;11| (|ps1| |ps2| $) (PROG (#0=#:G1564 #1=#:G1565 #2=#:G1566 |p| #3=#:G1567) @@ -305,7 +305,7 @@ |PSETCAT-;=;2SB;11|))) (LETT #1# (CDR #1#) |PSETCAT-;=;2SB;11|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 37)) + (|getShellEntry| $ 42)) (SPADCALL (PROGN (LETT #2# NIL |PSETCAT-;=;2SB;11|) @@ -324,28 +324,28 @@ |PSETCAT-;=;2SB;11|))) (LETT #3# (CDR #3#) |PSETCAT-;=;2SB;11|) (GO G190) G191 (EXIT (NREVERSE0 #2#)))) - (|getShellEntry| $ 37)) - (|getShellEntry| $ 38)))))) + (|getShellEntry| $ 42)) + (|getShellEntry| $ 43)))))) (DEFUN |PSETCAT-;localInf?| (|p| |q| $) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 40)) - (SPADCALL |q| (|getShellEntry| $ 40)) (|getShellEntry| $ 41))) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 45)) + (SPADCALL |q| (|getShellEntry| $ 45)) (|getShellEntry| $ 46))) (DEFUN |PSETCAT-;localTriangular?| (|lp| $) (PROG (|q| |p|) (RETURN - (SEQ (LETT |lp| (SPADCALL (ELT $ 42) |lp| (|getShellEntry| $ 26)) + (SEQ (LETT |lp| (SPADCALL (ELT $ 47) |lp| (|getShellEntry| $ 26)) |PSETCAT-;localTriangular?|) (EXIT (COND ((NULL |lp|) 'T) - ((SPADCALL (ELT $ 24) |lp| (|getShellEntry| $ 43)) + ((SPADCALL (ELT $ 24) |lp| (|getShellEntry| $ 49)) 'NIL) ('T (SEQ (LETT |lp| (SPADCALL (CONS #'|PSETCAT-;localTriangular?!0| $) - |lp| (|getShellEntry| $ 45)) + |lp| (|getShellEntry| $ 51)) |PSETCAT-;localTriangular?|) (LETT |p| (|SPADfirst| |lp|) |PSETCAT-;localTriangular?|) @@ -382,31 +382,31 @@ (|PSETCAT-;localTriangular?| (|PSETCAT-;elements| |ps| $) $)) (DEFUN |PSETCAT-;trivialIdeal?;SB;15| (|ps| $) - (NULL (SPADCALL (ELT $ 42) (|PSETCAT-;elements| |ps| $) + (NULL (SPADCALL (ELT $ 47) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)))) (DEFUN |PSETCAT-;roughUnitIdeal?;SB;16| (|ps| $) (SPADCALL (ELT $ 24) - (SPADCALL (ELT $ 42) (|PSETCAT-;elements| |ps| $) + (SPADCALL (ELT $ 47) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) - (|getShellEntry| $ 43))) + (|getShellEntry| $ 49))) (DEFUN |PSETCAT-;relativelyPrimeLeadingMonomials?| (|p| |q| $) (PROG (|dp| |dq|) (RETURN - (SEQ (LETT |dp| (SPADCALL |p| (|getShellEntry| $ 40)) + (SEQ (LETT |dp| (SPADCALL |p| (|getShellEntry| $ 45)) |PSETCAT-;relativelyPrimeLeadingMonomials?|) - (LETT |dq| (SPADCALL |q| (|getShellEntry| $ 40)) + (LETT |dq| (SPADCALL |q| (|getShellEntry| $ 45)) |PSETCAT-;relativelyPrimeLeadingMonomials?|) - (EXIT (SPADCALL (SPADCALL |dp| |dq| (|getShellEntry| $ 49)) - (SPADCALL |dp| |dq| (|getShellEntry| $ 50)) - (|getShellEntry| $ 51))))))) + (EXIT (SPADCALL (SPADCALL |dp| |dq| (|getShellEntry| $ 55)) + (SPADCALL |dp| |dq| (|getShellEntry| $ 56)) + (|getShellEntry| $ 57))))))) (DEFUN |PSETCAT-;roughBase?;SB;18| (|ps| $) (PROG (|p| |lp| |rB?| |copylp|) (RETURN (SEQ (LETT |lp| - (SPADCALL (ELT $ 42) (|PSETCAT-;elements| |ps| $) + (SPADCALL (ELT $ 47) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) |PSETCAT-;roughBase?;SB;18|) (EXIT (COND @@ -450,16 +450,16 @@ (RETURN (SEQ (LETT |lp| (SPADCALL (|PSETCAT-;elements| |ps1| $) |ps2| - (|getShellEntry| $ 53)) + (|getShellEntry| $ 59)) |PSETCAT-;roughSubIdeal?;2SB;19|) - (EXIT (NULL (SPADCALL (ELT $ 42) |lp| + (EXIT (NULL (SPADCALL (ELT $ 47) |lp| (|getShellEntry| $ 26)))))))) (DEFUN |PSETCAT-;roughEqualIdeals?;2SB;20| (|ps1| |ps2| $) (COND - ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 55)) 'T) - ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 56)) - (SPADCALL |ps2| |ps1| (|getShellEntry| $ 56))) + ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 61)) 'T) + ((SPADCALL |ps1| |ps2| (|getShellEntry| $ 62)) + (SPADCALL |ps2| |ps1| (|getShellEntry| $ 62))) ('T 'NIL))) (DEFUN |PSETCAT-;exactQuo| (|r| |s| $) @@ -467,9 +467,9 @@ (RETURN (COND ((|HasCategory| (|getShellEntry| $ 7) '(|EuclideanDomain|)) - (SPADCALL |r| |s| (|getShellEntry| $ 58))) + (SPADCALL |r| |s| (|getShellEntry| $ 64))) ('T - (PROG2 (LETT #0# (SPADCALL |r| |s| (|getShellEntry| $ 60)) + (PROG2 (LETT #0# (SPADCALL |r| |s| (|getShellEntry| $ 66)) |PSETCAT-;exactQuo|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 7) #0#))))))) @@ -478,16 +478,16 @@ (PROG (|lp1| |p| |e| |g| |#G45| |#G46| |lca| |lcp| |r| |lp2|) (RETURN (SEQ (LETT |lp1| - (SPADCALL (ELT $ 42) (|PSETCAT-;elements| |ps| $) + (SPADCALL (ELT $ 47) (|PSETCAT-;elements| |ps| $) (|getShellEntry| $ 26)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (COND - ((NULL |lp1|) (CONS |a| (|spadConstant| $ 61))) - ((SPADCALL (ELT $ 24) |lp1| (|getShellEntry| $ 43)) - (CONS (SPADCALL |a| (|getShellEntry| $ 62)) - (|spadConstant| $ 61))) + ((NULL |lp1|) (CONS |a| (|spadConstant| $ 67))) + ((SPADCALL (ELT $ 24) |lp1| (|getShellEntry| $ 49)) + (CONS (SPADCALL |a| (|getShellEntry| $ 68)) + (|spadConstant| $ 67))) ('T - (SEQ (LETT |r| (|spadConstant| $ 61) + (SEQ (LETT |r| (|spadConstant| $ 67) |PSETCAT-;headRemainder;PSR;22|) (LETT |lp1| (SPADCALL @@ -496,7 +496,7 @@ $) (REVERSE (|PSETCAT-;elements| |ps| $)) - (|getShellEntry| $ 45)) + (|getShellEntry| $ 51)) |PSETCAT-;headRemainder;PSR;22|) (LETT |lp2| |lp1| |PSETCAT-;headRemainder;PSR;22|) @@ -504,7 +504,7 @@ (COND ((NULL (COND ((SPADCALL |a| - (|getShellEntry| $ 42)) + (|getShellEntry| $ 47)) 'NIL) ('T (NOT (NULL |lp2|))))) (GO G191))) @@ -513,10 +513,10 @@ (LETT |e| (SPADCALL (SPADCALL |a| - (|getShellEntry| $ 40)) + (|getShellEntry| $ 45)) (SPADCALL |p| - (|getShellEntry| $ 40)) - (|getShellEntry| $ 63)) + (|getShellEntry| $ 45)) + (|getShellEntry| $ 70)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (COND @@ -526,13 +526,13 @@ (SPADCALL (LETT |lca| (SPADCALL |a| - (|getShellEntry| $ 64)) + (|getShellEntry| $ 71)) |PSETCAT-;headRemainder;PSR;22|) (LETT |lcp| (SPADCALL |p| - (|getShellEntry| $ 64)) + (|getShellEntry| $ 71)) |PSETCAT-;headRemainder;PSR;22|) - (|getShellEntry| $ 65)) + (|getShellEntry| $ 72)) |PSETCAT-;headRemainder;PSR;22|) (PROGN (LETT |#G45| @@ -551,19 +551,19 @@ (SPADCALL (SPADCALL |lcp| (SPADCALL |a| - (|getShellEntry| $ 62)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 68)) + (|getShellEntry| $ 73)) (SPADCALL (SPADCALL |lca| (QCDR |e|) - (|getShellEntry| $ 67)) + (|getShellEntry| $ 74)) (SPADCALL |p| - (|getShellEntry| $ 62)) - (|getShellEntry| $ 68)) - (|getShellEntry| $ 69)) + (|getShellEntry| $ 68)) + (|getShellEntry| $ 75)) + (|getShellEntry| $ 76)) |PSETCAT-;headRemainder;PSR;22|) (LETT |r| (SPADCALL |r| |lcp| - (|getShellEntry| $ 70)) + (|getShellEntry| $ 77)) |PSETCAT-;headRemainder;PSR;22|) (EXIT (LETT |lp2| |lp1| @@ -579,15 +579,15 @@ (RETURN (SEQ (LETT |g| (SPADCALL (QCDR |frac|) (QCAR |frac|) - (|getShellEntry| $ 73)) + (|getShellEntry| $ 80)) |PSETCAT-;makeIrreducible!|) (EXIT (COND - ((SPADCALL |g| (|getShellEntry| $ 74)) |frac|) + ((SPADCALL |g| (|getShellEntry| $ 81)) |frac|) ('T (SEQ (PROGN (RPLACA |frac| (SPADCALL (QCAR |frac|) |g| - (|getShellEntry| $ 75))) + (|getShellEntry| $ 82))) (QCAR |frac|)) (PROGN (RPLACD |frac| @@ -601,22 +601,22 @@ (RETURN (SEQ (LETT |hRa| (|PSETCAT-;makeIrreducible!| - (SPADCALL |a| |ps| (|getShellEntry| $ 76)) $) + (SPADCALL |a| |ps| (|getShellEntry| $ 83)) $) |PSETCAT-;remainder;PSR;24|) (LETT |a| (QCAR |hRa|) |PSETCAT-;remainder;PSR;24|) (LETT |r| (QCDR |hRa|) |PSETCAT-;remainder;PSR;24|) (EXIT (COND - ((SPADCALL |a| (|getShellEntry| $ 42)) - (VECTOR (|spadConstant| $ 61) |a| |r|)) + ((SPADCALL |a| (|getShellEntry| $ 47)) + (VECTOR (|spadConstant| $ 67) |a| |r|)) ('T (SEQ (LETT |b| - (SPADCALL (|spadConstant| $ 61) + (SPADCALL (|spadConstant| $ 67) (SPADCALL |a| - (|getShellEntry| $ 40)) - (|getShellEntry| $ 67)) + (|getShellEntry| $ 45)) + (|getShellEntry| $ 74)) |PSETCAT-;remainder;PSR;24|) (LETT |c| - (SPADCALL |a| (|getShellEntry| $ 64)) + (SPADCALL |a| (|getShellEntry| $ 71)) |PSETCAT-;remainder;PSR;24|) (SEQ G190 (COND @@ -624,43 +624,43 @@ (SPADCALL (LETT |a| (SPADCALL |a| - (|getShellEntry| $ 62)) + (|getShellEntry| $ 68)) |PSETCAT-;remainder;PSR;24|) - (|getShellEntry| $ 42)))) + (|getShellEntry| $ 47)))) (GO G191))) (SEQ (LETT |hRa| (|PSETCAT-;makeIrreducible!| (SPADCALL |a| |ps| - (|getShellEntry| $ 76)) + (|getShellEntry| $ 83)) $) |PSETCAT-;remainder;PSR;24|) (LETT |a| (QCAR |hRa|) |PSETCAT-;remainder;PSR;24|) (LETT |r| (SPADCALL |r| (QCDR |hRa|) - (|getShellEntry| $ 70)) + (|getShellEntry| $ 77)) |PSETCAT-;remainder;PSR;24|) (LETT |g| (SPADCALL |c| (LETT |lca| (SPADCALL |a| - (|getShellEntry| $ 64)) + (|getShellEntry| $ 71)) |PSETCAT-;remainder;PSR;24|) - (|getShellEntry| $ 65)) + (|getShellEntry| $ 72)) |PSETCAT-;remainder;PSR;24|) (LETT |b| (SPADCALL (SPADCALL (SPADCALL (QCDR |hRa|) (|PSETCAT-;exactQuo| |c| |g| $) - (|getShellEntry| $ 70)) - |b| (|getShellEntry| $ 66)) + (|getShellEntry| $ 77)) + |b| (|getShellEntry| $ 73)) (SPADCALL (|PSETCAT-;exactQuo| |lca| |g| $) (SPADCALL |a| - (|getShellEntry| $ 40)) - (|getShellEntry| $ 67)) - (|getShellEntry| $ 77)) + (|getShellEntry| $ 45)) + (|getShellEntry| $ 74)) + (|getShellEntry| $ 84)) |PSETCAT-;remainder;PSR;24|) (EXIT (LETT |c| |g| @@ -672,19 +672,19 @@ (PROG (|p| |rs|) (RETURN (SEQ (COND - ((SPADCALL |cs| (|getShellEntry| $ 80)) |ps|) - ((SPADCALL |cs| (|getShellEntry| $ 81)) - (LIST (|spadConstant| $ 82))) + ((SPADCALL |cs| (|getShellEntry| $ 87)) |ps|) + ((SPADCALL |cs| (|getShellEntry| $ 88)) + (LIST (|spadConstant| $ 89))) ('T (SEQ (LETT |ps| - (SPADCALL (ELT $ 42) |ps| + (SPADCALL (ELT $ 47) |ps| (|getShellEntry| $ 26)) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (EXIT (COND ((NULL |ps|) |ps|) ((SPADCALL (ELT $ 24) |ps| - (|getShellEntry| $ 43)) - (LIST (|spadConstant| $ 83))) + (|getShellEntry| $ 49)) + (LIST (|spadConstant| $ 90))) ('T (SEQ (LETT |rs| NIL |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) @@ -700,13 +700,13 @@ (LETT |p| (QCAR (SPADCALL |p| |cs| - (|getShellEntry| $ 76))) + (|getShellEntry| $ 83))) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) (EXIT (COND ((NULL (SPADCALL |p| - (|getShellEntry| $ 42))) + (|getShellEntry| $ 47))) (COND ((SPADCALL |p| (|getShellEntry| $ 24)) @@ -716,37 +716,37 @@ (EXIT (LETT |rs| (LIST - (|spadConstant| $ 83)) + (|spadConstant| $ 90)) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|)))) ('T (SEQ (SPADCALL |p| - (|getShellEntry| $ 84)) + (|getShellEntry| $ 91)) (EXIT (LETT |rs| (CONS |p| |rs|) |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|))))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |rs| - (|getShellEntry| $ 85)))))))))))))) + (|getShellEntry| $ 92)))))))))))))) (DEFUN |PSETCAT-;rewriteIdealWithRemainder;LSL;26| (|ps| |cs| $) (PROG (|p| |rs|) (RETURN (SEQ (COND - ((SPADCALL |cs| (|getShellEntry| $ 80)) |ps|) - ((SPADCALL |cs| (|getShellEntry| $ 81)) - (LIST (|spadConstant| $ 82))) + ((SPADCALL |cs| (|getShellEntry| $ 87)) |ps|) + ((SPADCALL |cs| (|getShellEntry| $ 88)) + (LIST (|spadConstant| $ 89))) ('T (SEQ (LETT |ps| - (SPADCALL (ELT $ 42) |ps| + (SPADCALL (ELT $ 47) |ps| (|getShellEntry| $ 26)) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (EXIT (COND ((NULL |ps|) |ps|) ((SPADCALL (ELT $ 24) |ps| - (|getShellEntry| $ 43)) - (LIST (|spadConstant| $ 83))) + (|getShellEntry| $ 49)) + (LIST (|spadConstant| $ 90))) ('T (SEQ (LETT |rs| NIL |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) @@ -762,14 +762,14 @@ (LETT |p| (QVELT (SPADCALL |p| |cs| - (|getShellEntry| $ 87)) + (|getShellEntry| $ 94)) 1) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) (EXIT (COND ((NULL (SPADCALL |p| - (|getShellEntry| $ 42))) + (|getShellEntry| $ 47))) (COND ((SPADCALL |p| (|getShellEntry| $ 24)) @@ -779,18 +779,18 @@ (EXIT (LETT |rs| (LIST - (|spadConstant| $ 83)) + (|spadConstant| $ 90)) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|)))) ('T (LETT |rs| (CONS (SPADCALL |p| - (|getShellEntry| $ 88)) + (|getShellEntry| $ 95)) |rs|) |PSETCAT-;rewriteIdealWithRemainder;LSL;26|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |rs| - (|getShellEntry| $ 85)))))))))))))) + (|getShellEntry| $ 92)))))))))))))) (DEFUN |PolynomialSetCategory&| (|#1| |#2| |#3| |#4| |#5|) (PROG (|dv$1| |dv$2| |dv$3| |dv$4| |dv$5| |dv$| $ |pv$|) @@ -805,7 +805,7 @@ (LETT |dv$| (LIST '|PolynomialSetCategory&| |dv$1| |dv$2| |dv$3| |dv$4| |dv$5|) . #0#) - (LETT $ (|newShell| 90) . #0#) + (LETT $ (|newShell| 97) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -820,18 +820,18 @@ (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 48 + (|setShellEntry| $ 54 (CONS (|dispatchFunction| |PSETCAT-;roughUnitIdeal?;SB;16|) $)) - (|setShellEntry| $ 52 + (|setShellEntry| $ 58 (CONS (|dispatchFunction| |PSETCAT-;roughBase?;SB;18|) $)) - (|setShellEntry| $ 54 + (|setShellEntry| $ 60 (CONS (|dispatchFunction| |PSETCAT-;roughSubIdeal?;2SB;19|) $)) - (|setShellEntry| $ 57 + (|setShellEntry| $ 63 (CONS (|dispatchFunction| |PSETCAT-;roughEqualIdeals?;2SB;20|) $))))) @@ -840,19 +840,19 @@ (COND ((|HasCategory| |#4| '(|ConvertibleTo| (|Symbol|))) (PROGN - (|setShellEntry| $ 72 + (|setShellEntry| $ 79 (CONS (|dispatchFunction| |PSETCAT-;headRemainder;PSR;22|) $)) - (|setShellEntry| $ 79 + (|setShellEntry| $ 86 (CONS (|dispatchFunction| |PSETCAT-;remainder;PSR;24|) $)) - (|setShellEntry| $ 86 + (|setShellEntry| $ 93 (CONS (|dispatchFunction| |PSETCAT-;rewriteIdealWithHeadRemainder;LSL;25|) $)) - (|setShellEntry| $ 89 + (|setShellEntry| $ 96 (CONS (|dispatchFunction| |PSETCAT-;rewriteIdealWithRemainder;LSL;26|) $))))))) @@ -866,73 +866,79 @@ (21 . |removeDuplicates|) (|Mapping| 15 9 9) (26 . |sort|) (32 . |mvar|) |PSETCAT-;variables;SL;4| (37 . |ground?|) (|Mapping| 15 10) (42 . |remove|) - |PSETCAT-;mainVariables;SL;5| (48 . =) - |PSETCAT-;mainVariable?;VarSetSB;6| (54 . |construct|) - |PSETCAT-;collectUnder;SVarSetS;7| + |PSETCAT-;mainVariables;SL;5| (48 . |empty?|) + (53 . |false|) (57 . |first|) (62 . =) (68 . |rest|) + |PSETCAT-;mainVariable?;VarSetSB;6| (73 . |cons|) + (79 . |construct|) |PSETCAT-;collectUnder;SVarSetS;7| |PSETCAT-;collectUpper;SVarSetS;8| |PSETCAT-;collect;SVarSetS;9| (|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) - |PSETCAT-;sort;SVarSetR;10| (|Set| 10) (59 . |brace|) - (64 . =) |PSETCAT-;=;2SB;11| (70 . |degree|) (75 . <) - (81 . |zero?|) (86 . |any?|) (|Mapping| 15 10 10) - (92 . |sort|) |PSETCAT-;triangular?;SB;14| - |PSETCAT-;trivialIdeal?;SB;15| (98 . |roughUnitIdeal?|) - (103 . |sup|) (109 . +) (115 . =) (121 . |roughBase?|) - (126 . |rewriteIdealWithRemainder|) - (132 . |roughSubIdeal?|) (138 . =) - (144 . |roughSubIdeal?|) (150 . |roughEqualIdeals?|) - (156 . |quo|) (|Union| $ '"failed") (162 . |exquo|) - (168 . |One|) (172 . |reductum|) (177 . |subtractIfCan|) - (183 . |leadingCoefficient|) (188 . |gcd|) (194 . *) - (200 . |monomial|) (206 . *) (212 . -) (218 . *) + |PSETCAT-;sort;SVarSetR;10| (|Set| 10) (84 . |brace|) + (89 . =) |PSETCAT-;=;2SB;11| (95 . |degree|) (100 . <) + (106 . |zero?|) (111 . |true|) (115 . |any?|) + (|Mapping| 15 10 10) (121 . |sort|) + |PSETCAT-;triangular?;SB;14| + |PSETCAT-;trivialIdeal?;SB;15| (127 . |roughUnitIdeal?|) + (132 . |sup|) (138 . +) (144 . =) (150 . |roughBase?|) + (155 . |rewriteIdealWithRemainder|) + (161 . |roughSubIdeal?|) (167 . =) + (173 . |roughSubIdeal?|) (179 . |roughEqualIdeals?|) + (185 . |quo|) (|Union| $ '"failed") (191 . |exquo|) + (197 . |One|) (201 . |reductum|) (206 . |reverse|) + (211 . |subtractIfCan|) (217 . |leadingCoefficient|) + (222 . |gcd|) (228 . *) (234 . |monomial|) (240 . *) + (246 . -) (252 . *) (|Record| (|:| |num| 10) (|:| |den| 7)) - (224 . |headRemainder|) (230 . |gcd|) (236 . |one?|) - (241 . |exactQuotient!|) (247 . |headRemainder|) (253 . +) + (258 . |headRemainder|) (264 . |gcd|) (270 . |one?|) + (275 . |exactQuotient!|) (281 . |headRemainder|) (287 . +) (|Record| (|:| |rnum| 7) (|:| |polnum| 10) (|:| |den| 7)) - (259 . |remainder|) (265 . |trivialIdeal?|) - (270 . |roughUnitIdeal?|) (275 . |Zero|) (279 . |One|) - (283 . |primitivePart!|) (288 . |removeDuplicates|) - (293 . |rewriteIdealWithHeadRemainder|) - (299 . |remainder|) (305 . |unitCanonical|) - (310 . |rewriteIdealWithRemainder|)) - '#(|variables| 316 |trivialIdeal?| 321 |triangular?| 326 - |sort| 331 |roughUnitIdeal?| 337 |roughSubIdeal?| 342 - |roughEqualIdeals?| 348 |roughBase?| 354 - |rewriteIdealWithRemainder| 359 - |rewriteIdealWithHeadRemainder| 365 |remainder| 371 - |mainVariables| 377 |mainVariable?| 382 |headRemainder| - 388 |collectUpper| 394 |collectUnder| 400 |collect| 406 = - 412) + (293 . |remainder|) (299 . |trivialIdeal?|) + (304 . |roughUnitIdeal?|) (309 . |Zero|) (313 . |One|) + (317 . |primitivePart!|) (322 . |removeDuplicates|) + (327 . |rewriteIdealWithHeadRemainder|) + (333 . |remainder|) (339 . |unitCanonical|) + (344 . |rewriteIdealWithRemainder|)) + '#(|variables| 350 |trivialIdeal?| 355 |triangular?| 360 + |sort| 365 |roughUnitIdeal?| 371 |roughSubIdeal?| 376 + |roughEqualIdeals?| 382 |roughBase?| 388 + |rewriteIdealWithRemainder| 393 + |rewriteIdealWithHeadRemainder| 399 |remainder| 405 + |mainVariables| 411 |mainVariable?| 416 |headRemainder| + 422 |collectUpper| 428 |collectUnder| 434 |collect| 440 = + 446) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 89 + (|makeByteWordVec2| 96 '(1 6 11 0 12 1 10 13 0 14 2 9 15 0 0 16 1 13 0 17 18 1 13 0 0 19 2 13 0 20 0 21 1 10 9 0 22 1 10 15 0 24 2 11 0 - 25 0 26 2 9 15 0 0 28 1 6 0 11 30 1 - 36 0 11 37 2 36 15 0 0 38 1 10 8 0 40 - 2 8 15 0 0 41 1 10 15 0 42 2 11 15 25 - 0 43 2 11 0 44 0 45 1 0 15 0 48 2 8 0 - 0 0 49 2 8 0 0 0 50 2 8 15 0 0 51 1 0 - 15 0 52 2 6 11 11 0 53 2 0 15 0 0 54 - 2 6 15 0 0 55 2 6 15 0 0 56 2 0 15 0 - 0 57 2 7 0 0 0 58 2 7 59 0 0 60 0 7 0 - 61 1 10 0 0 62 2 8 59 0 0 63 1 10 7 0 - 64 2 7 0 0 0 65 2 10 0 7 0 66 2 10 0 - 7 8 67 2 10 0 0 0 68 2 10 0 0 0 69 2 - 7 0 0 0 70 2 0 71 10 0 72 2 10 7 7 0 - 73 1 7 15 0 74 2 10 0 0 7 75 2 6 71 - 10 0 76 2 10 0 0 0 77 2 0 78 10 0 79 - 1 6 15 0 80 1 6 15 0 81 0 10 0 82 0 - 10 0 83 1 10 0 0 84 1 11 0 0 85 2 0 - 11 11 0 86 2 6 78 10 0 87 1 10 0 0 88 - 2 0 11 11 0 89 1 0 13 0 23 1 0 15 0 - 47 1 0 15 0 46 2 0 34 0 9 35 1 0 15 0 - 48 2 0 15 0 0 54 2 0 15 0 0 57 1 0 15 - 0 52 2 0 11 11 0 89 2 0 11 11 0 86 2 - 0 78 10 0 79 1 0 13 0 27 2 0 15 9 0 - 29 2 0 71 10 0 72 2 0 0 0 9 32 2 0 0 - 0 9 31 2 0 0 0 9 33 2 0 15 0 0 39))))) + 25 0 26 1 11 15 0 28 0 15 0 29 1 11 + 10 0 30 2 9 15 0 0 31 1 11 0 0 32 2 + 11 0 10 0 34 1 6 0 11 35 1 41 0 11 42 + 2 41 15 0 0 43 1 10 8 0 45 2 8 15 0 0 + 46 1 10 15 0 47 0 15 0 48 2 11 15 25 + 0 49 2 11 0 50 0 51 1 0 15 0 54 2 8 0 + 0 0 55 2 8 0 0 0 56 2 8 15 0 0 57 1 0 + 15 0 58 2 6 11 11 0 59 2 0 15 0 0 60 + 2 6 15 0 0 61 2 6 15 0 0 62 2 0 15 0 + 0 63 2 7 0 0 0 64 2 7 65 0 0 66 0 7 0 + 67 1 10 0 0 68 1 11 0 0 69 2 8 65 0 0 + 70 1 10 7 0 71 2 7 0 0 0 72 2 10 0 7 + 0 73 2 10 0 7 8 74 2 10 0 0 0 75 2 10 + 0 0 0 76 2 7 0 0 0 77 2 0 78 10 0 79 + 2 10 7 7 0 80 1 7 15 0 81 2 10 0 0 7 + 82 2 6 78 10 0 83 2 10 0 0 0 84 2 0 + 85 10 0 86 1 6 15 0 87 1 6 15 0 88 0 + 10 0 89 0 10 0 90 1 10 0 0 91 1 11 0 + 0 92 2 0 11 11 0 93 2 6 85 10 0 94 1 + 10 0 0 95 2 0 11 11 0 96 1 0 13 0 23 + 1 0 15 0 53 1 0 15 0 52 2 0 39 0 9 40 + 1 0 15 0 54 2 0 15 0 0 60 2 0 15 0 0 + 63 1 0 15 0 58 2 0 11 11 0 96 2 0 11 + 11 0 93 2 0 85 10 0 86 1 0 13 0 27 2 + 0 15 9 0 33 2 0 78 10 0 79 2 0 0 0 9 + 37 2 0 0 0 9 36 2 0 0 0 9 38 2 0 15 0 + 0 44))))) '|lookupComplete|)) diff --git a/src/algebra/strap/QFCAT-.lsp b/src/algebra/strap/QFCAT-.lsp index 78512ea8..3d8412d1 100644 --- a/src/algebra/strap/QFCAT-.lsp +++ b/src/algebra/strap/QFCAT-.lsp @@ -116,8 +116,7 @@ (DEFUN |QFCAT-;reducedSystem;MM;6| (|m| $) (SPADCALL |m| (|getShellEntry| $ 26))) -(DEFUN |QFCAT-;characteristic;Nni;7| ($) - (SPADCALL (|getShellEntry| $ 30))) +(DEFUN |QFCAT-;characteristic;Nni;7| ($) (|spadConstant| $ 30)) (DEFUN |QFCAT-;differentiate;AMA;8| (|x| |deriv| $) (PROG (|n| |d|) @@ -164,14 +163,14 @@ (SPADCALL |y| (|getShellEntry| $ 11)) (|getShellEntry| $ 32)) (SPADCALL (SPADCALL |y| (|getShellEntry| $ 8)) (SPADCALL |x| (|getShellEntry| $ 11)) (|getShellEntry| $ 32)) - (|getShellEntry| $ 49))) + (|getShellEntry| $ 50))) (DEFUN |QFCAT-;<;2AB;13| (|x| |y| $) (PROG (|#G19| |#G20| |#G21| |#G22|) (RETURN (SEQ (COND ((SPADCALL (SPADCALL |x| (|getShellEntry| $ 11)) - (|spadConstant| $ 51) (|getShellEntry| $ 49)) + (|spadConstant| $ 52) (|getShellEntry| $ 50)) (PROGN (LETT |#G19| |y| |QFCAT-;<;2AB;13|) (LETT |#G20| |x| |QFCAT-;<;2AB;13|) @@ -179,7 +178,7 @@ (LETT |y| |#G20| |QFCAT-;<;2AB;13|)))) (COND ((SPADCALL (SPADCALL |y| (|getShellEntry| $ 11)) - (|spadConstant| $ 51) (|getShellEntry| $ 49)) + (|spadConstant| $ 52) (|getShellEntry| $ 50)) (PROGN (LETT |#G21| |y| |QFCAT-;<;2AB;13|) (LETT |#G22| |x| |QFCAT-;<;2AB;13|) @@ -192,7 +191,7 @@ (SPADCALL (SPADCALL |y| (|getShellEntry| $ 8)) (SPADCALL |x| (|getShellEntry| $ 11)) (|getShellEntry| $ 32)) - (|getShellEntry| $ 49))))))) + (|getShellEntry| $ 50))))))) (DEFUN |QFCAT-;<;2AB;14| (|x| |y| $) (SPADCALL @@ -200,73 +199,73 @@ (SPADCALL |y| (|getShellEntry| $ 11)) (|getShellEntry| $ 32)) (SPADCALL (SPADCALL |y| (|getShellEntry| $ 8)) (SPADCALL |x| (|getShellEntry| $ 11)) (|getShellEntry| $ 32)) - (|getShellEntry| $ 49))) + (|getShellEntry| $ 50))) (DEFUN |QFCAT-;fractionPart;2A;15| (|x| $) (SPADCALL |x| - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 52)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 53)) (|getShellEntry| $ 9)) - (|getShellEntry| $ 53))) + (|getShellEntry| $ 54))) (DEFUN |QFCAT-;coerce;SA;16| (|s| $) - (SPADCALL (SPADCALL |s| (|getShellEntry| $ 56)) + (SPADCALL (SPADCALL |s| (|getShellEntry| $ 57)) (|getShellEntry| $ 9))) (DEFUN |QFCAT-;retract;AS;17| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 58)) - (|getShellEntry| $ 59))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 59)) + (|getShellEntry| $ 60))) (DEFUN |QFCAT-;retractIfCan;AU;18| (|x| $) (PROG (|r|) (RETURN - (SEQ (LETT |r| (SPADCALL |x| (|getShellEntry| $ 62)) + (SEQ (LETT |r| (SPADCALL |x| (|getShellEntry| $ 63)) |QFCAT-;retractIfCan;AU;18|) (EXIT (COND ((QEQCAR |r| 1) (CONS 1 "failed")) - ('T (SPADCALL (QCDR |r|) (|getShellEntry| $ 64))))))))) + ('T (SPADCALL (QCDR |r|) (|getShellEntry| $ 65))))))))) (DEFUN |QFCAT-;convert;AP;19| (|x| $) (SPADCALL (SPADCALL (SPADCALL |x| (|getShellEntry| $ 8)) - (|getShellEntry| $ 68)) + (|getShellEntry| $ 69)) (SPADCALL (SPADCALL |x| (|getShellEntry| $ 11)) - (|getShellEntry| $ 68)) - (|getShellEntry| $ 69))) + (|getShellEntry| $ 69)) + (|getShellEntry| $ 70))) (DEFUN |QFCAT-;patternMatch;AP2Pmr;20| (|x| |p| |l| $) - (SPADCALL |x| |p| |l| (|getShellEntry| $ 73))) + (SPADCALL |x| |p| |l| (|getShellEntry| $ 74))) (DEFUN |QFCAT-;convert;AP;21| (|x| $) (SPADCALL (SPADCALL (SPADCALL |x| (|getShellEntry| $ 8)) - (|getShellEntry| $ 77)) + (|getShellEntry| $ 78)) (SPADCALL (SPADCALL |x| (|getShellEntry| $ 11)) - (|getShellEntry| $ 77)) - (|getShellEntry| $ 78))) + (|getShellEntry| $ 78)) + (|getShellEntry| $ 79))) (DEFUN |QFCAT-;patternMatch;AP2Pmr;22| (|x| |p| |l| $) - (SPADCALL |x| |p| |l| (|getShellEntry| $ 82))) + (SPADCALL |x| |p| |l| (|getShellEntry| $ 83))) (DEFUN |QFCAT-;coerce;FA;23| (|x| $) (SPADCALL - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 86)) - (|getShellEntry| $ 87)) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 88)) - (|getShellEntry| $ 87)) - (|getShellEntry| $ 89))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 87)) + (|getShellEntry| $ 88)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 89)) + (|getShellEntry| $ 88)) + (|getShellEntry| $ 90))) (DEFUN |QFCAT-;retract;AI;24| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 58)) - (|getShellEntry| $ 91))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 59)) + (|getShellEntry| $ 92))) (DEFUN |QFCAT-;retractIfCan;AU;25| (|x| $) (PROG (|u|) (RETURN - (SEQ (LETT |u| (SPADCALL |x| (|getShellEntry| $ 62)) + (SEQ (LETT |u| (SPADCALL |x| (|getShellEntry| $ 63)) |QFCAT-;retractIfCan;AU;25|) (EXIT (COND ((QEQCAR |u| 1) (CONS 1 "failed")) - ('T (SPADCALL (QCDR |u|) (|getShellEntry| $ 94))))))))) + ('T (SPADCALL (QCDR |u|) (|getShellEntry| $ 95))))))))) (DEFUN |QFCAT-;random;A;26| ($) (PROG (|d|) @@ -275,12 +274,12 @@ (COND ((NULL (SPADCALL (LETT |d| - (SPADCALL (|getShellEntry| $ 96)) + (SPADCALL (|getShellEntry| $ 97)) |QFCAT-;random;A;26|) - (|getShellEntry| $ 97))) + (|getShellEntry| $ 98))) (GO G191))) (SEQ (EXIT |d|)) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL (SPADCALL (|getShellEntry| $ 96)) |d| + (EXIT (SPADCALL (SPADCALL (|getShellEntry| $ 97)) |d| (|getShellEntry| $ 15))))))) (DEFUN |QFCAT-;reducedSystem;MVR;27| (|m| |v| $) @@ -288,19 +287,19 @@ (RETURN (SEQ (LETT |n| (SPADCALL - (SPADCALL (SPADCALL |v| (|getShellEntry| $ 100)) - |m| (|getShellEntry| $ 101)) - (|getShellEntry| $ 102)) + (SPADCALL (SPADCALL |v| (|getShellEntry| $ 101)) + |m| (|getShellEntry| $ 102)) + (|getShellEntry| $ 103)) |QFCAT-;reducedSystem;MVR;27|) (EXIT (CONS (SPADCALL |n| - (SPADCALL |n| (|getShellEntry| $ 103)) (SPADCALL |n| (|getShellEntry| $ 104)) - (+ 1 (SPADCALL |n| (|getShellEntry| $ 105))) - (SPADCALL |n| (|getShellEntry| $ 106)) - (|getShellEntry| $ 107)) - (SPADCALL |n| (SPADCALL |n| (|getShellEntry| $ 105)) - (|getShellEntry| $ 109)))))))) + (+ 1 (SPADCALL |n| (|getShellEntry| $ 107))) + (SPADCALL |n| (|getShellEntry| $ 109)) + (|getShellEntry| $ 110)) + (SPADCALL |n| + (SPADCALL |n| (|getShellEntry| $ 107)) + (|getShellEntry| $ 112)))))))) (DEFUN |QuotientFieldCategory&| (|#1| |#2|) (PROG (|dv$1| |dv$2| |dv$| $ |pv$|) @@ -311,7 +310,7 @@ (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|QuotientFieldCategory&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 120) . #0#) + (LETT $ (|newShell| 123) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -355,44 +354,44 @@ (PROGN (|setShellEntry| $ 44 (CONS (|dispatchFunction| |QFCAT-;convert;AF;10|) $)) - (|setShellEntry| $ 47 + (|setShellEntry| $ 48 (CONS (|dispatchFunction| |QFCAT-;convert;ADf;11|) $))))) (COND ((|testBitVector| |pv$| 9) (COND ((|HasAttribute| |#2| '|canonicalUnitNormal|) - (|setShellEntry| $ 50 + (|setShellEntry| $ 51 (CONS (|dispatchFunction| |QFCAT-;<;2AB;12|) $))) ('T - (|setShellEntry| $ 50 + (|setShellEntry| $ 51 (CONS (|dispatchFunction| |QFCAT-;<;2AB;13|) $))))) ((|testBitVector| |pv$| 10) - (|setShellEntry| $ 50 + (|setShellEntry| $ 51 (CONS (|dispatchFunction| |QFCAT-;<;2AB;14|) $)))) (COND ((|testBitVector| |pv$| 3) - (|setShellEntry| $ 54 + (|setShellEntry| $ 55 (CONS (|dispatchFunction| |QFCAT-;fractionPart;2A;15|) $)))) (COND ((|testBitVector| |pv$| 4) (PROGN - (|setShellEntry| $ 57 + (|setShellEntry| $ 58 (CONS (|dispatchFunction| |QFCAT-;coerce;SA;16|) $)) - (|setShellEntry| $ 60 + (|setShellEntry| $ 61 (CONS (|dispatchFunction| |QFCAT-;retract;AS;17|) $)) - (|setShellEntry| $ 65 + (|setShellEntry| $ 66 (CONS (|dispatchFunction| |QFCAT-;retractIfCan;AU;18|) $))))) (COND ((|HasCategory| |#2| '(|ConvertibleTo| (|Pattern| (|Integer|)))) (PROGN - (|setShellEntry| $ 70 + (|setShellEntry| $ 71 (CONS (|dispatchFunction| |QFCAT-;convert;AP;19|) $)) (COND ((|HasCategory| |#2| '(|PatternMatchable| (|Integer|))) - (|setShellEntry| $ 75 + (|setShellEntry| $ 76 (CONS (|dispatchFunction| |QFCAT-;patternMatch;AP2Pmr;20|) $))))))) @@ -400,33 +399,33 @@ ((|HasCategory| |#2| '(|ConvertibleTo| (|Pattern| (|Float|)))) (PROGN - (|setShellEntry| $ 79 + (|setShellEntry| $ 80 (CONS (|dispatchFunction| |QFCAT-;convert;AP;21|) $)) (COND ((|HasCategory| |#2| '(|PatternMatchable| (|Float|))) - (|setShellEntry| $ 84 + (|setShellEntry| $ 85 (CONS (|dispatchFunction| |QFCAT-;patternMatch;AP2Pmr;22|) $))))))) (COND ((|testBitVector| |pv$| 11) (PROGN - (|setShellEntry| $ 90 + (|setShellEntry| $ 91 (CONS (|dispatchFunction| |QFCAT-;coerce;FA;23|) $)) (COND ((|domainEqual| |#2| (|Integer|))) ('T (PROGN - (|setShellEntry| $ 92 + (|setShellEntry| $ 93 (CONS (|dispatchFunction| |QFCAT-;retract;AI;24|) $)) - (|setShellEntry| $ 95 + (|setShellEntry| $ 96 (CONS (|dispatchFunction| |QFCAT-;retractIfCan;AU;25|) $)))))))) (COND ((|testBitVector| |pv$| 2) - (|setShellEntry| $ 98 + (|setShellEntry| $ 99 (CONS (|dispatchFunction| |QFCAT-;random;A;26|) $)))) $)))) @@ -445,77 +444,78 @@ |QFCAT-;differentiate;AMA;8| (|InputForm|) (74 . |convert|) (79 . /) (85 . |convert|) (|Float|) (90 . |convert|) (95 . /) (101 . |convert|) - (|DoubleFloat|) (106 . |convert|) (111 . |convert|) - (|Boolean|) (116 . <) (122 . <) (128 . |Zero|) - (132 . |wholePart|) (137 . -) (143 . |fractionPart|) - (|Symbol|) (148 . |coerce|) (153 . |coerce|) - (158 . |retract|) (163 . |retract|) (168 . |retract|) - (|Union| 7 '"failed") (173 . |retractIfCan|) - (|Union| 55 '"failed") (178 . |retractIfCan|) - (183 . |retractIfCan|) (|Integer|) (|Pattern| 66) - (188 . |convert|) (193 . /) (199 . |convert|) - (|PatternMatchResult| 66 6) - (|PatternMatchQuotientFieldCategory| 66 7 6) - (204 . |patternMatch|) (|PatternMatchResult| 66 $) - (211 . |patternMatch|) (|Pattern| 41) (218 . |convert|) - (223 . /) (229 . |convert|) (|PatternMatchResult| 41 6) + (|DoubleFloat|) (106 . |convert|) (111 . /) + (117 . |convert|) (|Boolean|) (122 . <) (128 . <) + (134 . |Zero|) (138 . |wholePart|) (143 . -) + (149 . |fractionPart|) (|Symbol|) (154 . |coerce|) + (159 . |coerce|) (164 . |retract|) (169 . |retract|) + (174 . |retract|) (|Union| 7 '"failed") + (179 . |retractIfCan|) (|Union| 56 '"failed") + (184 . |retractIfCan|) (189 . |retractIfCan|) (|Integer|) + (|Pattern| 67) (194 . |convert|) (199 . /) + (205 . |convert|) (|PatternMatchResult| 67 6) + (|PatternMatchQuotientFieldCategory| 67 7 6) + (210 . |patternMatch|) (|PatternMatchResult| 67 $) + (217 . |patternMatch|) (|Pattern| 41) (224 . |convert|) + (229 . /) (235 . |convert|) (|PatternMatchResult| 41 6) (|PatternMatchQuotientFieldCategory| 41 7 6) - (234 . |patternMatch|) (|PatternMatchResult| 41 $) - (241 . |patternMatch|) (|Fraction| 66) (248 . |numer|) - (253 . |coerce|) (258 . |denom|) (263 . /) - (269 . |coerce|) (274 . |retract|) (279 . |retract|) - (|Union| 66 '"failed") (284 . |retractIfCan|) - (289 . |retractIfCan|) (294 . |random|) (298 . |zero?|) - (303 . |random|) (|Vector| 6) (307 . |coerce|) - (312 . |horizConcat|) (318 . |reducedSystem|) - (323 . |minRowIndex|) (328 . |maxRowIndex|) - (333 . |minColIndex|) (338 . |maxColIndex|) - (343 . |subMatrix|) (|Vector| 7) (352 . |column|) - (|Record| (|:| |mat| 23) (|:| |vec| 108)) (|Vector| $) - |QFCAT-;reducedSystem;MVR;27| (|Union| 85 '"failed") - (|Matrix| 66) (|Vector| 66) - (|Record| (|:| |mat| 114) (|:| |vec| 115)) (|List| 55) + (240 . |patternMatch|) (|PatternMatchResult| 41 $) + (247 . |patternMatch|) (|Fraction| 67) (254 . |numer|) + (259 . |coerce|) (264 . |denom|) (269 . /) + (275 . |coerce|) (280 . |retract|) (285 . |retract|) + (|Union| 67 '"failed") (290 . |retractIfCan|) + (295 . |retractIfCan|) (300 . |random|) (304 . |zero?|) + (309 . |random|) (|Vector| 6) (313 . |coerce|) + (318 . |horizConcat|) (324 . |reducedSystem|) + (329 . |minRowIndex|) (334 . |maxRowIndex|) (339 . |One|) + (343 . |minColIndex|) (348 . +) (354 . |maxColIndex|) + (359 . |subMatrix|) (|Vector| 7) (368 . |column|) + (|Record| (|:| |mat| 23) (|:| |vec| 111)) (|Vector| $) + |QFCAT-;reducedSystem;MVR;27| (|Union| 86 '"failed") + (|Matrix| 67) (|Vector| 67) + (|Record| (|:| |mat| 117) (|:| |vec| 118)) (|List| 56) (|List| 29) (|OutputForm|)) - '#(|retractIfCan| 358 |retract| 368 |reducedSystem| 378 - |random| 389 |patternMatch| 393 |numerator| 407 |nextItem| - 412 |map| 417 |init| 423 |fractionPart| 427 - |differentiate| 432 |denominator| 438 |convert| 443 - |coerce| 468 |characteristic| 478 < 482) + '#(|retractIfCan| 374 |retract| 384 |reducedSystem| 394 + |random| 405 |patternMatch| 409 |numerator| 423 |nextItem| + 428 |map| 433 |init| 439 |fractionPart| 443 + |differentiate| 448 |denominator| 454 |convert| 459 + |coerce| 484 |characteristic| 494 < 498) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 112 + (|makeByteWordVec2| 115 '(1 6 7 0 8 1 6 0 7 9 1 6 7 0 11 0 7 0 13 0 7 0 14 2 6 0 7 7 15 0 0 0 16 1 7 17 0 18 0 6 0 19 1 0 17 0 20 1 25 23 24 26 0 7 29 30 2 7 0 0 0 32 2 7 0 0 0 33 2 7 0 0 34 35 1 7 37 0 38 2 37 0 0 0 39 1 0 37 0 40 1 7 41 0 42 2 41 0 - 0 0 43 1 0 41 0 44 1 7 45 0 46 1 0 45 - 0 47 2 7 48 0 0 49 2 0 48 0 0 50 0 7 - 0 51 1 6 7 0 52 2 6 0 0 0 53 1 0 0 0 - 54 1 7 0 55 56 1 0 0 55 57 1 6 7 0 58 - 1 7 55 0 59 1 0 55 0 60 1 6 61 0 62 1 - 7 63 0 64 1 0 63 0 65 1 7 67 0 68 2 - 67 0 0 0 69 1 0 67 0 70 3 72 71 6 67 - 71 73 3 0 74 0 67 74 75 1 7 76 0 77 2 - 76 0 0 0 78 1 0 76 0 79 3 81 80 6 76 - 80 82 3 0 83 0 76 83 84 1 85 66 0 86 - 1 6 0 66 87 1 85 66 0 88 2 6 0 0 0 89 - 1 0 0 85 90 1 7 66 0 91 1 0 66 0 92 1 - 7 93 0 94 1 0 93 0 95 0 7 0 96 1 7 48 - 0 97 0 0 0 98 1 24 0 99 100 2 24 0 0 - 0 101 1 6 23 27 102 1 23 66 0 103 1 - 23 66 0 104 1 23 66 0 105 1 23 66 0 - 106 5 23 0 0 66 66 66 66 107 2 23 108 - 0 66 109 1 0 93 0 95 1 0 63 0 65 1 0 - 66 0 92 1 0 55 0 60 2 0 110 27 111 - 112 1 0 23 27 28 0 0 0 98 3 0 83 0 76 - 83 84 3 0 74 0 67 74 75 1 0 0 0 10 1 + 0 0 43 1 0 41 0 44 1 7 45 0 46 2 45 0 + 0 0 47 1 0 45 0 48 2 7 49 0 0 50 2 0 + 49 0 0 51 0 7 0 52 1 6 7 0 53 2 6 0 0 + 0 54 1 0 0 0 55 1 7 0 56 57 1 0 0 56 + 58 1 6 7 0 59 1 7 56 0 60 1 0 56 0 61 + 1 6 62 0 63 1 7 64 0 65 1 0 64 0 66 1 + 7 68 0 69 2 68 0 0 0 70 1 0 68 0 71 3 + 73 72 6 68 72 74 3 0 75 0 68 75 76 1 + 7 77 0 78 2 77 0 0 0 79 1 0 77 0 80 3 + 82 81 6 77 81 83 3 0 84 0 77 84 85 1 + 86 67 0 87 1 6 0 67 88 1 86 67 0 89 2 + 6 0 0 0 90 1 0 0 86 91 1 7 67 0 92 1 + 0 67 0 93 1 7 94 0 95 1 0 94 0 96 0 7 + 0 97 1 7 49 0 98 0 0 0 99 1 24 0 100 + 101 2 24 0 0 0 102 1 6 23 27 103 1 23 + 67 0 104 1 23 67 0 105 0 67 0 106 1 + 23 67 0 107 2 67 0 0 0 108 1 23 67 0 + 109 5 23 0 0 67 67 67 67 110 2 23 111 + 0 67 112 1 0 94 0 96 1 0 64 0 66 1 0 + 67 0 93 1 0 56 0 61 2 0 113 27 114 + 115 1 0 23 27 28 0 0 0 99 3 0 84 0 77 + 84 85 3 0 75 0 68 75 76 1 0 0 0 10 1 0 17 0 20 2 0 0 21 0 22 0 0 0 16 1 0 - 0 0 54 2 0 0 0 21 36 1 0 0 0 12 1 0 - 45 0 47 1 0 37 0 40 1 0 41 0 44 1 0 - 67 0 70 1 0 76 0 79 1 0 0 55 57 1 0 0 - 85 90 0 0 29 31 2 0 48 0 0 50))))) + 0 0 55 2 0 0 0 21 36 1 0 0 0 12 1 0 + 45 0 48 1 0 37 0 40 1 0 41 0 44 1 0 + 68 0 71 1 0 77 0 80 1 0 0 56 58 1 0 0 + 86 91 0 0 29 31 2 0 49 0 0 51))))) '|lookupComplete|)) diff --git a/src/algebra/strap/RNS-.lsp b/src/algebra/strap/RNS-.lsp index 042d128b..04fe9f0d 100644 --- a/src/algebra/strap/RNS-.lsp +++ b/src/algebra/strap/RNS-.lsp @@ -37,102 +37,102 @@ (DEFUN |RNS-;characteristic;Nni;1| ($) (DECLARE (IGNORE $)) 0) (DEFUN |RNS-;fractionPart;2S;2| (|x| $) - (SPADCALL |x| (SPADCALL |x| (|getShellEntry| $ 9)) - (|getShellEntry| $ 10))) + (SPADCALL |x| (SPADCALL |x| (|getShellEntry| $ 10)) + (|getShellEntry| $ 11))) (DEFUN |RNS-;truncate;2S;3| (|x| $) (COND - ((SPADCALL |x| (|getShellEntry| $ 13)) + ((SPADCALL |x| (|getShellEntry| $ 14)) (SPADCALL - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 14)) - (|getShellEntry| $ 15)) - (|getShellEntry| $ 14))) - ('T (SPADCALL |x| (|getShellEntry| $ 15))))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 15)) + (|getShellEntry| $ 16)) + (|getShellEntry| $ 15))) + ('T (SPADCALL |x| (|getShellEntry| $ 16))))) (DEFUN |RNS-;round;2S;4| (|x| $) (COND - ((SPADCALL |x| (|getShellEntry| $ 13)) + ((SPADCALL |x| (|getShellEntry| $ 14)) (SPADCALL (SPADCALL |x| - (SPADCALL (|spadConstant| $ 17) - (SPADCALL 2 (|getShellEntry| $ 19)) - (|getShellEntry| $ 20)) - (|getShellEntry| $ 10)) - (|getShellEntry| $ 9))) + (SPADCALL (|spadConstant| $ 18) + (SPADCALL 2 (|getShellEntry| $ 20)) + (|getShellEntry| $ 21)) + (|getShellEntry| $ 11)) + (|getShellEntry| $ 10))) ('T (SPADCALL (SPADCALL |x| - (SPADCALL (|spadConstant| $ 17) - (SPADCALL 2 (|getShellEntry| $ 19)) - (|getShellEntry| $ 20)) - (|getShellEntry| $ 21)) - (|getShellEntry| $ 9))))) + (SPADCALL (|spadConstant| $ 18) + (SPADCALL 2 (|getShellEntry| $ 20)) + (|getShellEntry| $ 21)) + (|getShellEntry| $ 24)) + (|getShellEntry| $ 10))))) -(DEFUN |RNS-;norm;2S;5| (|x| $) (SPADCALL |x| (|getShellEntry| $ 23))) +(DEFUN |RNS-;norm;2S;5| (|x| $) (SPADCALL |x| (|getShellEntry| $ 26))) (DEFUN |RNS-;coerce;FS;6| (|x| $) (SPADCALL - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) - (|getShellEntry| $ 19)) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 27)) - (|getShellEntry| $ 19)) - (|getShellEntry| $ 20))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 29)) + (|getShellEntry| $ 20)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30)) + (|getShellEntry| $ 20)) + (|getShellEntry| $ 21))) (DEFUN |RNS-;convert;SP;7| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 30)) - (|getShellEntry| $ 32))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 33)) + (|getShellEntry| $ 35))) (DEFUN |RNS-;floor;2S;8| (|x| $) (PROG (|x1|) (RETURN (SEQ (LETT |x1| - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 34)) - (|getShellEntry| $ 19)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 37)) + (|getShellEntry| $ 20)) |RNS-;floor;2S;8|) (EXIT (COND - ((SPADCALL |x| |x1| (|getShellEntry| $ 35)) |x|) - ((SPADCALL |x| (|spadConstant| $ 36) - (|getShellEntry| $ 37)) - (SPADCALL |x1| (|spadConstant| $ 17) - (|getShellEntry| $ 10))) + ((SPADCALL |x| |x1| (|getShellEntry| $ 38)) |x|) + ((SPADCALL |x| (|spadConstant| $ 39) + (|getShellEntry| $ 41)) + (SPADCALL |x1| (|spadConstant| $ 18) + (|getShellEntry| $ 11))) ('T |x1|))))))) (DEFUN |RNS-;ceiling;2S;9| (|x| $) (PROG (|x1|) (RETURN (SEQ (LETT |x1| - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 34)) - (|getShellEntry| $ 19)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 37)) + (|getShellEntry| $ 20)) |RNS-;ceiling;2S;9|) (EXIT (COND - ((SPADCALL |x| |x1| (|getShellEntry| $ 35)) |x|) - ((SPADCALL |x| (|spadConstant| $ 36) - (|getShellEntry| $ 37)) + ((SPADCALL |x| |x1| (|getShellEntry| $ 38)) |x|) + ((SPADCALL |x| (|spadConstant| $ 39) + (|getShellEntry| $ 41)) |x1|) ('T - (SPADCALL |x1| (|spadConstant| $ 17) - (|getShellEntry| $ 21))))))))) + (SPADCALL |x1| (|spadConstant| $ 18) + (|getShellEntry| $ 24))))))))) (DEFUN |RNS-;patternMatch;SP2Pmr;10| (|x| |p| |l| $) (PROG (|r|) (RETURN (SEQ (COND - ((SPADCALL |p| (|getShellEntry| $ 40)) - (SPADCALL |p| |x| |l| (|getShellEntry| $ 42))) - ((SPADCALL |p| (|getShellEntry| $ 43)) - (SEQ (LETT |r| (SPADCALL |p| (|getShellEntry| $ 45)) + ((SPADCALL |p| (|getShellEntry| $ 45)) + (SPADCALL |p| |x| |l| (|getShellEntry| $ 47))) + ((SPADCALL |p| (|getShellEntry| $ 48)) + (SEQ (LETT |r| (SPADCALL |p| (|getShellEntry| $ 50)) |RNS-;patternMatch;SP2Pmr;10|) (EXIT (COND ((QEQCAR |r| 0) (COND ((SPADCALL (SPADCALL |x| - (|getShellEntry| $ 30)) - (QCDR |r|) (|getShellEntry| $ 46)) + (|getShellEntry| $ 33)) + (QCDR |r|) (|getShellEntry| $ 51)) |l|) - ('T (SPADCALL (|getShellEntry| $ 47))))) - ('T (SPADCALL (|getShellEntry| $ 47))))))) - ('T (SPADCALL (|getShellEntry| $ 47)))))))) + ('T (SPADCALL (|getShellEntry| $ 52))))) + ('T (SPADCALL (|getShellEntry| $ 52))))))) + ('T (SPADCALL (|getShellEntry| $ 52)))))))) (DEFUN |RealNumberSystem&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) @@ -140,7 +140,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|RealNumberSystem&|)) (LETT |dv$| (LIST '|RealNumberSystem&| |dv$1|) . #0#) - (LETT $ (|newShell| 52) . #0#) + (LETT $ (|newShell| 57) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -150,40 +150,42 @@ (MAKEPROP '|RealNumberSystem&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) - (|NonNegativeInteger|) |RNS-;characteristic;Nni;1| - (0 . |truncate|) (5 . -) |RNS-;fractionPart;2S;2| - (|Boolean|) (11 . |negative?|) (16 . -) (21 . |floor|) - |RNS-;truncate;2S;3| (26 . |One|) (|Integer|) - (30 . |coerce|) (35 . /) (41 . +) |RNS-;round;2S;4| - (47 . |abs|) |RNS-;norm;2S;5| (|Fraction| 18) - (52 . |numer|) (57 . |denom|) |RNS-;coerce;FS;6| (|Float|) - (62 . |convert|) (|Pattern| 29) (67 . |coerce|) - |RNS-;convert;SP;7| (72 . |wholePart|) (77 . =) - (83 . |Zero|) (87 . <) |RNS-;floor;2S;8| - |RNS-;ceiling;2S;9| (93 . |generic?|) - (|PatternMatchResult| 29 6) (98 . |addMatch|) - (105 . |constant?|) (|Union| 29 '"failed") - (110 . |retractIfCan|) (115 . =) (121 . |failed|) - (|PatternMatchResult| 29 $) |RNS-;patternMatch;SP2Pmr;10| + (|NonNegativeInteger|) (0 . |Zero|) + |RNS-;characteristic;Nni;1| (4 . |truncate|) (9 . -) + |RNS-;fractionPart;2S;2| (|Boolean|) (15 . |negative?|) + (20 . -) (25 . |floor|) |RNS-;truncate;2S;3| (30 . |One|) + (|Integer|) (34 . |coerce|) (39 . /) (|PositiveInteger|) + (45 . |One|) (49 . +) |RNS-;round;2S;4| (55 . |abs|) + |RNS-;norm;2S;5| (|Fraction| 19) (60 . |numer|) + (65 . |denom|) |RNS-;coerce;FS;6| (|Float|) + (70 . |convert|) (|Pattern| 32) (75 . |coerce|) + |RNS-;convert;SP;7| (80 . |wholePart|) (85 . =) + (91 . |Zero|) (95 . |Zero|) (99 . <) (105 . |One|) + |RNS-;floor;2S;8| |RNS-;ceiling;2S;9| (109 . |generic?|) + (|PatternMatchResult| 32 6) (114 . |addMatch|) + (121 . |constant?|) (|Union| 32 '"failed") + (126 . |retractIfCan|) (131 . =) (137 . |failed|) + (|PatternMatchResult| 32 $) |RNS-;patternMatch;SP2Pmr;10| (|DoubleFloat|) (|OutputForm|)) - '#(|truncate| 125 |round| 130 |patternMatch| 135 |norm| 142 - |fractionPart| 147 |floor| 152 |convert| 157 |coerce| 162 - |characteristic| 172 |ceiling| 176) + '#(|truncate| 141 |round| 146 |patternMatch| 151 |norm| 158 + |fractionPart| 163 |floor| 168 |convert| 173 |coerce| 178 + |characteristic| 188 |ceiling| 192) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 49 - '(1 6 0 0 9 2 6 0 0 0 10 1 6 12 0 13 1 - 6 0 0 14 1 6 0 0 15 0 6 0 17 1 6 0 18 - 19 2 6 0 0 0 20 2 6 0 0 0 21 1 6 0 0 - 23 1 25 18 0 26 1 25 18 0 27 1 6 29 0 - 30 1 31 0 29 32 1 6 18 0 34 2 6 12 0 - 0 35 0 6 0 36 2 6 12 0 0 37 1 31 12 0 - 40 3 41 0 31 6 0 42 1 31 12 0 43 1 31 - 44 0 45 2 29 12 0 0 46 0 41 0 47 1 0 - 0 0 16 1 0 0 0 22 3 0 48 0 31 48 49 1 - 0 0 0 24 1 0 0 0 11 1 0 0 0 38 1 0 31 - 0 33 1 0 0 25 28 1 0 0 25 28 0 0 7 8 - 1 0 0 0 39))))) + (|makeByteWordVec2| 54 + '(0 7 0 8 1 6 0 0 10 2 6 0 0 0 11 1 6 + 13 0 14 1 6 0 0 15 1 6 0 0 16 0 6 0 + 18 1 6 0 19 20 2 6 0 0 0 21 0 22 0 23 + 2 6 0 0 0 24 1 6 0 0 26 1 28 19 0 29 + 1 28 19 0 30 1 6 32 0 33 1 34 0 32 35 + 1 6 19 0 37 2 6 13 0 0 38 0 6 0 39 0 + 19 0 40 2 6 13 0 0 41 0 19 0 42 1 34 + 13 0 45 3 46 0 34 6 0 47 1 34 13 0 48 + 1 34 49 0 50 2 32 13 0 0 51 0 46 0 52 + 1 0 0 0 17 1 0 0 0 25 3 0 53 0 34 53 + 54 1 0 0 0 27 1 0 0 0 12 1 0 0 0 43 1 + 0 34 0 36 1 0 0 28 31 1 0 0 28 31 0 0 + 7 9 1 0 0 0 44))))) '|lookupComplete|)) diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp index f656b3f8..a3d38ee1 100644 --- a/src/algebra/strap/SINT.lsp +++ b/src/algebra/strap/SINT.lsp @@ -256,12 +256,12 @@ (DEFUN |SINT;writeOMSingleInt| (|dev| |x| $) (SEQ (COND ((QSLESSP |x| 0) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 9)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 13)) (SPADCALL |dev| "arith1" "unaryminus" - (|getShellEntry| $ 11)) - (SPADCALL |dev| (QSMINUS |x|) (|getShellEntry| $ 12)) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 13))))) - ('T (SPADCALL |dev| |x| (|getShellEntry| $ 12)))))) + (|getShellEntry| $ 15)) + (SPADCALL |dev| (QSMINUS |x|) (|getShellEntry| $ 18)) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 19))))) + ('T (SPADCALL |dev| |x| (|getShellEntry| $ 18)))))) (DEFUN |SINT;OMwrite;$S;2| (|x| $) (PROG (|sp| |dev| |s|) @@ -269,13 +269,13 @@ (SEQ (LETT |s| "" |SINT;OMwrite;$S;2|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SINT;OMwrite;$S;2|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 15)) - (|getShellEntry| $ 16)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 21)) + (|getShellEntry| $ 22)) |SINT;OMwrite;$S;2|) - (SPADCALL |dev| (|getShellEntry| $ 17)) + (SPADCALL |dev| (|getShellEntry| $ 23)) (|SINT;writeOMSingleInt| |dev| |x| $) - (SPADCALL |dev| (|getShellEntry| $ 18)) - (SPADCALL |dev| (|getShellEntry| $ 19)) + (SPADCALL |dev| (|getShellEntry| $ 24)) + (SPADCALL |dev| (|getShellEntry| $ 25)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SINT;OMwrite;$S;2|) (EXIT |s|))))) @@ -285,36 +285,36 @@ (SEQ (LETT |s| "" |SINT;OMwrite;$BS;3|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SINT;OMwrite;$BS;3|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 15)) - (|getShellEntry| $ 16)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 21)) + (|getShellEntry| $ 22)) |SINT;OMwrite;$BS;3|) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17)))) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23)))) (|SINT;writeOMSingleInt| |dev| |x| $) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18)))) - (SPADCALL |dev| (|getShellEntry| $ 19)) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 24)))) + (SPADCALL |dev| (|getShellEntry| $ 25)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SINT;OMwrite;$BS;3|) (EXIT |s|))))) (DEFUN |SINT;OMwrite;Omd$V;4| (|dev| |x| $) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 17)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 23)) (|SINT;writeOMSingleInt| |dev| |x| $) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 18))))) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 24))))) (DEFUN |SINT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $) - (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17)))) + (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 23)))) (|SINT;writeOMSingleInt| |dev| |x| $) (EXIT (COND - (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18))))))) + (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 24))))))) (DEFUN |SINT;reducedSystem;MM;6| (|m| $) (DECLARE (IGNORE $)) |m|) (DEFUN |SINT;coerce;$Of;7| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 29))) + (SPADCALL |x| (|getShellEntry| $ 34))) (DEFUN |SINT;convert;$I;8| (|x| $) (DECLARE (IGNORE $)) |x|) (DEFUN |SINT;*;I2$;9| (|i| |y| $) - (QSTIMES (SPADCALL |i| (|getShellEntry| $ 32)) |y|)) + (QSTIMES (SPADCALL |i| (|getShellEntry| $ 36)) |y|)) (DEFUN |SINT;Zero;$;10| ($) (DECLARE (IGNORE $)) 0) @@ -377,7 +377,7 @@ (QSTIMES |x| |y|)) (DEFUN |SINT;**;$Nni$;31| (|x| |n| $) - (SPADCALL (EXPT |x| |n|) (|getShellEntry| $ 32))) + (SPADCALL (EXPT |x| |n|) (|getShellEntry| $ 36))) (DEFUN |SINT;quo;3$;32| (|x| |y| $) (DECLARE (IGNORE $)) @@ -505,7 +505,7 @@ (RETURN (PROGN (LETT |dv$| '(|SingleInteger|) . #0=(|SingleInteger|)) - (LETT $ (|newShell| 107) . #0#) + (LETT $ (|newShell| 111) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -516,20 +516,21 @@ $)))) (MAKEPROP '|SingleInteger| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL (|Integer|) '|seed| (|Void|) - (|OpenMathDevice|) (0 . |OMputApp|) (|String|) - (5 . |OMputSymbol|) (12 . |OMputInteger|) - (18 . |OMputEndApp|) (|OpenMathEncoding|) - (23 . |OMencodingXML|) (27 . |OMopenString|) - (33 . |OMputObject|) (38 . |OMputEndObject|) - (43 . |OMclose|) |SINT;OMwrite;$S;2| (|Boolean|) - |SINT;OMwrite;$BS;3| |SINT;OMwrite;Omd$V;4| - |SINT;OMwrite;Omd$BV;5| (|Matrix| 5) (|Matrix| $) - |SINT;reducedSystem;MM;6| (|OutputForm|) (48 . |coerce|) - |SINT;coerce;$Of;7| |SINT;convert;$I;8| (53 . |coerce|) - |SINT;*;I2$;9| + (LIST '#(NIL NIL NIL NIL NIL (|Integer|) '|seed| (CONS IDENTITY (FUNCALL (|dispatchFunction| |SINT;Zero;$;10|) $)) + (0 . |Zero|) (|Boolean|) |SINT;<;2$B;24| (|Void|) + (|OpenMathDevice|) (4 . |OMputApp|) (|String|) + (9 . |OMputSymbol|) |SINT;-;2$;27| |SINT;convert;$I;8| + (16 . |OMputInteger|) (22 . |OMputEndApp|) + (|OpenMathEncoding|) (27 . |OMencodingXML|) + (31 . |OMopenString|) (37 . |OMputObject|) + (42 . |OMputEndObject|) (47 . |OMclose|) + |SINT;OMwrite;$S;2| |SINT;OMwrite;$BS;3| + |SINT;OMwrite;Omd$V;4| |SINT;OMwrite;Omd$BV;5| + (|Matrix| 5) (|Matrix| $) |SINT;reducedSystem;MM;6| + (|OutputForm|) (52 . |coerce|) |SINT;coerce;$Of;7| + (57 . |coerce|) |SINT;*;3$;30| |SINT;*;I2$;9| (CONS IDENTITY (FUNCALL (|dispatchFunction| |SINT;One;$;11|) $)) |SINT;base;$;12| @@ -540,57 +541,56 @@ |SINT;=;2$B;15| |SINT;~;2$;16| |SINT;not;2$;17| |SINT;/\\;3$;18| |SINT;\\/;3$;19| |SINT;Not;2$;20| |SINT;And;3$;21| |SINT;Or;3$;22| |SINT;xor;3$;23| - |SINT;<;2$B;24| |SINT;inc;2$;25| |SINT;dec;2$;26| - |SINT;-;2$;27| |SINT;+;3$;28| |SINT;-;3$;29| - |SINT;*;3$;30| (|NonNegativeInteger|) |SINT;**;$Nni$;31| + |SINT;inc;2$;25| |SINT;dec;2$;26| |SINT;+;3$;28| + |SINT;-;3$;29| (|NonNegativeInteger|) |SINT;**;$Nni$;31| |SINT;quo;3$;32| |SINT;rem;3$;33| (|Record| (|:| |quotient| $) (|:| |remainder| $)) |SINT;divide;2$R;34| |SINT;gcd;3$;35| |SINT;abs;2$;36| - |SINT;odd?;$B;37| |SINT;zero?;$B;38| |SINT;one?;$B;39| - |SINT;max;3$;40| |SINT;min;3$;41| (|SingleInteger|) - |SINT;hash;2$;42| |SINT;length;2$;43| |SINT;shift;3$;44| - |SINT;mulmod;4$;45| |SINT;addmod;4$;46| + |SINT;odd?;$B;37| |SINT;zero?;$B;38| (62 . |One|) + |SINT;one?;$B;39| |SINT;max;3$;40| |SINT;min;3$;41| + (|SingleInteger|) |SINT;hash;2$;42| |SINT;length;2$;43| + |SINT;shift;3$;44| |SINT;mulmod;4$;45| |SINT;addmod;4$;46| |SINT;submod;4$;47| |SINT;negative?;$B;48| - |SINT;size;Nni;49| (|PositiveInteger|) |SINT;index;Pi$;50| - |SINT;lookup;$Pi;51| (|Vector| 5) - (|Record| (|:| |mat| 25) (|:| |vec| 80)) (|Vector| $) + |SINT;size;Nni;49| (|PositiveInteger|) (66 . +) (72 . -) + |SINT;index;Pi$;50| |SINT;lookup;$Pi;51| (|Vector| 5) + (|Record| (|:| |mat| 30) (|:| |vec| 84)) (|Vector| $) |SINT;reducedSystem;MVR;52| |SINT;positiveRemainder;3$;53| |SINT;coerce;I$;54| |SINT;random;$;55| |SINT;random;2$;56| (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) |SINT;unitNormal;$R;57| (|Fraction| 5) - (|Union| 90 '"failed") (|Union| $ '"failed") (|Float|) + (|Union| 94 '"failed") (|Union| $ '"failed") (|Float|) (|DoubleFloat|) (|Pattern| 5) (|PatternMatchResult| 5 $) (|InputForm|) (|Union| 5 '"failed") (|List| $) - (|Record| (|:| |coef| 99) (|:| |generator| $)) - (|Union| 99 '"failed") + (|Record| (|:| |coef| 103) (|:| |generator| $)) + (|Union| 103 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 103 '"failed") (|Factored| $) + (|Union| 107 '"failed") (|Factored| $) (|SparseUnivariatePolynomial| $)) - '#(~= 58 ~ 64 |zero?| 69 |xor| 74 |unitNormal| 80 - |unitCanonical| 85 |unit?| 90 |symmetricRemainder| 95 - |subtractIfCan| 101 |submod| 107 |squareFreePart| 114 - |squareFree| 119 |sizeLess?| 124 |size| 130 |sign| 134 - |shift| 139 |sample| 145 |retractIfCan| 149 |retract| 154 - |rem| 159 |reducedSystem| 165 |recip| 176 |rationalIfCan| - 181 |rational?| 186 |rational| 191 |random| 196 |quo| 205 - |principalIdeal| 211 |prime?| 216 |powmod| 221 - |positiveRemainder| 228 |positive?| 234 |permutation| 239 - |patternMatch| 245 |one?| 252 |odd?| 257 |not| 262 - |nextItem| 267 |negative?| 272 |multiEuclidean| 277 - |mulmod| 283 |min| 290 |max| 300 |mask| 310 |lookup| 315 - |length| 320 |lcm| 325 |latex| 336 |invmod| 341 |init| 347 - |index| 351 |inc| 356 |hash| 361 |gcdPolynomial| 366 |gcd| - 372 |factorial| 383 |factor| 388 |extendedEuclidean| 393 - |exquo| 406 |expressIdealMember| 412 |even?| 418 - |euclideanSize| 423 |divide| 428 |differentiate| 434 |dec| - 445 |copy| 450 |convert| 455 |coerce| 480 |characteristic| - 500 |bit?| 504 |binomial| 510 |base| 516 |associates?| 520 - |addmod| 526 |abs| 533 |\\/| 538 |Zero| 544 |Or| 548 |One| - 554 |OMwrite| 558 |Not| 582 D 587 |And| 598 >= 604 > 610 = - 616 <= 622 < 628 |/\\| 634 - 640 + 651 ** 657 * 669) + '#(~= 78 ~ 84 |zero?| 89 |xor| 94 |unitNormal| 100 + |unitCanonical| 105 |unit?| 110 |symmetricRemainder| 115 + |subtractIfCan| 121 |submod| 127 |squareFreePart| 134 + |squareFree| 139 |sizeLess?| 144 |size| 150 |sign| 154 + |shift| 159 |sample| 165 |retractIfCan| 169 |retract| 174 + |rem| 179 |reducedSystem| 185 |recip| 196 |rationalIfCan| + 201 |rational?| 206 |rational| 211 |random| 216 |quo| 225 + |principalIdeal| 231 |prime?| 236 |powmod| 241 + |positiveRemainder| 248 |positive?| 254 |permutation| 259 + |patternMatch| 265 |one?| 272 |odd?| 277 |not| 282 + |nextItem| 287 |negative?| 292 |multiEuclidean| 297 + |mulmod| 303 |min| 310 |max| 320 |mask| 330 |lookup| 335 + |length| 340 |lcm| 345 |latex| 356 |invmod| 361 |init| 367 + |index| 371 |inc| 376 |hash| 381 |gcdPolynomial| 386 |gcd| + 392 |factorial| 403 |factor| 408 |extendedEuclidean| 413 + |exquo| 426 |expressIdealMember| 432 |even?| 438 + |euclideanSize| 443 |divide| 448 |differentiate| 454 |dec| + 465 |copy| 470 |convert| 475 |coerce| 500 |characteristic| + 520 |bit?| 524 |binomial| 530 |base| 536 |associates?| 540 + |addmod| 546 |abs| 553 |\\/| 558 |Zero| 564 |Or| 568 |One| + 574 |OMwrite| 578 |Not| 602 D 607 |And| 618 >= 624 > 630 = + 636 <= 642 < 648 |/\\| 654 - 660 + 671 ** 677 * 689) '((|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) (|noZeroDivisors| . 0) @@ -636,56 +636,58 @@ (|OrderedSet|) (|AbelianSemiGroup|) (|SemiGroup|) (|Logic|) (|RealConstant|) (|RetractableTo| 5) (|SetCategory|) - (|OpenMath|) (|ConvertibleTo| 93) - (|ConvertibleTo| 94) + (|OpenMath|) (|ConvertibleTo| 97) + (|ConvertibleTo| 98) (|CombinatorialFunctionCategory|) - (|ConvertibleTo| 95) - (|ConvertibleTo| 97) (|ConvertibleTo| 5) - (|CoercibleFrom| $$) (|CoercibleFrom| 5) - (|BasicType|) (|CoercibleTo| 28)) - (|makeByteWordVec2| 106 - '(1 8 7 0 9 3 8 7 0 10 10 11 2 8 7 0 5 - 12 1 8 7 0 13 0 14 0 15 2 8 0 10 14 - 16 1 8 7 0 17 1 8 7 0 18 1 8 7 0 19 1 - 5 28 0 29 1 0 0 5 32 2 0 21 0 0 1 1 0 - 0 0 40 1 0 21 0 64 2 0 0 0 0 47 1 0 - 88 0 89 1 0 0 0 1 1 0 21 0 1 2 0 0 0 - 0 1 2 0 92 0 0 1 3 0 0 0 0 0 74 1 0 0 - 0 1 1 0 105 0 1 2 0 21 0 0 1 0 0 55 - 76 1 0 5 0 1 2 0 0 0 0 71 0 0 0 1 1 0 - 98 0 1 1 0 5 0 1 2 0 0 0 0 58 1 0 25 - 26 27 2 0 81 26 82 83 1 0 92 0 1 1 0 - 91 0 1 1 0 21 0 1 1 0 90 0 1 1 0 0 0 - 87 0 0 0 86 2 0 0 0 0 57 1 0 100 99 1 - 1 0 21 0 1 3 0 0 0 0 0 1 2 0 0 0 0 84 - 1 0 21 0 1 2 0 0 0 0 1 3 0 96 0 95 96 - 1 1 0 21 0 65 1 0 21 0 63 1 0 0 0 41 - 1 0 92 0 1 1 0 21 0 75 2 0 101 99 0 1 - 3 0 0 0 0 0 72 0 0 0 38 2 0 0 0 0 67 - 0 0 0 37 2 0 0 0 0 66 1 0 0 0 1 1 0 - 77 0 79 1 0 0 0 70 1 0 0 99 1 2 0 0 0 - 0 1 1 0 10 0 1 2 0 0 0 0 1 0 0 0 1 1 - 0 0 77 78 1 0 0 0 49 1 0 68 0 69 2 0 - 106 106 106 1 1 0 0 99 1 2 0 0 0 0 61 - 1 0 0 0 1 1 0 105 0 1 2 0 102 0 0 1 3 - 0 104 0 0 0 1 2 0 92 0 0 1 2 0 101 99 - 0 1 1 0 21 0 1 1 0 55 0 1 2 0 59 0 0 - 60 1 0 0 0 1 2 0 0 0 55 1 1 0 0 0 50 - 1 0 0 0 1 1 0 93 0 1 1 0 94 0 1 1 0 - 95 0 1 1 0 97 0 1 1 0 5 0 31 1 0 0 5 - 85 1 0 0 0 1 1 0 0 5 85 1 0 28 0 30 0 - 0 55 1 2 0 21 0 0 1 2 0 0 0 0 1 0 0 0 - 36 2 0 21 0 0 1 3 0 0 0 0 0 73 1 0 0 - 0 62 2 0 0 0 0 43 0 0 0 34 2 0 0 0 0 - 46 0 0 0 35 2 0 7 8 0 23 3 0 7 8 0 21 - 24 2 0 10 0 21 22 1 0 10 0 20 1 0 0 0 - 44 1 0 0 0 1 2 0 0 0 55 1 2 0 0 0 0 - 45 2 0 21 0 0 1 2 0 21 0 0 1 2 0 21 0 - 0 39 2 0 21 0 0 1 2 0 21 0 0 48 2 0 0 - 0 0 42 1 0 0 0 51 2 0 0 0 0 53 2 0 0 - 0 0 52 2 0 0 0 55 56 2 0 0 0 77 1 2 0 - 0 0 0 54 2 0 0 5 0 33 2 0 0 55 0 1 2 - 0 0 77 0 1))))) + (|ConvertibleTo| 99) + (|ConvertibleTo| 101) + (|ConvertibleTo| 5) (|CoercibleFrom| $$) + (|CoercibleFrom| 5) (|BasicType|) + (|CoercibleTo| 33)) + (|makeByteWordVec2| 110 + '(0 5 0 8 1 12 11 0 13 3 12 11 0 14 14 + 15 2 12 11 0 5 18 1 12 11 0 19 0 20 0 + 21 2 12 0 14 20 22 1 12 11 0 23 1 12 + 11 0 24 1 12 11 0 25 1 5 33 0 34 1 0 + 0 5 36 0 5 0 66 2 79 0 0 0 80 2 5 0 0 + 0 81 2 0 9 0 0 1 1 0 0 0 44 1 0 9 0 + 65 2 0 0 0 0 51 1 0 92 0 93 1 0 0 0 1 + 1 0 9 0 1 2 0 0 0 0 1 2 0 96 0 0 1 3 + 0 0 0 0 0 76 1 0 0 0 1 1 0 109 0 1 2 + 0 9 0 0 1 0 0 56 78 1 0 5 0 1 2 0 0 0 + 0 73 0 0 0 1 1 0 102 0 1 1 0 5 0 1 2 + 0 0 0 0 59 1 0 30 31 32 2 0 85 31 86 + 87 1 0 96 0 1 1 0 95 0 1 1 0 9 0 1 1 + 0 94 0 1 1 0 0 0 91 0 0 0 90 2 0 0 0 + 0 58 1 0 104 103 1 1 0 9 0 1 3 0 0 0 + 0 0 1 2 0 0 0 0 88 1 0 9 0 1 2 0 0 0 + 0 1 3 0 100 0 99 100 1 1 0 9 0 67 1 0 + 9 0 64 1 0 0 0 45 1 0 96 0 1 1 0 9 0 + 77 2 0 105 103 0 1 3 0 0 0 0 0 74 0 0 + 0 42 2 0 0 0 0 69 0 0 0 41 2 0 0 0 0 + 68 1 0 0 0 1 1 0 79 0 83 1 0 0 0 72 1 + 0 0 103 1 2 0 0 0 0 1 1 0 14 0 1 2 0 + 0 0 0 1 0 0 0 1 1 0 0 79 82 1 0 0 0 + 52 1 0 70 0 71 2 0 110 110 110 1 1 0 + 0 103 1 2 0 0 0 0 62 1 0 0 0 1 1 0 + 109 0 1 2 0 106 0 0 1 3 0 108 0 0 0 1 + 2 0 96 0 0 1 2 0 105 103 0 1 1 0 9 0 + 1 1 0 56 0 1 2 0 60 0 0 61 1 0 0 0 1 + 2 0 0 0 56 1 1 0 0 0 53 1 0 0 0 1 1 0 + 97 0 1 1 0 98 0 1 1 0 99 0 1 1 0 101 + 0 1 1 0 5 0 17 1 0 0 5 89 1 0 0 0 1 1 + 0 0 5 89 1 0 33 0 35 0 0 56 1 2 0 9 0 + 0 1 2 0 0 0 0 1 0 0 0 40 2 0 9 0 0 1 + 3 0 0 0 0 0 75 1 0 0 0 63 2 0 0 0 0 + 47 0 0 0 7 2 0 0 0 0 50 0 0 0 39 2 0 + 11 12 0 28 3 0 11 12 0 9 29 2 0 14 0 + 9 27 1 0 14 0 26 1 0 0 0 48 1 0 0 0 1 + 2 0 0 0 56 1 2 0 0 0 0 49 2 0 9 0 0 1 + 2 0 9 0 0 1 2 0 9 0 0 43 2 0 9 0 0 1 + 2 0 9 0 0 10 2 0 0 0 0 46 1 0 0 0 16 + 2 0 0 0 0 55 2 0 0 0 0 54 2 0 0 0 56 + 57 2 0 0 0 79 1 2 0 0 0 0 37 2 0 0 5 + 0 38 2 0 0 56 0 1 2 0 0 79 0 1))))) '|lookupComplete|)) (MAKEPROP '|SingleInteger| 'NILADIC T) diff --git a/src/algebra/strap/STAGG-.lsp b/src/algebra/strap/STAGG-.lsp index ab9ad2bc..0048a3c3 100644 --- a/src/algebra/strap/STAGG-.lsp +++ b/src/algebra/strap/STAGG-.lsp @@ -62,23 +62,23 @@ (|STAGG-;c2| |x| (LETT |x| (SPADCALL |x| - (|getShellEntry| $ 12)) + (|getShellEntry| $ 16)) |STAGG-;first;ANniA;3|) $) #0#) |STAGG-;first;ANniA;3|))) (LETT |i| (QSADD1 |i|) |STAGG-;first;ANniA;3|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 14)))))) + (|getShellEntry| $ 18)))))) (DEFUN |STAGG-;c2| (|x| |r| $) (COND - ((SPADCALL |x| (|getShellEntry| $ 17)) + ((SPADCALL |x| (|getShellEntry| $ 20)) (|error| "Index out of range")) - ('T (SPADCALL |x| (|getShellEntry| $ 18))))) + ('T (SPADCALL |x| (|getShellEntry| $ 21))))) (DEFUN |STAGG-;elt;AIS;5| (|x| |i| $) - (SEQ (LETT |i| (- |i| (SPADCALL |x| (|getShellEntry| $ 20))) + (SEQ (LETT |i| (- |i| (SPADCALL |x| (|getShellEntry| $ 23))) |STAGG-;elt;AIS;5|) (COND ((OR (< |i| 0) @@ -89,38 +89,38 @@ (|check-subtype| (COND ((< |i| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |i|)) - (|getShellEntry| $ 21)) + (|getShellEntry| $ 27)) |STAGG-;elt;AIS;5|) - (|getShellEntry| $ 17))) + (|getShellEntry| $ 20))) (EXIT (|error| "index out of range")))) - (EXIT (SPADCALL |x| (|getShellEntry| $ 18))))) + (EXIT (SPADCALL |x| (|getShellEntry| $ 21))))) (DEFUN |STAGG-;elt;AUsA;6| (|x| |i| $) (PROG (|l| |h| #0=#:G1418) (RETURN (SEQ (LETT |l| - (- (SPADCALL |i| (|getShellEntry| $ 24)) - (SPADCALL |x| (|getShellEntry| $ 20))) + (- (SPADCALL |i| (|getShellEntry| $ 30)) + (SPADCALL |x| (|getShellEntry| $ 23))) |STAGG-;elt;AUsA;6|) (EXIT (COND ((< |l| 0) (|error| "index out of range")) - ((NULL (SPADCALL |i| (|getShellEntry| $ 25))) + ((NULL (SPADCALL |i| (|getShellEntry| $ 31))) (SPADCALL (SPADCALL |x| (PROG1 |l| (|check-subtype| (COND ((< |l| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |l|)) - (|getShellEntry| $ 21)) - (|getShellEntry| $ 26))) + (|getShellEntry| $ 27)) + (|getShellEntry| $ 32))) ('T (SEQ (LETT |h| - (- (SPADCALL |i| (|getShellEntry| $ 27)) - (SPADCALL |x| (|getShellEntry| $ 20))) + (- (SPADCALL |i| (|getShellEntry| $ 33)) + (SPADCALL |x| (|getShellEntry| $ 23))) |STAGG-;elt;AUsA;6|) (EXIT (COND ((< |h| |l|) - (SPADCALL (|getShellEntry| $ 28))) + (SPADCALL (|getShellEntry| $ 34))) ('T (SPADCALL (SPADCALL |x| @@ -130,7 +130,7 @@ ((< |l| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |l|)) - (|getShellEntry| $ 21)) + (|getShellEntry| $ 27)) (PROG1 (LETT #0# (+ (- |h| |l|) 1) |STAGG-;elt;AUsA;6|) @@ -139,19 +139,19 @@ ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 29))))))))))))) + (|getShellEntry| $ 36))))))))))))) (DEFUN |STAGG-;concat;3A;7| (|x| |y| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 26)) |y| - (|getShellEntry| $ 31))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 32)) |y| + (|getShellEntry| $ 38))) (DEFUN |STAGG-;concat;LA;8| (|l| $) (COND - ((NULL |l|) (SPADCALL (|getShellEntry| $ 28))) + ((NULL |l|) (SPADCALL (|getShellEntry| $ 34))) ('T - (SPADCALL (SPADCALL (|SPADfirst| |l|) (|getShellEntry| $ 26)) - (SPADCALL (CDR |l|) (|getShellEntry| $ 34)) - (|getShellEntry| $ 31))))) + (SPADCALL (SPADCALL (|SPADfirst| |l|) (|getShellEntry| $ 32)) + (SPADCALL (CDR |l|) (|getShellEntry| $ 45)) + (|getShellEntry| $ 38))))) (DEFUN |STAGG-;map!;M2A;9| (|f| |l| $) (PROG (|y|) @@ -159,14 +159,14 @@ (SEQ (LETT |y| |l| |STAGG-;map!;M2A;9|) (SEQ G190 (COND - ((NULL (NOT (SPADCALL |l| (|getShellEntry| $ 17)))) + ((NULL (NOT (SPADCALL |l| (|getShellEntry| $ 20)))) (GO G191))) (SEQ (SPADCALL |l| (SPADCALL - (SPADCALL |l| (|getShellEntry| $ 18)) |f|) - (|getShellEntry| $ 36)) + (SPADCALL |l| (|getShellEntry| $ 21)) |f|) + (|getShellEntry| $ 47)) (EXIT (LETT |l| - (SPADCALL |l| (|getShellEntry| $ 12)) + (SPADCALL |l| (|getShellEntry| $ 16)) |STAGG-;map!;M2A;9|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |y|))))) @@ -177,17 +177,17 @@ (SEQ (LETT |y| |x| |STAGG-;fill!;ASA;10|) (SEQ G190 (COND - ((NULL (NOT (SPADCALL |y| (|getShellEntry| $ 17)))) + ((NULL (NOT (SPADCALL |y| (|getShellEntry| $ 20)))) (GO G191))) - (SEQ (SPADCALL |y| |s| (|getShellEntry| $ 36)) + (SEQ (SPADCALL |y| |s| (|getShellEntry| $ 47)) (EXIT (LETT |y| - (SPADCALL |y| (|getShellEntry| $ 12)) + (SPADCALL |y| (|getShellEntry| $ 16)) |STAGG-;fill!;ASA;10|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |x|))))) (DEFUN |STAGG-;setelt;AI2S;11| (|x| |i| |s| $) - (SEQ (LETT |i| (- |i| (SPADCALL |x| (|getShellEntry| $ 20))) + (SEQ (LETT |i| (- |i| (SPADCALL |x| (|getShellEntry| $ 23))) |STAGG-;setelt;AI2S;11|) (COND ((OR (< |i| 0) @@ -198,31 +198,31 @@ (|check-subtype| (COND ((< |i| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |i|)) - (|getShellEntry| $ 21)) + (|getShellEntry| $ 27)) |STAGG-;setelt;AI2S;11|) - (|getShellEntry| $ 17))) + (|getShellEntry| $ 20))) (EXIT (|error| "index out of range")))) - (EXIT (SPADCALL |x| |s| (|getShellEntry| $ 36))))) + (EXIT (SPADCALL |x| |s| (|getShellEntry| $ 47))))) (DEFUN |STAGG-;setelt;AUs2S;12| (|x| |i| |s| $) (PROG (|l| |h| #0=#:G1438 |z| |y|) (RETURN (SEQ (LETT |l| - (- (SPADCALL |i| (|getShellEntry| $ 24)) - (SPADCALL |x| (|getShellEntry| $ 20))) + (- (SPADCALL |i| (|getShellEntry| $ 30)) + (SPADCALL |x| (|getShellEntry| $ 23))) |STAGG-;setelt;AUs2S;12|) (EXIT (COND ((< |l| 0) (|error| "index out of range")) ('T (SEQ (LETT |h| (COND - ((SPADCALL |i| (|getShellEntry| $ 25)) + ((SPADCALL |i| (|getShellEntry| $ 31)) (- (SPADCALL |i| - (|getShellEntry| $ 27)) + (|getShellEntry| $ 33)) (SPADCALL |x| - (|getShellEntry| $ 20)))) + (|getShellEntry| $ 23)))) ('T - (SPADCALL |x| (|getShellEntry| $ 41)))) + (SPADCALL |x| (|getShellEntry| $ 52)))) |STAGG-;setelt;AUs2S;12|) (EXIT (COND ((< |h| |l|) |s|) @@ -236,7 +236,7 @@ ('T 'T)) '(|NonNegativeInteger|) |l|)) - (|getShellEntry| $ 21)) + (|getShellEntry| $ 27)) |STAGG-;setelt;AUs2S;12|) (LETT |z| (SPADCALL |y| @@ -249,32 +249,32 @@ ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 21)) + (|getShellEntry| $ 27)) |STAGG-;setelt;AUs2S;12|) (SEQ G190 (COND ((NULL (NOT (SPADCALL |y| |z| - (|getShellEntry| $ 42)))) + (|getShellEntry| $ 53)))) (GO G191))) (SEQ (SPADCALL |y| |s| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 47)) (EXIT (LETT |y| (SPADCALL |y| - (|getShellEntry| $ 12)) + (|getShellEntry| $ 16)) |STAGG-;setelt;AUs2S;12|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |s|))))))))))))) (DEFUN |STAGG-;concat!;3A;13| (|x| |y| $) (SEQ (COND - ((SPADCALL |x| (|getShellEntry| $ 17)) |y|) + ((SPADCALL |x| (|getShellEntry| $ 20)) |y|) ('T - (SEQ (SPADCALL (SPADCALL |x| (|getShellEntry| $ 44)) |y| - (|getShellEntry| $ 45)) + (SEQ (SPADCALL (SPADCALL |x| (|getShellEntry| $ 55)) |y| + (|getShellEntry| $ 56)) (EXIT |x|)))))) (DEFUN |StreamAggregate&| (|#1| |#2|) @@ -284,7 +284,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|StreamAggregate&|)) (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|StreamAggregate&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 51) . #0#) + (LETT $ (|newShell| 62) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -294,19 +294,19 @@ (COND ((|HasAttribute| |#1| '|shallowlyMutable|) (PROGN - (|setShellEntry| $ 32 + (|setShellEntry| $ 39 (CONS (|dispatchFunction| |STAGG-;concat;3A;7|) $)) - (|setShellEntry| $ 35 + (|setShellEntry| $ 46 (CONS (|dispatchFunction| |STAGG-;concat;LA;8|) $)) - (|setShellEntry| $ 38 + (|setShellEntry| $ 49 (CONS (|dispatchFunction| |STAGG-;map!;M2A;9|) $)) - (|setShellEntry| $ 39 + (|setShellEntry| $ 50 (CONS (|dispatchFunction| |STAGG-;fill!;ASA;10|) $)) - (|setShellEntry| $ 40 + (|setShellEntry| $ 51 (CONS (|dispatchFunction| |STAGG-;setelt;AI2S;11|) $)) - (|setShellEntry| $ 43 + (|setShellEntry| $ 54 (CONS (|dispatchFunction| |STAGG-;setelt;AUs2S;12|) $)) - (|setShellEntry| $ 46 + (|setShellEntry| $ 57 (CONS (|dispatchFunction| |STAGG-;concat!;3A;13|) $))))) $)))) @@ -314,39 +314,45 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|Boolean|) (0 . |cyclic?|) |STAGG-;explicitlyFinite?;AB;1| - |STAGG-;possiblyInfinite?;AB;2| (5 . |rest|) (|List| 7) - (10 . |construct|) (|NonNegativeInteger|) - |STAGG-;first;ANniA;3| (15 . |empty?|) (20 . |first|) - (|Integer|) (25 . |minIndex|) (30 . |rest|) - |STAGG-;elt;AIS;5| (|UniversalSegment| 19) (36 . |lo|) - (41 . |hasHi|) (46 . |copy|) (51 . |hi|) (56 . |empty|) - (60 . |first|) |STAGG-;elt;AUsA;6| (66 . |concat!|) - (72 . |concat|) (|List| $) (78 . |concat|) (83 . |concat|) - (88 . |setfirst!|) (|Mapping| 7 7) (94 . |map!|) - (100 . |fill!|) (106 . |setelt|) (113 . |maxIndex|) - (118 . |eq?|) (124 . |setelt|) (131 . |tail|) - (136 . |setrest!|) (142 . |concat!|) '"rest" '"last" - '"first" '"value") - '#(|setelt| 148 |possiblyInfinite?| 162 |map!| 167 |first| - 173 |fill!| 179 |explicitlyFinite?| 185 |elt| 190 - |concat!| 202 |concat| 208) + |STAGG-;possiblyInfinite?;AB;2| (|SingleInteger|) + (5 . |One|) (|NonNegativeInteger|) (9 . |One|) + (13 . |rest|) (|List| 7) (18 . |construct|) + |STAGG-;first;ANniA;3| (23 . |empty?|) (28 . |first|) + (|Integer|) (33 . |minIndex|) (38 . -) (44 . |Zero|) + (48 . <) (54 . |rest|) |STAGG-;elt;AIS;5| + (|UniversalSegment| 22) (60 . |lo|) (65 . |hasHi|) + (70 . |copy|) (75 . |hi|) (80 . |empty|) (84 . +) + (90 . |first|) |STAGG-;elt;AUsA;6| (96 . |concat!|) + (102 . |concat|) (|List| 6) (108 . |empty?|) + (113 . |first|) (118 . |rest|) (|List| $) (123 . |concat|) + (128 . |concat|) (133 . |setfirst!|) (|Mapping| 7 7) + (139 . |map!|) (145 . |fill!|) (151 . |setelt|) + (158 . |maxIndex|) (163 . |eq?|) (169 . |setelt|) + (176 . |tail|) (181 . |setrest!|) (187 . |concat!|) + '"rest" '"last" '"first" '"value") + '#(|setelt| 193 |possiblyInfinite?| 207 |map!| 212 |first| + 218 |fill!| 224 |explicitlyFinite?| 230 |elt| 235 + |concat!| 247 |concat| 253) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 46 - '(1 6 8 0 9 1 6 0 0 12 1 6 0 13 14 1 6 - 8 0 17 1 6 7 0 18 1 6 19 0 20 2 6 0 0 - 15 21 1 23 19 0 24 1 23 8 0 25 1 6 0 - 0 26 1 23 19 0 27 0 6 0 28 2 6 0 0 15 - 29 2 6 0 0 0 31 2 0 0 0 0 32 1 6 0 33 - 34 1 0 0 33 35 2 6 7 0 7 36 2 0 0 37 - 0 38 2 0 0 0 7 39 3 0 7 0 19 7 40 1 6 - 19 0 41 2 6 8 0 0 42 3 0 7 0 23 7 43 - 1 6 0 0 44 2 6 0 0 0 45 2 0 0 0 0 46 - 3 0 7 0 19 7 40 3 0 7 0 23 7 43 1 0 8 - 0 11 2 0 0 37 0 38 2 0 0 0 15 16 2 0 - 0 0 7 39 1 0 8 0 10 2 0 7 0 19 22 2 0 - 0 0 23 30 2 0 0 0 0 46 1 0 0 33 35 2 - 0 0 0 0 32))))) + (|makeByteWordVec2| 57 + '(1 6 8 0 9 0 12 0 13 0 14 0 15 1 6 0 0 + 16 1 6 0 17 18 1 6 8 0 20 1 6 7 0 21 + 1 6 22 0 23 2 22 0 0 0 24 0 22 0 25 2 + 22 8 0 0 26 2 6 0 0 14 27 1 29 22 0 + 30 1 29 8 0 31 1 6 0 0 32 1 29 22 0 + 33 0 6 0 34 2 22 0 0 0 35 2 6 0 0 14 + 36 2 6 0 0 0 38 2 0 0 0 0 39 1 40 8 0 + 41 1 40 6 0 42 1 40 0 0 43 1 6 0 44 + 45 1 0 0 44 46 2 6 7 0 7 47 2 0 0 48 + 0 49 2 0 0 0 7 50 3 0 7 0 22 7 51 1 6 + 22 0 52 2 6 8 0 0 53 3 0 7 0 29 7 54 + 1 6 0 0 55 2 6 0 0 0 56 2 0 0 0 0 57 + 3 0 7 0 22 7 51 3 0 7 0 29 7 54 1 0 8 + 0 11 2 0 0 48 0 49 2 0 0 0 14 19 2 0 + 0 0 7 50 1 0 8 0 10 2 0 7 0 22 28 2 0 + 0 0 29 37 2 0 0 0 0 57 1 0 0 44 46 2 + 0 0 0 0 39))))) '|lookupComplete|)) diff --git a/src/algebra/strap/SYMBOL.lsp b/src/algebra/strap/SYMBOL.lsp index 6529e944..933198cc 100644 --- a/src/algebra/strap/SYMBOL.lsp +++ b/src/algebra/strap/SYMBOL.lsp @@ -117,7 +117,7 @@ (COND ((|SYMBOL;scripted?;$B;30| |x| $) (|error| "Cannot convert a scripted symbol to OpenMath")) - ('T (SPADCALL |dev| |x| (|getShellEntry| $ 26))))) + ('T (SPADCALL |dev| |x| (|getShellEntry| $ 27))))) (DEFUN |SYMBOL;OMwrite;$S;2| (|x| $) (PROG (|sp| |dev| |s|) @@ -125,13 +125,13 @@ (SEQ (LETT |s| "" |SYMBOL;OMwrite;$S;2|) (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SYMBOL;OMwrite;$S;2|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 28)) - (|getShellEntry| $ 29)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 29)) + (|getShellEntry| $ 30)) |SYMBOL;OMwrite;$S;2|) - (SPADCALL |dev| (|getShellEntry| $ 30)) - (|SYMBOL;writeOMSym| |dev| |x| $) (SPADCALL |dev| (|getShellEntry| $ 31)) + (|SYMBOL;writeOMSym| |dev| |x| $) (SPADCALL |dev| (|getShellEntry| $ 32)) + (SPADCALL |dev| (|getShellEntry| $ 33)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SYMBOL;OMwrite;$S;2|) (EXIT |s|))))) @@ -142,30 +142,30 @@ (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SYMBOL;OMwrite;$BS;3|) (LETT |dev| - (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 28)) - (|getShellEntry| $ 29)) + (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 29)) + (|getShellEntry| $ 30)) |SYMBOL;OMwrite;$BS;3|) - (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 30)))) - (|SYMBOL;writeOMSym| |dev| |x| $) (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 31)))) - (SPADCALL |dev| (|getShellEntry| $ 32)) + (|SYMBOL;writeOMSym| |dev| |x| $) + (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 32)))) + (SPADCALL |dev| (|getShellEntry| $ 33)) (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SYMBOL;OMwrite;$BS;3|) (EXIT |s|))))) (DEFUN |SYMBOL;OMwrite;Omd$V;4| (|dev| |x| $) - (SEQ (SPADCALL |dev| (|getShellEntry| $ 30)) + (SEQ (SPADCALL |dev| (|getShellEntry| $ 31)) (|SYMBOL;writeOMSym| |dev| |x| $) - (EXIT (SPADCALL |dev| (|getShellEntry| $ 31))))) + (EXIT (SPADCALL |dev| (|getShellEntry| $ 32))))) (DEFUN |SYMBOL;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $) - (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 30)))) + (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 31)))) (|SYMBOL;writeOMSym| |dev| |x| $) (EXIT (COND - (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 31))))))) + (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 32))))))) (DEFUN |SYMBOL;convert;$If;6| (|s| $) - (SPADCALL |s| (|getShellEntry| $ 45))) + (SPADCALL |s| (|getShellEntry| $ 47))) (DEFUN |SYMBOL;convert;2$;7| (|s| $) (DECLARE (IGNORE $)) |s|) @@ -180,7 +180,7 @@ (GGREATERP |y| |x|)) (DEFUN |SYMBOL;coerce;$Of;11| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 52))) + (SPADCALL |x| (|getShellEntry| $ 54))) (DEFUN |SYMBOL;subscript;$L$;12| (|sy| |lx| $) (|SYMBOL;script;$L$;22| |sy| (LIST |lx| NIL NIL NIL NIL) $)) @@ -195,19 +195,19 @@ (|SYMBOL;script;$L$;22| |sy| (LIST NIL NIL NIL NIL |lx|) $)) (DEFUN |SYMBOL;patternMatch;$P2Pmr;16| (|x| |p| |l| $) - (SPADCALL |x| |p| |l| (|getShellEntry| $ 64))) + (SPADCALL |x| |p| |l| (|getShellEntry| $ 69))) (DEFUN |SYMBOL;patternMatch;$P2Pmr;17| (|x| |p| |l| $) - (SPADCALL |x| |p| |l| (|getShellEntry| $ 71))) + (SPADCALL |x| |p| |l| (|getShellEntry| $ 76))) (DEFUN |SYMBOL;convert;$P;18| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 74))) + (SPADCALL |x| (|getShellEntry| $ 79))) (DEFUN |SYMBOL;convert;$P;19| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 76))) + (SPADCALL |x| (|getShellEntry| $ 81))) (DEFUN |SYMBOL;syprefix| (|sc| $) - (PROG (|ns| #0=#:G1549 |n| #1=#:G1550) + (PROG (|ns| #0=#:G1550 |n| #1=#:G1551) (RETURN (SEQ (LETT |ns| (LIST (LENGTH (QVELT |sc| 3)) (LENGTH (QVELT |sc| 2)) @@ -222,7 +222,7 @@ (SEQ (EXIT (LETT |ns| (CDR |ns|) |SYMBOL;syprefix|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL - (CONS (STRCONC (|getShellEntry| $ 37) + (CONS (STRCONC (|getShellEntry| $ 38) (|SYMBOL;istring| (LENGTH (QVELT |sc| 4)) $)) (PROGN @@ -247,22 +247,22 @@ |SYMBOL;syprefix|) (GO G190) G191 (EXIT (NREVERSE0 #0#))))) - (|getShellEntry| $ 79))))))) + (|getShellEntry| $ 95))))))) (DEFUN |SYMBOL;syscripts| (|sc| $) (PROG (|all|) (RETURN (SEQ (LETT |all| (QVELT |sc| 3) |SYMBOL;syscripts|) (LETT |all| - (SPADCALL (QVELT |sc| 2) |all| (|getShellEntry| $ 80)) + (SPADCALL (QVELT |sc| 2) |all| (|getShellEntry| $ 96)) |SYMBOL;syscripts|) (LETT |all| - (SPADCALL (QVELT |sc| 1) |all| (|getShellEntry| $ 80)) + (SPADCALL (QVELT |sc| 1) |all| (|getShellEntry| $ 96)) |SYMBOL;syscripts|) (LETT |all| - (SPADCALL (QVELT |sc| 0) |all| (|getShellEntry| $ 80)) + (SPADCALL (QVELT |sc| 0) |all| (|getShellEntry| $ 96)) |SYMBOL;syscripts|) - (EXIT (SPADCALL |all| (QVELT |sc| 4) (|getShellEntry| $ 80))))))) + (EXIT (SPADCALL |all| (QVELT |sc| 4) (|getShellEntry| $ 96))))))) (DEFUN |SYMBOL;script;$L$;22| (|sy| |ls| $) (PROG (|sc|) @@ -318,9 +318,9 @@ (COND ((< 1 (QCSIZE |s|)) (COND - ((SPADCALL (SPADCALL |s| 1 (|getShellEntry| $ 85)) - (SPADCALL "\\" (|getShellEntry| $ 40)) - (|getShellEntry| $ 86)) + ((SPADCALL (SPADCALL |s| 1 (|getShellEntry| $ 107)) + (SPADCALL "\\" (|getShellEntry| $ 43)) + (|getShellEntry| $ 108)) (LETT |s| (STRCONC "\\mbox{\\it " (STRCONC |s| "}")) |SYMBOL;latex;$S;25|))))) (COND ((NULL (|SYMBOL;scripted?;$B;30| |e| $)) (EXIT |s|))) @@ -335,7 +335,7 @@ (SEQ (LETT |sc| (STRCONC |sc| (SPADCALL (|SPADfirst| |lo|) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 112))) |SYMBOL;latex;$S;25|) (LETT |lo| (CDR |lo|) |SYMBOL;latex;$S;25|) @@ -356,7 +356,7 @@ (SEQ (LETT |sc| (STRCONC |sc| (SPADCALL (|SPADfirst| |lo|) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 112))) |SYMBOL;latex;$S;25|) (LETT |lo| (CDR |lo|) |SYMBOL;latex;$S;25|) @@ -377,7 +377,7 @@ (SEQ (LETT |sc| (STRCONC |sc| (SPADCALL (|SPADfirst| |lo|) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 112))) |SYMBOL;latex;$S;25|) (LETT |lo| (CDR |lo|) |SYMBOL;latex;$S;25|) @@ -398,7 +398,7 @@ (SEQ (LETT |sc| (STRCONC |sc| (SPADCALL (|SPADfirst| |lo|) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 112))) |SYMBOL;latex;$S;25|) (LETT |lo| (CDR |lo|) |SYMBOL;latex;$S;25|) @@ -419,7 +419,7 @@ (SEQ (LETT |sc| (STRCONC |sc| (SPADCALL (|SPADfirst| |lo|) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 112))) |SYMBOL;latex;$S;25|) (LETT |lo| (CDR |lo|) |SYMBOL;latex;$S;25|) @@ -435,7 +435,7 @@ (EXIT |s|))))) (DEFUN |SYMBOL;anyRadix| (|n| |s| $) - (PROG (|qr| |ns| #0=#:G1504) + (PROG (|qr| |ns| #0=#:G1505) (RETURN (SEQ (EXIT (SEQ (LETT |ns| "" |SYMBOL;anyRadix|) (EXIT (SEQ G190 NIL @@ -449,9 +449,9 @@ (SPADCALL |s| (+ (QCDR |qr|) (SPADCALL |s| - (|getShellEntry| $ 90))) - (|getShellEntry| $ 85)) - |ns| (|getShellEntry| $ 91)) + (|getShellEntry| $ 117))) + (|getShellEntry| $ 107)) + |ns| (|getShellEntry| $ 119)) |SYMBOL;anyRadix|) (EXIT (COND @@ -468,15 +468,15 @@ (RETURN (SEQ (LETT |sym| (|SYMBOL;anyRadix| - (SPADCALL (|getShellEntry| $ 9) - (|getShellEntry| $ 92)) - (|getShellEntry| $ 19) $) + (SPADCALL (|getShellEntry| $ 10) + (|getShellEntry| $ 120)) + (|getShellEntry| $ 20) $) |SYMBOL;new;$;27|) - (SPADCALL (|getShellEntry| $ 9) - (+ (SPADCALL (|getShellEntry| $ 9) - (|getShellEntry| $ 92)) + (SPADCALL (|getShellEntry| $ 10) + (+ (SPADCALL (|getShellEntry| $ 10) + (|getShellEntry| $ 120)) 1) - (|getShellEntry| $ 93)) + (|getShellEntry| $ 121)) (EXIT (|SYMBOL;coerce;S$;8| (STRCONC "%" |sym|) $)))))) (DEFUN |SYMBOL;new;2$;28| (|x| $) @@ -484,15 +484,15 @@ (RETURN (SEQ (LETT |n| (SEQ (LETT |u| - (SPADCALL |x| (|getShellEntry| $ 12) - (|getShellEntry| $ 96)) + (SPADCALL |x| (|getShellEntry| $ 13) + (|getShellEntry| $ 124)) |SYMBOL;new;2$;28|) (EXIT (COND ((QEQCAR |u| 1) 0) ('T (+ (QCDR |u|) 1))))) |SYMBOL;new;2$;28|) - (SPADCALL (|getShellEntry| $ 12) |x| |n| - (|getShellEntry| $ 97)) + (SPADCALL (|getShellEntry| $ 13) |x| |n| + (|getShellEntry| $ 127)) (LETT |xx| (COND ((NULL (|SYMBOL;scripted?;$B;30| |x| $)) @@ -507,19 +507,19 @@ ((NULL (< (SPADCALL (SPADCALL |xx| (SPADCALL |xx| - (|getShellEntry| $ 98)) - (|getShellEntry| $ 85)) - (|getShellEntry| $ 18) - (|getShellEntry| $ 99)) - (SPADCALL (|getShellEntry| $ 18) - (|getShellEntry| $ 90)))) + (|getShellEntry| $ 128)) + (|getShellEntry| $ 107)) + (|getShellEntry| $ 19) + (|getShellEntry| $ 129)) + (SPADCALL (|getShellEntry| $ 19) + (|getShellEntry| $ 117)))) (STRCONC |xx| (|SYMBOL;anyRadix| |n| - (|getShellEntry| $ 20) $))) + (|getShellEntry| $ 21) $))) ('T (STRCONC |xx| (|SYMBOL;anyRadix| |n| - (|getShellEntry| $ 18) $)))) + (|getShellEntry| $ 19) $)))) |SYMBOL;new;2$;28|) (COND ((NULL (|SYMBOL;scripted?;$B;30| |x| $)) @@ -528,13 +528,13 @@ (|SYMBOL;scripts;$R;32| |x| $) $)))))) (DEFUN |SYMBOL;resetNew;V;29| ($) - (PROG (|k| #0=#:G1551) + (PROG (|k| #0=#:G1552) (RETURN - (SEQ (SPADCALL (|getShellEntry| $ 9) 0 (|getShellEntry| $ 93)) + (SEQ (SPADCALL (|getShellEntry| $ 10) 0 (|getShellEntry| $ 121)) (SEQ (LETT |k| NIL |SYMBOL;resetNew;V;29|) (LETT #0# - (SPADCALL (|getShellEntry| $ 12) - (|getShellEntry| $ 102)) + (SPADCALL (|getShellEntry| $ 13) + (|getShellEntry| $ 133)) |SYMBOL;resetNew;V;29|) G190 (COND @@ -543,16 +543,16 @@ (LETT |k| (CAR #0#) |SYMBOL;resetNew;V;29|) NIL)) (GO G191))) - (SEQ (EXIT (SPADCALL |k| (|getShellEntry| $ 12) - (|getShellEntry| $ 103)))) + (SEQ (EXIT (SPADCALL |k| (|getShellEntry| $ 13) + (|getShellEntry| $ 134)))) (LETT #0# (CDR #0#) |SYMBOL;resetNew;V;29|) (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL (|getShellEntry| $ 104))))))) + (EXIT (SPADCALL (|getShellEntry| $ 135))))))) (DEFUN |SYMBOL;scripted?;$B;30| (|sy| $) (NOT (ATOM |sy|))) (DEFUN |SYMBOL;name;2$;31| (|sy| $) - (PROG (|str| |i| #0=#:G1552 #1=#:G1532 #2=#:G1530) + (PROG (|str| |i| #0=#:G1553 #1=#:G1533 #2=#:G1531) (RETURN (SEQ (EXIT (COND ((NULL (|SYMBOL;scripted?;$B;30| |sy| $)) |sy|) @@ -561,12 +561,12 @@ (|SYMBOL;string;$S;24| (SPADCALL (|SYMBOL;list;$L;34| |sy| $) - (|getShellEntry| $ 107)) + (|getShellEntry| $ 139)) $) |SYMBOL;name;2$;31|) (SEQ (EXIT (SEQ (LETT |i| - (+ (|getShellEntry| $ 38) 1) + (+ (|getShellEntry| $ 41) 1) |SYMBOL;name;2$;31|) (LETT #0# (QCSIZE |str|) |SYMBOL;name;2$;31|) @@ -578,8 +578,8 @@ ((NULL (SPADCALL (SPADCALL |str| |i| - (|getShellEntry| $ 85)) - (|getShellEntry| $ 108))) + (|getShellEntry| $ 107)) + (|getShellEntry| $ 143))) (PROGN (LETT #2# (PROGN @@ -589,9 +589,9 @@ (SPADCALL |i| (QCSIZE |str|) (|getShellEntry| $ - 110)) + 145)) (|getShellEntry| $ - 111)) + 146)) $) |SYMBOL;name;2$;31|) (GO #1#)) @@ -605,8 +605,8 @@ #1# (EXIT #1#))))) (DEFUN |SYMBOL;scripts;$R;32| (|sy| $) - (PROG (|lscripts| |str| |nstr| |j| #0=#:G1535 |nscripts| |m| |n| - #1=#:G1553 |i| #2=#:G1554 |a| #3=#:G1555 |allscripts|) + (PROG (|lscripts| |str| |nstr| |j| #0=#:G1536 |nscripts| |m| |n| + #1=#:G1554 |i| #2=#:G1555 |a| #3=#:G1556 |allscripts|) (RETURN (SEQ (COND ((NULL (|SYMBOL;scripted?;$B;30| |sy| $)) @@ -619,22 +619,22 @@ (LETT |str| (|SYMBOL;string;$S;24| (SPADCALL (|SYMBOL;list;$L;34| |sy| $) - (|getShellEntry| $ 107)) + (|getShellEntry| $ 139)) $) |SYMBOL;scripts;$R;32|) (LETT |nstr| (QCSIZE |str|) |SYMBOL;scripts;$R;32|) (LETT |m| - (SPADCALL |nscripts| (|getShellEntry| $ 113)) + (SPADCALL |nscripts| (|getShellEntry| $ 148)) |SYMBOL;scripts;$R;32|) - (SEQ (LETT |j| (+ (|getShellEntry| $ 38) 1) + (SEQ (LETT |j| (+ (|getShellEntry| $ 41) 1) |SYMBOL;scripts;$R;32|) (LETT |i| |m| |SYMBOL;scripts;$R;32|) G190 (COND ((OR (> |j| |nstr|) (NULL (SPADCALL (SPADCALL |str| |j| - (|getShellEntry| $ 85)) - (|getShellEntry| $ 108)))) + (|getShellEntry| $ 107)) + (|getShellEntry| $ 143)))) (GO G191))) (SEQ (EXIT (SPADCALL |nscripts| |i| (PROG1 @@ -642,14 +642,14 @@ (- (SPADCALL (SPADCALL |str| |j| - (|getShellEntry| $ 85)) - (|getShellEntry| $ 42)) - (|getShellEntry| $ 43)) + (|getShellEntry| $ 107)) + (|getShellEntry| $ 44)) + (|getShellEntry| $ 45)) |SYMBOL;scripts;$R;32|) (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 114)))) + (|getShellEntry| $ 150)))) (LETT |i| (PROG1 (+ |i| 1) (LETT |j| (+ |j| 1) @@ -659,14 +659,14 @@ (LETT |nscripts| (SPADCALL (CDR |nscripts|) (|SPADfirst| |nscripts|) - (|getShellEntry| $ 115)) + (|getShellEntry| $ 153)) |SYMBOL;scripts;$R;32|) (LETT |allscripts| (SPADCALL (|SYMBOL;list;$L;34| |sy| $) - (|getShellEntry| $ 116)) + (|getShellEntry| $ 154)) |SYMBOL;scripts;$R;32|) (LETT |m| - (SPADCALL |lscripts| (|getShellEntry| $ 117)) + (SPADCALL |lscripts| (|getShellEntry| $ 155)) |SYMBOL;scripts;$R;32|) (SEQ (LETT |n| NIL |SYMBOL;scripts;$R;32|) (LETT #1# |nscripts| |SYMBOL;scripts;$R;32|) @@ -681,7 +681,7 @@ (SEQ (EXIT (COND ((< (SPADCALL |allscripts| - (|getShellEntry| $ 118)) + (|getShellEntry| $ 156)) |n|) (|error| "Improper script count in symbol")) @@ -696,7 +696,7 @@ |SYMBOL;scripts;$R;32|) (LETT #3# (SPADCALL |allscripts| |n| - (|getShellEntry| $ 119)) + (|getShellEntry| $ 157)) |SYMBOL;scripts;$R;32|) G190 (COND @@ -718,11 +718,11 @@ |SYMBOL;scripts;$R;32|) (GO G190) G191 (EXIT (NREVERSE0 #2#)))) - (|getShellEntry| $ 120)) + (|getShellEntry| $ 158)) (EXIT (LETT |allscripts| (SPADCALL |allscripts| |n| - (|getShellEntry| $ 121)) + (|getShellEntry| $ 159)) |SYMBOL;scripts;$R;32|))))))) (LETT |i| (PROG1 (+ |i| 1) @@ -731,20 +731,20 @@ |SYMBOL;scripts;$R;32|) (GO G190) G191 (EXIT NIL)) (EXIT (VECTOR (SPADCALL |lscripts| |m| - (|getShellEntry| $ 122)) + (|getShellEntry| $ 160)) (SPADCALL |lscripts| (+ |m| 1) - (|getShellEntry| $ 122)) + (|getShellEntry| $ 160)) (SPADCALL |lscripts| (+ |m| 2) - (|getShellEntry| $ 122)) + (|getShellEntry| $ 160)) (SPADCALL |lscripts| (+ |m| 3) - (|getShellEntry| $ 122)) + (|getShellEntry| $ 160)) (SPADCALL |lscripts| (+ |m| 4) - (|getShellEntry| $ 122))))))))))) + (|getShellEntry| $ 160))))))))))) (DEFUN |SYMBOL;istring| (|n| $) (COND ((< 9 |n|) (|error| "Can have at most 9 scripts of each kind")) - ('T (|getSimpleArrayEntry| (|getShellEntry| $ 17) (+ |n| 0))))) + ('T (|getSimpleArrayEntry| (|getShellEntry| $ 18) (+ |n| 0))))) (DEFUN |SYMBOL;list;$L;34| (|sy| $) (COND @@ -757,7 +757,7 @@ (DEFUN |Symbol| () (PROG () (RETURN - (PROG (#0=#:G1557) + (PROG (#0=#:G1558) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|Symbol|) |Symbol|) @@ -775,129 +775,153 @@ (RETURN (PROGN (LETT |dv$| '(|Symbol|) . #0=(|Symbol|)) - (LETT $ (|newShell| 125) . #0#) + (LETT $ (|newShell| 164) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) (|haddProp| |$ConstructorCache| '|Symbol| NIL (CONS 1 $)) (|stuffDomainSlots| $) - (|setShellEntry| $ 9 (SPADCALL 0 (|getShellEntry| $ 8))) - (|setShellEntry| $ 12 (SPADCALL (|getShellEntry| $ 11))) - (|setShellEntry| $ 17 + (|setShellEntry| $ 10 (SPADCALL 0 (|getShellEntry| $ 9))) + (|setShellEntry| $ 13 (SPADCALL (|getShellEntry| $ 12))) + (|setShellEntry| $ 18 (SPADCALL (LIST "0" "1" "2" "3" "4" "5" "6" "7" "8" "9") - (|getShellEntry| $ 16))) - (|setShellEntry| $ 18 "0123456789") - (|setShellEntry| $ 19 "ABCDEFGHIJKLMNOPQRSTUVWXYZ") - (|setShellEntry| $ 20 "abcdefghijklmnopqrstuvwxyz") - (|setShellEntry| $ 37 "*") - (|setShellEntry| $ 38 (QCSIZE (|getShellEntry| $ 37))) - (|setShellEntry| $ 43 - (SPADCALL (SPADCALL "0" (|getShellEntry| $ 40)) - (|getShellEntry| $ 42))) + (|getShellEntry| $ 17))) + (|setShellEntry| $ 19 "0123456789") + (|setShellEntry| $ 20 "ABCDEFGHIJKLMNOPQRSTUVWXYZ") + (|setShellEntry| $ 21 "abcdefghijklmnopqrstuvwxyz") + (|setShellEntry| $ 38 "*") + (|setShellEntry| $ 41 (QCSIZE (|getShellEntry| $ 38))) + (|setShellEntry| $ 45 + (SPADCALL (SPADCALL "0" (|getShellEntry| $ 43)) + (|getShellEntry| $ 44))) $)))) (MAKEPROP '|Symbol| '|infovec| - (LIST '#(NIL NIL NIL NIL NIL NIL (|Integer|) (|Reference| 6) - (0 . |ref|) '|count| (|AssociationList| $$ 6) - (5 . |empty|) '|xcount| (|String|) (|List| 13) - (|PrimitiveArray| 13) (9 . |construct|) '|istrings| - '|nums| 'ALPHAS '|alphas| (|Boolean|) - |SYMBOL;scripted?;$B;30| (|Void|) (|Symbol|) - (|OpenMathDevice|) (14 . |OMputVariable|) - (|OpenMathEncoding|) (20 . |OMencodingXML|) - (24 . |OMopenString|) (30 . |OMputObject|) - (35 . |OMputEndObject|) (40 . |OMclose|) + (LIST '#(NIL NIL NIL NIL NIL NIL (|Integer|) (0 . |Zero|) + (|Reference| 6) (4 . |ref|) '|count| + (|AssociationList| $$ 6) (9 . |empty|) '|xcount| + (|String|) (|List| 14) (|PrimitiveArray| 14) + (13 . |construct|) '|istrings| '|nums| 'ALPHAS '|alphas| + (|Boolean|) |SYMBOL;scripted?;$B;30| (|Void|) (|Symbol|) + (|OpenMathDevice|) (18 . |OMputVariable|) + (|OpenMathEncoding|) (24 . |OMencodingXML|) + (28 . |OMopenString|) (34 . |OMputObject|) + (39 . |OMputEndObject|) (44 . |OMclose|) |SYMBOL;OMwrite;$S;2| |SYMBOL;OMwrite;$BS;3| |SYMBOL;OMwrite;Omd$V;4| |SYMBOL;OMwrite;Omd$BV;5| '|hd| - '|lhd| (|Character|) (45 . |char|) (|NonNegativeInteger|) - (50 . |ord|) '|ord0| (|InputForm|) (55 . |convert|) - |SYMBOL;convert;$If;6| |SYMBOL;convert;2$;7| - |SYMBOL;coerce;S$;8| |SYMBOL;=;2$B;9| |SYMBOL;<;2$B;10| - (|OutputForm|) (60 . |outputForm|) |SYMBOL;coerce;$Of;11| - (|List| 51) (|List| 54) |SYMBOL;script;$L$;22| - |SYMBOL;subscript;$L$;12| |SYMBOL;elt;$L$;13| - |SYMBOL;superscript;$L$;14| |SYMBOL;argscript;$L$;15| - (|PatternMatchResult| 6 24) (|Pattern| 6) - (|PatternMatchSymbol| 6) (65 . |patternMatch|) - (|PatternMatchResult| 6 $) |SYMBOL;patternMatch;$P2Pmr;16| - (|Float|) (|PatternMatchResult| 67 24) (|Pattern| 67) - (|PatternMatchSymbol| 67) (72 . |patternMatch|) - (|PatternMatchResult| 67 $) - |SYMBOL;patternMatch;$P2Pmr;17| (79 . |coerce|) - |SYMBOL;convert;$P;18| (84 . |coerce|) - |SYMBOL;convert;$P;19| (|List| $) (89 . |concat|) - (94 . |concat|) - (|Record| (|:| |sub| 54) (|:| |sup| 54) (|:| |presup| 54) - (|:| |presub| 54) (|:| |args| 54)) + (|NonNegativeInteger|) (49 . |#|) '|lhd| (|Character|) + (54 . |char|) (59 . |ord|) '|ord0| (|InputForm|) + (64 . |convert|) |SYMBOL;convert;$If;6| + |SYMBOL;convert;2$;7| |SYMBOL;coerce;S$;8| + |SYMBOL;=;2$B;9| |SYMBOL;<;2$B;10| (|OutputForm|) + (69 . |outputForm|) |SYMBOL;coerce;$Of;11| (74 . |nil|) + (|List| 53) (78 . |nil|) (|List| 57) (82 . |nil|) + |SYMBOL;script;$L$;22| |SYMBOL;subscript;$L$;12| + |SYMBOL;elt;$L$;13| |SYMBOL;superscript;$L$;14| + |SYMBOL;argscript;$L$;15| (|PatternMatchResult| 6 25) + (|Pattern| 6) (|PatternMatchSymbol| 6) + (86 . |patternMatch|) (|PatternMatchResult| 6 $) + |SYMBOL;patternMatch;$P2Pmr;16| (|Float|) + (|PatternMatchResult| 72 25) (|Pattern| 72) + (|PatternMatchSymbol| 72) (93 . |patternMatch|) + (|PatternMatchResult| 72 $) + |SYMBOL;patternMatch;$P2Pmr;17| (100 . |coerce|) + |SYMBOL;convert;$P;18| (105 . |coerce|) + |SYMBOL;convert;$P;19| (110 . |#|) (|List| 6) (115 . |#|) + (120 . <) (126 . |false|) (130 . |first|) (135 . |zero?|) + (140 . |rest|) (145 . |concat|) (151 . |reverse!|) + (156 . |concat|) (|List| $) (162 . |concat|) + (167 . |concat|) (173 . |null|) (178 . |first|) + (183 . |rest|) + (|Record| (|:| |sub| 57) (|:| |sup| 57) (|:| |presup| 57) + (|:| |presub| 57) (|:| |args| 57)) |SYMBOL;script;$R$;23| |SYMBOL;name;2$;31| - |SYMBOL;string;$S;24| (100 . |elt|) (106 . ~=) - |SYMBOL;scripts;$R;32| (112 . |latex|) - |SYMBOL;latex;$S;25| (117 . |minIndex|) (122 . |concat|) - (128 . |elt|) (133 . |setelt|) |SYMBOL;new;$;27| - (|Union| 6 '"failed") (139 . |search|) (145 . |setelt|) - (152 . |maxIndex|) (157 . |position|) |SYMBOL;new;2$;28| - (|List| $$) (163 . |keys|) (168 . |remove!|) - (174 . |void|) |SYMBOL;resetNew;V;29| |SYMBOL;list;$L;34| - (178 . |first|) (183 . |digit?|) (|UniversalSegment| 6) - (188 . SEGMENT) (194 . |elt|) (|List| 41) - (200 . |minIndex|) (205 . |setelt|) (212 . |concat|) - (218 . |rest|) (223 . |minIndex|) (228 . |#|) - (233 . |first|) (239 . |setelt|) (246 . |rest|) - (252 . |elt|) + |SYMBOL;string;$S;24| (188 . |concat|) (194 . |One|) + (198 . |One|) (202 . |elt|) (208 . ~=) + |SYMBOL;scripts;$R;32| (214 . |empty?|) (219 . |first|) + (224 . |latex|) (229 . |rest|) |SYMBOL;latex;$S;25| + (|Record| (|:| |quotient| $) (|:| |remainder| $)) + (234 . |divide|) (240 . |minIndex|) (245 . +) + (251 . |concat|) (257 . |elt|) (262 . |setelt|) + |SYMBOL;new;$;27| (|Union| 6 '"failed") (268 . |search|) + (274 . |Zero|) (278 . |inc|) (283 . |setelt|) + (290 . |maxIndex|) (295 . |position|) (301 . <) + |SYMBOL;new;2$;28| (|List| $$) (307 . |keys|) + (312 . |remove!|) (318 . |void|) |SYMBOL;resetNew;V;29| + (322 . |not|) |SYMBOL;list;$L;34| (327 . |first|) + (|SingleInteger|) (332 . |One|) (336 . +) (342 . |digit?|) + (|UniversalSegment| 6) (347 . SEGMENT) (353 . |elt|) + (|List| 39) (359 . |minIndex|) (364 . -) (370 . |setelt|) + (377 . |rest|) (382 . |first|) (387 . |concat|) + (393 . |rest|) (398 . |minIndex|) (403 . |#|) + (408 . |first|) (414 . |setelt|) (421 . |rest|) + (427 . |elt|) (433 . |minIndex|) (438 . |elt|) (CONS IDENTITY (FUNCALL (|dispatchFunction| |SYMBOL;sample;$;35|) - $)) - (|SingleInteger|)) - '#(~= 258 |superscript| 264 |subscript| 270 |string| 276 - |scripts| 281 |scripted?| 286 |script| 291 |sample| 303 - |resetNew| 307 |patternMatch| 311 |new| 325 |name| 334 - |min| 339 |max| 345 |list| 351 |latex| 356 |hash| 361 - |elt| 366 |convert| 372 |coerce| 392 |argscript| 402 - |OMwrite| 408 >= 432 > 438 = 444 <= 450 < 456) + $))) + '#(~= 444 |superscript| 450 |subscript| 456 |string| 462 + |scripts| 467 |scripted?| 472 |script| 477 |sample| 489 + |resetNew| 493 |patternMatch| 497 |new| 511 |name| 520 + |min| 525 |max| 531 |list| 537 |latex| 542 |hash| 547 + |elt| 552 |convert| 558 |coerce| 578 |argscript| 588 + |OMwrite| 594 >= 618 > 624 = 630 <= 636 < 642) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0 0 0 0 0)) (CONS '#(|OrderedSet&| NIL NIL |SetCategory&| |BasicType&| NIL NIL NIL NIL NIL NIL NIL) - (CONS '#((|OrderedSet|) (|PatternMatchable| 67) + (CONS '#((|OrderedSet|) (|PatternMatchable| 72) (|PatternMatchable| 6) (|SetCategory|) - (|BasicType|) (|ConvertibleTo| 69) - (|ConvertibleTo| 62) - (|CoercibleFrom| 13) - (|ConvertibleTo| 24) (|OpenMath|) - (|ConvertibleTo| 44) (|CoercibleTo| 51)) - (|makeByteWordVec2| 124 - '(1 7 0 6 8 0 10 0 11 1 15 0 14 16 2 25 - 23 0 24 26 0 27 0 28 2 25 0 13 27 29 - 1 25 23 0 30 1 25 23 0 31 1 25 23 0 - 32 1 39 0 13 40 1 39 41 0 42 1 44 0 - 24 45 1 51 0 24 52 3 63 61 24 62 61 - 64 3 70 68 24 69 68 71 1 69 0 24 74 1 - 62 0 24 76 1 13 0 78 79 2 54 0 0 0 80 - 2 13 39 0 6 85 2 39 21 0 0 86 1 51 13 - 0 88 1 13 6 0 90 2 13 0 39 0 91 1 7 6 - 0 92 2 7 6 0 6 93 2 10 95 2 0 96 3 10 - 6 0 2 6 97 1 13 6 0 98 2 13 6 39 0 99 - 1 10 101 0 102 2 10 95 2 0 103 0 23 0 - 104 1 101 2 0 107 1 39 21 0 108 2 109 - 0 6 6 110 2 13 0 0 109 111 1 112 6 0 - 113 3 112 41 0 6 41 114 2 112 0 0 41 - 115 1 101 0 0 116 1 55 6 0 117 1 101 - 41 0 118 2 101 0 0 41 119 3 55 54 0 6 - 54 120 2 101 0 0 41 121 2 55 54 0 6 - 122 2 0 21 0 0 1 2 0 0 0 54 59 2 0 0 - 0 54 57 1 0 13 0 84 1 0 81 0 87 1 0 - 21 0 22 2 0 0 0 55 56 2 0 0 0 81 82 0 - 0 0 123 0 0 23 105 3 0 72 0 69 72 73 - 3 0 65 0 62 65 66 0 0 0 94 1 0 0 0 - 100 1 0 0 0 83 2 0 0 0 0 1 2 0 0 0 0 - 1 1 0 78 0 106 1 0 13 0 89 1 0 124 0 - 1 2 0 0 0 54 58 1 0 69 0 75 1 0 62 0 - 77 1 0 24 0 47 1 0 44 0 46 1 0 0 13 - 48 1 0 51 0 53 2 0 0 0 54 60 3 0 23 - 25 0 21 36 2 0 13 0 21 34 2 0 23 25 0 - 35 1 0 13 0 33 2 0 21 0 0 1 2 0 21 0 - 0 1 2 0 21 0 0 49 2 0 21 0 0 1 2 0 21 - 0 0 50))))) + (|BasicType|) (|ConvertibleTo| 74) + (|ConvertibleTo| 67) + (|CoercibleFrom| 14) + (|ConvertibleTo| 25) (|OpenMath|) + (|ConvertibleTo| 46) (|CoercibleTo| 53)) + (|makeByteWordVec2| 163 + '(0 6 0 7 1 8 0 6 9 0 11 0 12 1 16 0 15 + 17 2 26 24 0 25 27 0 28 0 29 2 26 0 + 14 28 30 1 26 24 0 31 1 26 24 0 32 1 + 26 24 0 33 1 14 39 0 40 1 42 0 14 43 + 1 42 39 0 44 1 46 0 25 47 1 53 0 25 + 54 0 15 0 56 0 57 0 58 0 59 0 60 3 68 + 66 25 67 66 69 3 75 73 25 74 73 76 1 + 74 0 25 79 1 67 0 25 81 1 57 39 0 83 + 1 84 39 0 85 2 39 22 0 0 86 0 22 0 87 + 1 84 6 0 88 1 6 22 0 89 1 84 0 0 90 2 + 14 0 0 0 91 1 84 0 0 92 2 15 0 14 0 + 93 1 14 0 94 95 2 57 0 0 0 96 1 59 22 + 0 97 1 59 57 0 98 1 59 0 0 99 2 57 0 + 53 0 104 0 39 0 105 0 6 0 106 2 14 42 + 0 6 107 2 42 22 0 0 108 1 57 22 0 110 + 1 57 53 0 111 1 53 14 0 112 1 57 0 0 + 113 2 6 115 0 0 116 1 14 6 0 117 2 6 + 0 0 0 118 2 14 0 42 0 119 1 8 6 0 120 + 2 8 6 0 6 121 2 11 123 2 0 124 0 39 0 + 125 1 6 0 0 126 3 11 6 0 2 6 127 1 14 + 6 0 128 2 14 6 42 0 129 2 6 22 0 0 + 130 1 11 132 0 133 2 11 123 2 0 134 0 + 24 0 135 1 22 0 0 137 1 132 2 0 139 0 + 140 0 141 2 39 0 0 0 142 1 42 22 0 + 143 2 144 0 6 6 145 2 14 0 0 144 146 + 1 147 6 0 148 2 6 0 0 0 149 3 147 39 + 0 6 39 150 1 147 0 0 151 1 147 39 0 + 152 2 147 0 0 39 153 1 132 0 0 154 1 + 59 6 0 155 1 132 39 0 156 2 132 0 0 + 39 157 3 59 57 0 6 57 158 2 132 0 0 + 39 159 2 59 57 0 6 160 1 16 6 0 161 2 + 16 14 0 6 162 2 0 22 0 0 1 2 0 0 0 57 + 64 2 0 0 0 57 62 1 0 14 0 103 1 0 100 + 0 109 1 0 22 0 23 2 0 0 0 59 61 2 0 0 + 0 100 101 0 0 0 163 0 0 24 136 3 0 77 + 0 74 77 78 3 0 70 0 67 70 71 0 0 0 + 122 1 0 0 0 131 1 0 0 0 102 2 0 0 0 0 + 1 2 0 0 0 0 1 1 0 94 0 138 1 0 14 0 + 114 1 0 140 0 1 2 0 0 0 57 63 1 0 74 + 0 80 1 0 67 0 82 1 0 25 0 49 1 0 46 0 + 48 1 0 0 14 50 1 0 53 0 55 2 0 0 0 57 + 65 3 0 24 26 0 22 37 2 0 14 0 22 35 2 + 0 24 26 0 36 1 0 14 0 34 2 0 22 0 0 1 + 2 0 22 0 0 1 2 0 22 0 0 51 2 0 22 0 0 + 1 2 0 22 0 0 52))))) '|lookupComplete|)) (MAKEPROP '|Symbol| 'NILADIC T) diff --git a/src/algebra/strap/TSETCAT-.lsp b/src/algebra/strap/TSETCAT-.lsp index 847746a2..c54146fb 100644 --- a/src/algebra/strap/TSETCAT-.lsp +++ b/src/algebra/strap/TSETCAT-.lsp @@ -132,31 +132,31 @@ (NULL (SPADCALL (PROG2 (LETT #0# (SPADCALL |ts| - (|getShellEntry| $ 14)) + (|getShellEntry| $ 15)) |TSETCAT-;=;2SB;1|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 10) #0#)) (PROG2 (LETT #0# (SPADCALL |us| - (|getShellEntry| $ 14)) + (|getShellEntry| $ 15)) |TSETCAT-;=;2SB;1|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 10) #0#)) - (|getShellEntry| $ 15)))) + (|getShellEntry| $ 16)))) 'NIL) ('T (SPADCALL - (PROG2 (LETT #1# (SPADCALL |ts| (|getShellEntry| $ 17)) + (PROG2 (LETT #1# (SPADCALL |ts| (|getShellEntry| $ 18)) |TSETCAT-;=;2SB;1|) (QCDR #1#) (|check-union| (QEQCAR #1# 0) (|getShellEntry| $ 6) #1#)) - (PROG2 (LETT #1# (SPADCALL |us| (|getShellEntry| $ 17)) + (PROG2 (LETT #1# (SPADCALL |us| (|getShellEntry| $ 18)) |TSETCAT-;=;2SB;1|) (QCDR #1#) (|check-union| (QEQCAR #1# 0) (|getShellEntry| $ 6) #1#)) - (|getShellEntry| $ 18))))))) + (|getShellEntry| $ 19))))))) (DEFUN |TSETCAT-;infRittWu?;2SB;2| (|ts| |us| $) (PROG (|p| #0=#:G1470 |q| |v|) @@ -169,7 +169,7 @@ (SEQ (LETT |p| (PROG2 (LETT #0# (SPADCALL |ts| - (|getShellEntry| $ 20)) + (|getShellEntry| $ 21)) |TSETCAT-;infRittWu?;2SB;2|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -178,33 +178,33 @@ (LETT |q| (PROG2 (LETT #0# (SPADCALL |us| - (|getShellEntry| $ 20)) + (|getShellEntry| $ 21)) |TSETCAT-;infRittWu?;2SB;2|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 10) #0#)) |TSETCAT-;infRittWu?;2SB;2|) (EXIT (COND - ((SPADCALL |p| |q| (|getShellEntry| $ 21)) - 'T) ((SPADCALL |p| |q| (|getShellEntry| $ 22)) + 'T) + ((SPADCALL |p| |q| (|getShellEntry| $ 24)) 'NIL) ('T (SEQ (LETT |v| (SPADCALL |p| - (|getShellEntry| $ 23)) + (|getShellEntry| $ 25)) |TSETCAT-;infRittWu?;2SB;2|) (EXIT (SPADCALL (SPADCALL |ts| |v| - (|getShellEntry| $ 24)) + (|getShellEntry| $ 26)) (SPADCALL |us| |v| - (|getShellEntry| $ 24)) - (|getShellEntry| $ 25)))))))))))))) + (|getShellEntry| $ 26)) + (|getShellEntry| $ 27)))))))))))))) (DEFUN |TSETCAT-;reduced?;PSMB;3| (|p| |ts| |redOp?| $) (PROG (|lp|) (RETURN - (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 28)) + (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;reduced?;PSMB;3|) (SEQ G190 (COND @@ -221,17 +221,17 @@ (DEFUN |TSETCAT-;basicSet;LMU;4| (|ps| |redOp?| $) (PROG (|b| |bs| |p| |ts|) (RETURN - (SEQ (LETT |ps| (SPADCALL (ELT $ 31) |ps| (|getShellEntry| $ 33)) + (SEQ (LETT |ps| (SPADCALL (ELT $ 36) |ps| (|getShellEntry| $ 38)) |TSETCAT-;basicSet;LMU;4|) (EXIT (COND - ((SPADCALL (ELT $ 34) |ps| (|getShellEntry| $ 35)) + ((SPADCALL (ELT $ 39) |ps| (|getShellEntry| $ 40)) (CONS 1 "failed")) ('T (SEQ (LETT |ps| - (SPADCALL (ELT $ 21) |ps| - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 22) |ps| + (|getShellEntry| $ 41)) |TSETCAT-;basicSet;LMU;4|) - (LETT |bs| (SPADCALL (|getShellEntry| $ 37)) + (LETT |bs| (SPADCALL (|getShellEntry| $ 42)) |TSETCAT-;basicSet;LMU;4|) (LETT |ts| NIL |TSETCAT-;basicSet;LMU;4|) (SEQ G190 @@ -241,7 +241,7 @@ |TSETCAT-;basicSet;LMU;4|) (LETT |bs| (SPADCALL |bs| |b| - (|getShellEntry| $ 38)) + (|getShellEntry| $ 43)) |TSETCAT-;basicSet;LMU;4|) (LETT |ps| (CDR |ps|) |TSETCAT-;basicSet;LMU;4|) @@ -258,7 +258,7 @@ (|SPADfirst| |ps|) |TSETCAT-;basicSet;LMU;4|) |bs| |redOp?| - (|getShellEntry| $ 39)))))) + (|getShellEntry| $ 44)))))) (GO G191))) (SEQ (LETT |ts| (CONS |p| |ts|) @@ -273,10 +273,10 @@ (DEFUN |TSETCAT-;basicSet;LMMU;5| (|ps| |pred?| |redOp?| $) (PROG (|bps| |b| |bs| |p| |gps| |ts|) (RETURN - (SEQ (LETT |ps| (SPADCALL (ELT $ 31) |ps| (|getShellEntry| $ 33)) + (SEQ (LETT |ps| (SPADCALL (ELT $ 36) |ps| (|getShellEntry| $ 38)) |TSETCAT-;basicSet;LMMU;5|) (EXIT (COND - ((SPADCALL (ELT $ 34) |ps| (|getShellEntry| $ 35)) + ((SPADCALL (ELT $ 39) |ps| (|getShellEntry| $ 40)) (CONS 1 "failed")) ('T (SEQ (LETT |gps| NIL |TSETCAT-;basicSet;LMMU;5|) @@ -298,10 +298,10 @@ |TSETCAT-;basicSet;LMMU;5|))))) NIL (GO G190) G191 (EXIT NIL)) (LETT |gps| - (SPADCALL (ELT $ 21) |gps| - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 22) |gps| + (|getShellEntry| $ 41)) |TSETCAT-;basicSet;LMMU;5|) - (LETT |bs| (SPADCALL (|getShellEntry| $ 37)) + (LETT |bs| (SPADCALL (|getShellEntry| $ 42)) |TSETCAT-;basicSet;LMMU;5|) (LETT |ts| NIL |TSETCAT-;basicSet;LMMU;5|) (SEQ G190 @@ -311,7 +311,7 @@ |TSETCAT-;basicSet;LMMU;5|) (LETT |bs| (SPADCALL |bs| |b| - (|getShellEntry| $ 38)) + (|getShellEntry| $ 43)) |TSETCAT-;basicSet;LMMU;5|) (LETT |gps| (CDR |gps|) |TSETCAT-;basicSet;LMMU;5|) @@ -328,7 +328,7 @@ (|SPADfirst| |gps|) |TSETCAT-;basicSet;LMMU;5|) |bs| |redOp?| - (|getShellEntry| $ 39)))))) + (|getShellEntry| $ 44)))))) (GO G191))) (SEQ (LETT |ts| (CONS |p| |ts|) @@ -339,10 +339,10 @@ NIL (GO G190) G191 (EXIT NIL)))) NIL (GO G190) G191 (EXIT NIL)) (LETT |ts| - (SPADCALL (ELT $ 21) + (SPADCALL (ELT $ 22) (SPADCALL |ts| |bps| - (|getShellEntry| $ 43)) - (|getShellEntry| $ 36)) + (|getShellEntry| $ 49)) + (|getShellEntry| $ 41)) |TSETCAT-;basicSet;LMMU;5|) (EXIT (CONS 0 (CONS |bs| |ts|))))))))))) @@ -354,7 +354,7 @@ ((SPADCALL |ts| (|getShellEntry| $ 12)) |lip|) ('T (SEQ (LETT |lp| - (SPADCALL |ts| (|getShellEntry| $ 28)) + (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;initials;SL;6|) (SEQ G190 (COND @@ -366,20 +366,20 @@ (SPADCALL (LETT |ip| (SPADCALL |p| - (|getShellEntry| $ 45)) + (|getShellEntry| $ 51)) |TSETCAT-;initials;SL;6|) - (|getShellEntry| $ 34))) + (|getShellEntry| $ 39))) (LETT |lip| (CONS (SPADCALL |ip| - (|getShellEntry| $ 46)) + (|getShellEntry| $ 52)) |lip|) |TSETCAT-;initials;SL;6|))) (EXIT (LETT |lp| (CDR |lp|) |TSETCAT-;initials;SL;6|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |lip| (|getShellEntry| $ 47))))))))))) + (EXIT (SPADCALL |lip| (|getShellEntry| $ 53))))))))))) (DEFUN |TSETCAT-;degree;SNni;7| (|ts| $) (PROG (|lp| |d|) @@ -387,11 +387,11 @@ (SEQ (COND ((SPADCALL |ts| (|getShellEntry| $ 12)) 0) ('T - (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 28)) + (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;degree;SNni;7|) (LETT |d| (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 50)) + (|getShellEntry| $ 57)) |TSETCAT-;degree;SNni;7|) (SEQ G190 (COND @@ -402,38 +402,38 @@ (SEQ (EXIT (LETT |d| (* |d| (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 50))) + (|getShellEntry| $ 57))) |TSETCAT-;degree;SNni;7|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |d|)))))))) (DEFUN |TSETCAT-;quasiComponent;SR;8| (|ts| $) - (CONS (SPADCALL |ts| (|getShellEntry| $ 28)) - (SPADCALL |ts| (|getShellEntry| $ 52)))) + (CONS (SPADCALL |ts| (|getShellEntry| $ 30)) + (SPADCALL |ts| (|getShellEntry| $ 60)))) (DEFUN |TSETCAT-;normalized?;PSB;9| (|p| |ts| $) - (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 56))) + (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 64))) (DEFUN |TSETCAT-;stronglyReduced?;PSB;10| (|p| |ts| $) - (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 58))) + (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 66))) (DEFUN |TSETCAT-;headReduced?;PSB;11| (|p| |ts| $) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 60)) |ts| - (|getShellEntry| $ 61))) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 68)) |ts| + (|getShellEntry| $ 69))) (DEFUN |TSETCAT-;initiallyReduced?;PSB;12| (|p| |ts| $) (PROG (|lp| |red|) (RETURN - (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 28)) + (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;initiallyReduced?;PSB;12|) (LETT |red| 'T |TSETCAT-;initiallyReduced?;PSB;12|) (SEQ G190 (COND ((NULL (COND ((OR (NULL |lp|) - (SPADCALL |p| (|getShellEntry| $ 34))) + (SPADCALL |p| (|getShellEntry| $ 39))) 'NIL) ('T |red|))) (GO G191))) @@ -444,10 +444,10 @@ ('T (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 23)) + (|getShellEntry| $ 25)) (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 23)) - (|getShellEntry| $ 63))))) + (|getShellEntry| $ 25)) + (|getShellEntry| $ 71))))) (GO G191))) (SEQ (EXIT (LETT |lp| (CDR |lp|) |TSETCAT-;initiallyReduced?;PSB;12|))) @@ -457,20 +457,20 @@ (COND ((SPADCALL (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 23)) + (|getShellEntry| $ 25)) (SPADCALL |p| - (|getShellEntry| $ 23)) - (|getShellEntry| $ 64)) + (|getShellEntry| $ 25)) + (|getShellEntry| $ 72)) (COND ((SPADCALL |p| (|SPADfirst| |lp|) - (|getShellEntry| $ 65)) + (|getShellEntry| $ 73)) (SEQ (LETT |lp| (CDR |lp|) |TSETCAT-;initiallyReduced?;PSB;12|) (EXIT (LETT |p| (SPADCALL |p| - (|getShellEntry| $ 45)) + (|getShellEntry| $ 51)) |TSETCAT-;initiallyReduced?;PSB;12|)))) ('T (LETT |red| 'NIL @@ -478,7 +478,7 @@ ('T (LETT |p| (SPADCALL |p| - (|getShellEntry| $ 45)) + (|getShellEntry| $ 51)) |TSETCAT-;initiallyReduced?;PSB;12|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |red|))))) @@ -488,7 +488,7 @@ (RETURN (SEQ (COND ((OR (SPADCALL |ts| (|getShellEntry| $ 12)) - (SPADCALL |p| (|getShellEntry| $ 34))) + (SPADCALL |p| (|getShellEntry| $ 39))) |p|) ('T (SEQ (LETT |ts0| |ts| |TSETCAT-;reduce;PSMMP;13|) @@ -501,13 +501,13 @@ ('T (NOT (SPADCALL |p| - (|getShellEntry| $ 34)))))) + (|getShellEntry| $ 39)))))) (GO G191))) (SEQ (LETT |reductor| (PROG2 (LETT #0# (SPADCALL |ts| - (|getShellEntry| $ 14)) + (|getShellEntry| $ 15)) |TSETCAT-;reduce;PSMMP;13|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -517,7 +517,7 @@ (PROG2 (LETT #1# (SPADCALL |ts| - (|getShellEntry| $ 17)) + (|getShellEntry| $ 18)) |TSETCAT-;reduce;PSMMP;13|) (QCDR #1#) (|check-union| (QEQCAR #1# 0) @@ -543,17 +543,17 @@ (PROG (|p| |rs|) (RETURN (SEQ (COND - ((SPADCALL |ts| (|getShellEntry| $ 69)) |lp|) + ((SPADCALL |ts| (|getShellEntry| $ 77)) |lp|) ('T (SEQ (LETT |lp| - (SPADCALL (ELT $ 31) |lp| - (|getShellEntry| $ 33)) + (SPADCALL (ELT $ 36) |lp| + (|getShellEntry| $ 38)) |TSETCAT-;rewriteSetWithReduction;LSMML;14|) (EXIT (COND ((NULL |lp|) |lp|) - ((SPADCALL (ELT $ 34) |lp| - (|getShellEntry| $ 35)) - (LIST (|spadConstant| $ 70))) + ((SPADCALL (ELT $ 39) |lp| + (|getShellEntry| $ 40)) + (LIST (|spadConstant| $ 78))) ('T (SEQ (LETT |rs| NIL |TSETCAT-;rewriteSetWithReduction;LSMML;14|) @@ -570,24 +570,24 @@ (SPADCALL (SPADCALL |p| |ts| |redOp| |redOp?| - (|getShellEntry| $ 71)) - (|getShellEntry| $ 46)) + (|getShellEntry| $ 79)) + (|getShellEntry| $ 52)) |TSETCAT-;rewriteSetWithReduction;LSMML;14|) (EXIT (COND ((NULL (SPADCALL |p| - (|getShellEntry| $ 31))) + (|getShellEntry| $ 36))) (COND ((SPADCALL |p| - (|getShellEntry| $ 34)) + (|getShellEntry| $ 39)) (SEQ (LETT |lp| NIL |TSETCAT-;rewriteSetWithReduction;LSMML;14|) (EXIT (LETT |rs| (LIST - (|spadConstant| $ 70)) + (|spadConstant| $ 78)) |TSETCAT-;rewriteSetWithReduction;LSMML;14|)))) ('T (LETT |rs| @@ -595,60 +595,60 @@ |TSETCAT-;rewriteSetWithReduction;LSMML;14|))))))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |rs| - (|getShellEntry| $ 47)))))))))))))) + (|getShellEntry| $ 53)))))))))))))) (DEFUN |TSETCAT-;stronglyReduce;PSP;15| (|p| |ts| $) - (SPADCALL |p| |ts| (ELT $ 73) (ELT $ 65) (|getShellEntry| $ 71))) + (SPADCALL |p| |ts| (ELT $ 81) (ELT $ 73) (|getShellEntry| $ 79))) (DEFUN |TSETCAT-;headReduce;PSP;16| (|p| |ts| $) - (SPADCALL |p| |ts| (ELT $ 75) (ELT $ 76) (|getShellEntry| $ 71))) + (SPADCALL |p| |ts| (ELT $ 83) (ELT $ 84) (|getShellEntry| $ 79))) (DEFUN |TSETCAT-;initiallyReduce;PSP;17| (|p| |ts| $) - (SPADCALL |p| |ts| (ELT $ 78) (ELT $ 79) (|getShellEntry| $ 71))) + (SPADCALL |p| |ts| (ELT $ 86) (ELT $ 87) (|getShellEntry| $ 79))) (DEFUN |TSETCAT-;removeZero;PSP;18| (|p| |ts| $) (PROG (|v| |tsv-| #0=#:G1571 #1=#:G1580 |q|) (RETURN (SEQ (EXIT (COND - ((OR (SPADCALL |p| (|getShellEntry| $ 34)) + ((OR (SPADCALL |p| (|getShellEntry| $ 39)) (SPADCALL |ts| (|getShellEntry| $ 12))) |p|) ('T (SEQ (LETT |v| - (SPADCALL |p| (|getShellEntry| $ 23)) + (SPADCALL |p| (|getShellEntry| $ 25)) |TSETCAT-;removeZero;PSP;18|) (LETT |tsv-| (SPADCALL |ts| |v| - (|getShellEntry| $ 81)) + (|getShellEntry| $ 89)) |TSETCAT-;removeZero;PSP;18|) (COND - ((SPADCALL |v| |ts| (|getShellEntry| $ 82)) + ((SPADCALL |v| |ts| (|getShellEntry| $ 90)) (SEQ (LETT |q| (SPADCALL |p| (PROG2 (LETT #0# (SPADCALL |ts| |v| - (|getShellEntry| $ 83)) + (|getShellEntry| $ 91)) |TSETCAT-;removeZero;PSP;18|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 10) #0#)) - (|getShellEntry| $ 73)) + (|getShellEntry| $ 81)) |TSETCAT-;removeZero;PSP;18|) (EXIT (COND ((SPADCALL |q| - (|getShellEntry| $ 31)) + (|getShellEntry| $ 36)) (PROGN (LETT #1# |q| |TSETCAT-;removeZero;PSP;18|) (GO #1#))) ((SPADCALL (SPADCALL |q| |tsv-| - (|getShellEntry| $ 84)) - (|getShellEntry| $ 31)) + (|getShellEntry| $ 92)) + (|getShellEntry| $ 36)) (PROGN (LETT #1# - (|spadConstant| $ 85) + (|spadConstant| $ 93) |TSETCAT-;removeZero;PSP;18|) (GO #1#)))))))) (EXIT (COND @@ -656,15 +656,15 @@ (|getShellEntry| $ 12)) |p|) ('T - (SEQ (LETT |q| (|spadConstant| $ 85) + (SEQ (LETT |q| (|spadConstant| $ 93) |TSETCAT-;removeZero;PSP;18|) (SEQ G190 (COND ((NULL (SPADCALL (SPADCALL |p| |v| - (|getShellEntry| $ 86)) - (|getShellEntry| $ 88))) + (|getShellEntry| $ 94)) + (|getShellEntry| $ 96))) (GO G191))) (SEQ (LETT |q| @@ -672,35 +672,35 @@ (SPADCALL (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 45)) + (|getShellEntry| $ 51)) |tsv-| - (|getShellEntry| $ 84)) + (|getShellEntry| $ 92)) (SPADCALL |p| - (|getShellEntry| $ 89)) - (|getShellEntry| $ 90)) - |q| (|getShellEntry| $ 91)) + (|getShellEntry| $ 97)) + (|getShellEntry| $ 98)) + |q| (|getShellEntry| $ 99)) |TSETCAT-;removeZero;PSP;18|) (EXIT (LETT |p| (SPADCALL |p| - (|getShellEntry| $ 92)) + (|getShellEntry| $ 100)) |TSETCAT-;removeZero;PSP;18|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |q| (SPADCALL |p| |tsv-| - (|getShellEntry| $ 84)) - (|getShellEntry| $ 91))))))))))) + (|getShellEntry| $ 92)) + (|getShellEntry| $ 99))))))))))) #1# (EXIT #1#))))) (DEFUN |TSETCAT-;reduceByQuasiMonic;PSP;19| (|p| |ts| $) (COND - ((OR (SPADCALL |p| (|getShellEntry| $ 34)) + ((OR (SPADCALL |p| (|getShellEntry| $ 39)) (SPADCALL |ts| (|getShellEntry| $ 12))) |p|) ('T - (QVELT (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 94)) - (|getShellEntry| $ 96)) + (QVELT (SPADCALL |p| (SPADCALL |ts| (|getShellEntry| $ 102)) + (|getShellEntry| $ 104)) 1)))) (DEFUN |TSETCAT-;autoReduced?;SMB;20| (|ts| |redOp?| $) @@ -709,7 +709,7 @@ (SEQ (COND ((SPADCALL |ts| (|getShellEntry| $ 12)) 'T) ('T - (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 28)) + (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;autoReduced?;SMB;20|) (LETT |p| (|SPADfirst| |lp|) |TSETCAT-;autoReduced?;SMB;20|) @@ -729,16 +729,16 @@ (EXIT (NULL |lp|))))))))) (DEFUN |TSETCAT-;stronglyReduced?;SB;21| (|ts| $) - (SPADCALL |ts| (ELT $ 58) (|getShellEntry| $ 100))) + (SPADCALL |ts| (ELT $ 66) (|getShellEntry| $ 108))) (DEFUN |TSETCAT-;normalized?;SB;22| (|ts| $) - (SPADCALL |ts| (ELT $ 56) (|getShellEntry| $ 100))) + (SPADCALL |ts| (ELT $ 64) (|getShellEntry| $ 108))) (DEFUN |TSETCAT-;headReduced?;SB;23| (|ts| $) - (SPADCALL |ts| (ELT $ 103) (|getShellEntry| $ 100))) + (SPADCALL |ts| (ELT $ 111) (|getShellEntry| $ 108))) (DEFUN |TSETCAT-;initiallyReduced?;SB;24| (|ts| $) - (SPADCALL |ts| (ELT $ 105) (|getShellEntry| $ 100))) + (SPADCALL |ts| (ELT $ 113) (|getShellEntry| $ 108))) (DEFUN |TSETCAT-;mvar;SV;25| (|ts| $) (PROG (#0=#:G1599) @@ -748,12 +748,12 @@ (|error| "Error from TSETCAT in mvar : #1 is empty")) ('T (SPADCALL - (PROG2 (LETT #0# (SPADCALL |ts| (|getShellEntry| $ 14)) + (PROG2 (LETT #0# (SPADCALL |ts| (|getShellEntry| $ 15)) |TSETCAT-;mvar;SV;25|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 10) #0#)) - (|getShellEntry| $ 23))))))) + (|getShellEntry| $ 25))))))) (DEFUN |TSETCAT-;first;SU;26| (|ts| $) (PROG (|lp|) @@ -762,9 +762,9 @@ ((SPADCALL |ts| (|getShellEntry| $ 12)) (CONS 1 "failed")) ('T (SEQ (LETT |lp| - (SPADCALL (ELT $ 22) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;first;SU;26|) (EXIT (CONS 0 (|SPADfirst| |lp|)))))))))) @@ -775,9 +775,9 @@ ((SPADCALL |ts| (|getShellEntry| $ 12)) (CONS 1 "failed")) ('T (SEQ (LETT |lp| - (SPADCALL (ELT $ 21) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 22) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;last;SU;27|) (EXIT (CONS 0 (|SPADfirst| |lp|)))))))))) @@ -788,17 +788,17 @@ ((SPADCALL |ts| (|getShellEntry| $ 12)) (CONS 1 "failed")) ('T (SEQ (LETT |lp| - (SPADCALL (ELT $ 22) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;rest;SU;28|) (EXIT (CONS 0 (SPADCALL (CDR |lp|) - (|getShellEntry| $ 110))))))))))) + (|getShellEntry| $ 118))))))))))) (DEFUN |TSETCAT-;coerce;SL;29| (|ts| $) - (SPADCALL (ELT $ 22) (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36))) + (SPADCALL (ELT $ 24) (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41))) (DEFUN |TSETCAT-;algebraicVariables;SL;30| (|ts| $) (PROG (#0=#:G1667 |p| #1=#:G1668) @@ -806,7 +806,7 @@ (SEQ (PROGN (LETT #0# NIL |TSETCAT-;algebraicVariables;SL;30|) (SEQ (LETT |p| NIL |TSETCAT-;algebraicVariables;SL;30|) - (LETT #1# (SPADCALL |ts| (|getShellEntry| $ 28)) + (LETT #1# (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;algebraicVariables;SL;30|) G190 (COND @@ -819,7 +819,7 @@ (SEQ (EXIT (LETT #0# (CONS (SPADCALL |p| - (|getShellEntry| $ 23)) + (|getShellEntry| $ 25)) #0#) |TSETCAT-;algebraicVariables;SL;30|))) (LETT #1# (CDR #1#) @@ -827,16 +827,16 @@ (GO G190) G191 (EXIT (NREVERSE0 #0#)))))))) (DEFUN |TSETCAT-;algebraic?;VSB;31| (|v| |ts| $) - (SPADCALL |v| (SPADCALL |ts| (|getShellEntry| $ 115)) - (|getShellEntry| $ 116))) + (SPADCALL |v| (SPADCALL |ts| (|getShellEntry| $ 123)) + (|getShellEntry| $ 124))) (DEFUN |TSETCAT-;select;SVU;32| (|ts| |v| $) (PROG (|lp|) (RETURN (SEQ (LETT |lp| - (SPADCALL (ELT $ 22) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;select;SVU;32|) (SEQ G190 (COND @@ -845,8 +845,8 @@ ('T (NOT (SPADCALL |v| (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 23)) - (|getShellEntry| $ 64)))))) + (|getShellEntry| $ 25)) + (|getShellEntry| $ 72)))))) (GO G191))) (SEQ (EXIT (LETT |lp| (CDR |lp|) |TSETCAT-;select;SVU;32|))) @@ -858,29 +858,29 @@ (DEFUN |TSETCAT-;collectQuasiMonic;2S;33| (|ts| $) (PROG (|newlp| |lp|) (RETURN - (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 28)) + (SEQ (LETT |lp| (SPADCALL |ts| (|getShellEntry| $ 30)) |TSETCAT-;collectQuasiMonic;2S;33|) (LETT |newlp| NIL |TSETCAT-;collectQuasiMonic;2S;33|) (SEQ G190 (COND ((NULL (NOT (NULL |lp|))) (GO G191))) (SEQ (COND ((SPADCALL (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 45)) - (|getShellEntry| $ 34)) + (|getShellEntry| $ 51)) + (|getShellEntry| $ 39)) (LETT |newlp| (CONS (|SPADfirst| |lp|) |newlp|) |TSETCAT-;collectQuasiMonic;2S;33|))) (EXIT (LETT |lp| (CDR |lp|) |TSETCAT-;collectQuasiMonic;2S;33|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |newlp| (|getShellEntry| $ 110))))))) + (EXIT (SPADCALL |newlp| (|getShellEntry| $ 118))))))) (DEFUN |TSETCAT-;collectUnder;SVS;34| (|ts| |v| $) (PROG (|lp|) (RETURN (SEQ (LETT |lp| - (SPADCALL (ELT $ 22) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;collectUnder;SVS;34|) (SEQ G190 (COND @@ -889,21 +889,21 @@ ('T (NOT (SPADCALL (SPADCALL (|SPADfirst| |lp|) - (|getShellEntry| $ 23)) - |v| (|getShellEntry| $ 63)))))) + (|getShellEntry| $ 25)) + |v| (|getShellEntry| $ 71)))))) (GO G191))) (SEQ (EXIT (LETT |lp| (CDR |lp|) |TSETCAT-;collectUnder;SVS;34|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |lp| (|getShellEntry| $ 110))))))) + (EXIT (SPADCALL |lp| (|getShellEntry| $ 118))))))) (DEFUN |TSETCAT-;collectUpper;SVS;35| (|ts| |v| $) (PROG (|lp2| |lp1|) (RETURN (SEQ (LETT |lp1| - (SPADCALL (ELT $ 22) - (SPADCALL |ts| (|getShellEntry| $ 28)) - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) + (SPADCALL |ts| (|getShellEntry| $ 30)) + (|getShellEntry| $ 41)) |TSETCAT-;collectUpper;SVS;35|) (LETT |lp2| NIL |TSETCAT-;collectUpper;SVS;35|) (SEQ G190 @@ -913,20 +913,20 @@ ('T (SPADCALL |v| (SPADCALL (|SPADfirst| |lp1|) - (|getShellEntry| $ 23)) - (|getShellEntry| $ 63))))) + (|getShellEntry| $ 25)) + (|getShellEntry| $ 71))))) (GO G191))) (SEQ (LETT |lp2| (CONS (|SPADfirst| |lp1|) |lp2|) |TSETCAT-;collectUpper;SVS;35|) (EXIT (LETT |lp1| (CDR |lp1|) |TSETCAT-;collectUpper;SVS;35|))) NIL (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL (REVERSE |lp2|) (|getShellEntry| $ 110))))))) + (EXIT (SPADCALL (REVERSE |lp2|) (|getShellEntry| $ 118))))))) (DEFUN |TSETCAT-;construct;LS;36| (|lp| $) (PROG (|rif|) (RETURN - (SEQ (LETT |rif| (SPADCALL |lp| (|getShellEntry| $ 122)) + (SEQ (LETT |rif| (SPADCALL |lp| (|getShellEntry| $ 131)) |TSETCAT-;construct;LS;36|) (EXIT (COND ((QEQCAR |rif| 0) (QCDR |rif|)) @@ -937,26 +937,26 @@ (PROG (|rif|) (RETURN (SEQ (COND - ((NULL |lp|) (CONS 0 (SPADCALL (|getShellEntry| $ 37)))) + ((NULL |lp|) (CONS 0 (SPADCALL (|getShellEntry| $ 42)))) ('T (SEQ (LETT |lp| - (SPADCALL (ELT $ 22) |lp| - (|getShellEntry| $ 36)) + (SPADCALL (ELT $ 24) |lp| + (|getShellEntry| $ 41)) |TSETCAT-;retractIfCan;LU;37|) (LETT |rif| - (SPADCALL (CDR |lp|) (|getShellEntry| $ 122)) + (SPADCALL (CDR |lp|) (|getShellEntry| $ 131)) |TSETCAT-;retractIfCan;LU;37|) (EXIT (COND ((QEQCAR |rif| 0) (SPADCALL (QCDR |rif|) (|SPADfirst| |lp|) - (|getShellEntry| $ 124))) + (|getShellEntry| $ 133))) ('T (|error| "in retractIfCan : LP -> ... from TSETCAT : bad arg"))))))))))) (DEFUN |TSETCAT-;extend;SPS;38| (|ts| |p| $) (PROG (|eif|) (RETURN - (SEQ (LETT |eif| (SPADCALL |ts| |p| (|getShellEntry| $ 124)) + (SEQ (LETT |eif| (SPADCALL |ts| |p| (|getShellEntry| $ 133)) |TSETCAT-;extend;SPS;38|) (EXIT (COND ((QEQCAR |eif| 0) (QCDR |eif|)) @@ -966,13 +966,13 @@ (DEFUN |TSETCAT-;coHeight;SNni;39| (|ts| $) (PROG (|n| |m| #0=#:G1663) (RETURN - (SEQ (LETT |n| (SPADCALL (|getShellEntry| $ 127)) + (SEQ (LETT |n| (SPADCALL (|getShellEntry| $ 136)) |TSETCAT-;coHeight;SNni;39|) - (LETT |m| (LENGTH (SPADCALL |ts| (|getShellEntry| $ 28))) + (LETT |m| (LENGTH (SPADCALL |ts| (|getShellEntry| $ 30))) |TSETCAT-;coHeight;SNni;39|) (EXIT (PROG2 (LETT #0# (SPADCALL |n| |m| - (|getShellEntry| $ 128)) + (|getShellEntry| $ 138)) |TSETCAT-;coHeight;SNni;39|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|NonNegativeInteger|) @@ -991,7 +991,7 @@ (LETT |dv$| (LIST '|TriangularSetCategory&| |dv$1| |dv$2| |dv$3| |dv$4| |dv$5|) . #0#) - (LETT $ (|newShell| 131) . #0#) + (LETT $ (|newShell| 141) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -1005,7 +1005,7 @@ (|setShellEntry| $ 10 |#5|) (COND ((|testBitVector| |pv$| 1) - (|setShellEntry| $ 129 + (|setShellEntry| $ 139 (CONS (|dispatchFunction| |TSETCAT-;coHeight;SNni;39|) $)))) $)))) @@ -1013,116 +1013,121 @@ (MAKEPROP '|TriangularSetCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|local| |#3|) (|local| |#4|) (|local| |#5|) (|Boolean|) - (0 . |empty?|) (|Union| 10 '"failed") (5 . |first|) - (10 . =) (|Union| $ '"failed") (16 . |rest|) (21 . =) - |TSETCAT-;=;2SB;1| (27 . |last|) (32 . |infRittWu?|) - (38 . |supRittWu?|) (44 . |mvar|) (49 . |collectUpper|) - (55 . |infRittWu?|) |TSETCAT-;infRittWu?;2SB;2| - (|List| 10) (61 . |members|) (|Mapping| 11 10 10) - |TSETCAT-;reduced?;PSMB;3| (66 . |zero?|) - (|Mapping| 11 10) (71 . |remove|) (77 . |ground?|) - (82 . |any?|) (88 . |sort|) (94 . |empty|) (98 . |extend|) - (104 . |reduced?|) (|Record| (|:| |bas| $) (|:| |top| 27)) - (|Union| 40 '"failed") |TSETCAT-;basicSet;LMU;4| - (111 . |concat|) |TSETCAT-;basicSet;LMMU;5| (117 . |init|) - (122 . |primPartElseUnitCanonical|) - (127 . |removeDuplicates|) |TSETCAT-;initials;SL;6| - (|NonNegativeInteger|) (132 . |mdeg|) - |TSETCAT-;degree;SNni;7| (137 . |initials|) - (|Record| (|:| |close| 27) (|:| |open| 27)) + (0 . |empty?|) (5 . |false|) (|Union| 10 '"failed") + (9 . |first|) (14 . =) (|Union| $ '"failed") (20 . |rest|) + (25 . =) |TSETCAT-;=;2SB;1| (31 . |last|) + (36 . |infRittWu?|) (42 . |true|) (46 . |supRittWu?|) + (52 . |mvar|) (57 . |collectUpper|) (63 . |infRittWu?|) + |TSETCAT-;infRittWu?;2SB;2| (|List| 10) (69 . |members|) + (74 . |empty?|) (79 . |first|) (84 . |rest|) + (|Mapping| 11 10 10) |TSETCAT-;reduced?;PSMB;3| + (89 . |zero?|) (|Mapping| 11 10) (94 . |remove|) + (100 . |ground?|) (105 . |any?|) (111 . |sort|) + (117 . |empty|) (121 . |extend|) (127 . |reduced?|) + (134 . |cons|) (|Record| (|:| |bas| $) (|:| |top| 29)) + (|Union| 46 '"failed") |TSETCAT-;basicSet;LMU;4| + (140 . |concat|) |TSETCAT-;basicSet;LMMU;5| (146 . |init|) + (151 . |primPartElseUnitCanonical|) + (156 . |removeDuplicates|) |TSETCAT-;initials;SL;6| + (|NonNegativeInteger|) (161 . |Zero|) (165 . |mdeg|) + (170 . *) |TSETCAT-;degree;SNni;7| (176 . |initials|) + (|Record| (|:| |close| 29) (|:| |open| 29)) |TSETCAT-;quasiComponent;SR;8| (|List| $) - (142 . |normalized?|) |TSETCAT-;normalized?;PSB;9| - (148 . |reduced?|) |TSETCAT-;stronglyReduced?;PSB;10| - (154 . |head|) (159 . |stronglyReduced?|) - |TSETCAT-;headReduced?;PSB;11| (165 . <) (171 . =) - (177 . |reduced?|) |TSETCAT-;initiallyReduced?;PSB;12| + (181 . |normalized?|) |TSETCAT-;normalized?;PSB;9| + (187 . |reduced?|) |TSETCAT-;stronglyReduced?;PSB;10| + (193 . |head|) (198 . |stronglyReduced?|) + |TSETCAT-;headReduced?;PSB;11| (204 . <) (210 . =) + (216 . |reduced?|) |TSETCAT-;initiallyReduced?;PSB;12| (|Mapping| 10 10 10) |TSETCAT-;reduce;PSMMP;13| - (183 . |trivialIdeal?|) (188 . |One|) (192 . |reduce|) + (222 . |trivialIdeal?|) (227 . |One|) (231 . |reduce|) |TSETCAT-;rewriteSetWithReduction;LSMML;14| - (200 . |lazyPrem|) |TSETCAT-;stronglyReduce;PSP;15| - (206 . |headReduce|) (212 . |headReduced?|) - |TSETCAT-;headReduce;PSP;16| (218 . |initiallyReduce|) - (224 . |initiallyReduced?|) - |TSETCAT-;initiallyReduce;PSP;17| (230 . |collectUnder|) - (236 . |algebraic?|) (242 . |select|) (248 . |removeZero|) - (254 . |Zero|) (258 . |degree|) (|Integer|) - (264 . |positive?|) (269 . |mainMonomial|) (274 . *) - (280 . +) (286 . |tail|) |TSETCAT-;removeZero;PSP;18| - (291 . |collectQuasiMonic|) + (239 . |lazyPrem|) |TSETCAT-;stronglyReduce;PSP;15| + (245 . |headReduce|) (251 . |headReduced?|) + |TSETCAT-;headReduce;PSP;16| (257 . |initiallyReduce|) + (263 . |initiallyReduced?|) + |TSETCAT-;initiallyReduce;PSP;17| (269 . |collectUnder|) + (275 . |algebraic?|) (281 . |select|) (287 . |removeZero|) + (293 . |Zero|) (297 . |degree|) (|Integer|) + (303 . |positive?|) (308 . |mainMonomial|) (313 . *) + (319 . +) (325 . |tail|) |TSETCAT-;removeZero;PSP;18| + (330 . |collectQuasiMonic|) (|Record| (|:| |rnum| 7) (|:| |polnum| 10) (|:| |den| 7)) - (296 . |remainder|) |TSETCAT-;reduceByQuasiMonic;PSP;19| - (|Mapping| 11 10 27) |TSETCAT-;autoReduced?;SMB;20| - (302 . |autoReduced?|) |TSETCAT-;stronglyReduced?;SB;21| - |TSETCAT-;normalized?;SB;22| (308 . |headReduced?|) - |TSETCAT-;headReduced?;SB;23| (314 . |initiallyReduced?|) + (335 . |remainder|) |TSETCAT-;reduceByQuasiMonic;PSP;19| + (|Mapping| 11 10 29) |TSETCAT-;autoReduced?;SMB;20| + (341 . |autoReduced?|) |TSETCAT-;stronglyReduced?;SB;21| + |TSETCAT-;normalized?;SB;22| (347 . |headReduced?|) + |TSETCAT-;headReduced?;SB;23| (353 . |initiallyReduced?|) |TSETCAT-;initiallyReduced?;SB;24| |TSETCAT-;mvar;SV;25| |TSETCAT-;first;SU;26| |TSETCAT-;last;SU;27| - (320 . |construct|) |TSETCAT-;rest;SU;28| + (359 . |construct|) |TSETCAT-;rest;SU;28| |TSETCAT-;coerce;SL;29| (|List| 9) |TSETCAT-;algebraicVariables;SL;30| - (325 . |algebraicVariables|) (330 . |member?|) + (364 . |algebraicVariables|) (369 . |member?|) |TSETCAT-;algebraic?;VSB;31| |TSETCAT-;select;SVU;32| |TSETCAT-;collectQuasiMonic;2S;33| - |TSETCAT-;collectUnder;SVS;34| - |TSETCAT-;collectUpper;SVS;35| (336 . |retractIfCan|) - |TSETCAT-;construct;LS;36| (341 . |extendIfCan|) + |TSETCAT-;collectUnder;SVS;34| (375 . |reverse|) + |TSETCAT-;collectUpper;SVS;35| (380 . |retractIfCan|) + |TSETCAT-;construct;LS;36| (385 . |extendIfCan|) |TSETCAT-;retractIfCan;LU;37| |TSETCAT-;extend;SPS;38| - (347 . |size|) (351 . |subtractIfCan|) (357 . |coHeight|) - (|OutputForm|)) - '#(|stronglyReduced?| 362 |stronglyReduce| 373 |select| 379 - |rewriteSetWithReduction| 385 |retractIfCan| 393 |rest| - 398 |removeZero| 403 |reduced?| 409 |reduceByQuasiMonic| - 416 |reduce| 422 |quasiComponent| 430 |normalized?| 435 - |mvar| 446 |last| 451 |initials| 456 |initiallyReduced?| - 461 |initiallyReduce| 472 |infRittWu?| 478 |headReduced?| - 484 |headReduce| 495 |first| 501 |extend| 506 |degree| 512 - |construct| 517 |collectUpper| 522 |collectUnder| 528 - |collectQuasiMonic| 534 |coerce| 539 |coHeight| 544 - |basicSet| 549 |autoReduced?| 562 |algebraicVariables| 568 - |algebraic?| 573 = 579) + (391 . |size|) (395 . |#|) (400 . |subtractIfCan|) + (406 . |coHeight|) (|OutputForm|)) + '#(|stronglyReduced?| 411 |stronglyReduce| 422 |select| 428 + |rewriteSetWithReduction| 434 |retractIfCan| 442 |rest| + 447 |removeZero| 452 |reduced?| 458 |reduceByQuasiMonic| + 465 |reduce| 471 |quasiComponent| 479 |normalized?| 484 + |mvar| 495 |last| 500 |initials| 505 |initiallyReduced?| + 510 |initiallyReduce| 521 |infRittWu?| 527 |headReduced?| + 533 |headReduce| 544 |first| 550 |extend| 555 |degree| 561 + |construct| 566 |collectUpper| 571 |collectUnder| 577 + |collectQuasiMonic| 583 |coerce| 588 |coHeight| 593 + |basicSet| 598 |autoReduced?| 611 |algebraicVariables| 617 + |algebraic?| 622 = 628) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 129 - '(1 6 11 0 12 1 6 13 0 14 2 10 11 0 0 - 15 1 6 16 0 17 2 6 11 0 0 18 1 6 13 0 - 20 2 10 11 0 0 21 2 10 11 0 0 22 1 10 - 9 0 23 2 6 0 0 9 24 2 6 11 0 0 25 1 6 - 27 0 28 1 10 11 0 31 2 27 0 32 0 33 1 - 10 11 0 34 2 27 11 32 0 35 2 27 0 29 - 0 36 0 6 0 37 2 6 0 0 10 38 3 6 11 10 - 0 29 39 2 27 0 0 0 43 1 10 0 0 45 1 - 10 0 0 46 1 27 0 0 47 1 10 49 0 50 1 - 6 27 0 52 2 10 11 0 55 56 2 10 11 0 - 55 58 1 10 0 0 60 2 6 11 10 0 61 2 9 - 11 0 0 63 2 9 11 0 0 64 2 10 11 0 0 - 65 1 6 11 0 69 0 10 0 70 4 6 10 10 0 - 67 29 71 2 10 0 0 0 73 2 10 0 0 0 75 - 2 10 11 0 0 76 2 10 0 0 0 78 2 10 11 - 0 0 79 2 6 0 0 9 81 2 6 11 9 0 82 2 6 - 13 0 9 83 2 6 10 10 0 84 0 10 0 85 2 - 10 49 0 9 86 1 87 11 0 88 1 10 0 0 89 - 2 10 0 0 0 90 2 10 0 0 0 91 1 10 0 0 - 92 1 6 0 0 94 2 6 95 10 0 96 2 6 11 0 - 98 100 2 10 11 0 55 103 2 10 11 0 55 - 105 1 6 0 27 110 1 6 113 0 115 2 113 - 11 9 0 116 1 6 16 27 122 2 6 16 0 10 - 124 0 9 49 127 2 49 16 0 0 128 1 0 49 - 0 129 1 0 11 0 101 2 0 11 10 0 59 2 0 - 10 10 0 74 2 0 13 0 9 118 4 0 27 27 0 - 67 29 72 1 0 16 27 125 1 0 16 0 111 2 - 0 10 10 0 93 3 0 11 10 0 29 30 2 0 10 - 10 0 97 4 0 10 10 0 67 29 68 1 0 53 0 - 54 1 0 11 0 102 2 0 11 10 0 57 1 0 9 - 0 107 1 0 13 0 109 1 0 27 0 48 1 0 11 - 0 106 2 0 11 10 0 66 2 0 10 10 0 80 2 - 0 11 0 0 26 1 0 11 0 104 2 0 11 10 0 - 62 2 0 10 10 0 77 1 0 13 0 108 2 0 0 - 0 10 126 1 0 49 0 51 1 0 0 27 123 2 0 - 0 0 9 121 2 0 0 0 9 120 1 0 0 0 119 1 - 0 27 0 112 1 0 49 0 129 3 0 41 27 32 - 29 44 2 0 41 27 29 42 2 0 11 0 98 99 - 1 0 113 0 114 2 0 11 9 0 117 2 0 11 0 - 0 19))))) + (|makeByteWordVec2| 139 + '(1 6 11 0 12 0 11 0 13 1 6 14 0 15 2 + 10 11 0 0 16 1 6 17 0 18 2 6 11 0 0 + 19 1 6 14 0 21 2 10 11 0 0 22 0 11 0 + 23 2 10 11 0 0 24 1 10 9 0 25 2 6 0 0 + 9 26 2 6 11 0 0 27 1 6 29 0 30 1 29 + 11 0 31 1 29 10 0 32 1 29 0 0 33 1 10 + 11 0 36 2 29 0 37 0 38 1 10 11 0 39 2 + 29 11 37 0 40 2 29 0 34 0 41 0 6 0 42 + 2 6 0 0 10 43 3 6 11 10 0 34 44 2 29 + 0 10 0 45 2 29 0 0 0 49 1 10 0 0 51 1 + 10 0 0 52 1 29 0 0 53 0 55 0 56 1 10 + 55 0 57 2 55 0 55 0 58 1 6 29 0 60 2 + 10 11 0 63 64 2 10 11 0 63 66 1 10 0 + 0 68 2 6 11 10 0 69 2 9 11 0 0 71 2 9 + 11 0 0 72 2 10 11 0 0 73 1 6 11 0 77 + 0 10 0 78 4 6 10 10 0 75 34 79 2 10 0 + 0 0 81 2 10 0 0 0 83 2 10 11 0 0 84 2 + 10 0 0 0 86 2 10 11 0 0 87 2 6 0 0 9 + 89 2 6 11 9 0 90 2 6 14 0 9 91 2 6 10 + 10 0 92 0 10 0 93 2 10 55 0 9 94 1 95 + 11 0 96 1 10 0 0 97 2 10 0 0 0 98 2 + 10 0 0 0 99 1 10 0 0 100 1 6 0 0 102 + 2 6 103 10 0 104 2 6 11 0 106 108 2 + 10 11 0 63 111 2 10 11 0 63 113 1 6 0 + 29 118 1 6 121 0 123 2 121 11 9 0 124 + 1 29 0 0 129 1 6 17 29 131 2 6 17 0 + 10 133 0 9 55 136 1 29 55 0 137 2 55 + 17 0 0 138 1 0 55 0 139 1 0 11 0 109 + 2 0 11 10 0 67 2 0 10 10 0 82 2 0 14 + 0 9 126 4 0 29 29 0 75 34 80 1 0 17 + 29 134 1 0 17 0 119 2 0 10 10 0 101 3 + 0 11 10 0 34 35 2 0 10 10 0 105 4 0 + 10 10 0 75 34 76 1 0 61 0 62 1 0 11 0 + 110 2 0 11 10 0 65 1 0 9 0 115 1 0 14 + 0 117 1 0 29 0 54 1 0 11 0 114 2 0 11 + 10 0 74 2 0 10 10 0 88 2 0 11 0 0 28 + 1 0 11 0 112 2 0 11 10 0 70 2 0 10 10 + 0 85 1 0 14 0 116 2 0 0 0 10 135 1 0 + 55 0 59 1 0 0 29 132 2 0 0 0 9 130 2 + 0 0 0 9 128 1 0 0 0 127 1 0 29 0 120 + 1 0 55 0 139 3 0 47 29 37 34 50 2 0 + 47 29 34 48 2 0 11 0 106 107 1 0 121 + 0 122 2 0 11 9 0 125 2 0 11 0 0 20))))) '|lookupComplete|)) diff --git a/src/algebra/strap/UFD-.lsp b/src/algebra/strap/UFD-.lsp index dee1d804..786f9f7f 100644 --- a/src/algebra/strap/UFD-.lsp +++ b/src/algebra/strap/UFD-.lsp @@ -60,7 +60,7 @@ (LETT |dv$1| (|devaluate| |#1|) . #0=(|UniqueFactorizationDomain&|)) (LETT |dv$| (LIST '|UniqueFactorizationDomain&| |dv$1|) . #0#) - (LETT $ (|newShell| 25) . #0#) + (LETT $ (|newShell| 29) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -76,14 +76,16 @@ |UFD-;squareFreePart;2S;1| (25 . |factor|) (|Union| '"nil" '"sqfr" '"irred" '"prime") (|Record| (|:| |flg| 19) (|:| |fctr| 6) (|:| |xpnt| 11)) - (|List| 20) (30 . |factorList|) (|Boolean|) + (|List| 20) (30 . |factorList|) (|NonNegativeInteger|) + (35 . |#|) (40 . |One|) (|Boolean|) (44 . =) |UFD-;prime?;SB;2|) - '#(|squareFreePart| 35 |prime?| 40) 'NIL + '#(|squareFreePart| 50 |prime?| 55) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 24 + (|makeByteWordVec2| 28 '(1 6 7 0 8 1 9 6 0 10 1 9 13 0 14 2 6 0 0 0 15 0 6 0 16 1 6 7 0 18 1 9 21 0 - 22 1 0 0 0 17 1 0 23 0 24))))) + 22 1 21 23 0 24 0 23 0 25 2 23 26 0 0 + 27 1 0 0 0 17 1 0 26 0 28))))) '|lookupComplete|)) diff --git a/src/algebra/strap/UPOLYC-.lsp b/src/algebra/strap/UPOLYC-.lsp index 87756379..49994497 100644 --- a/src/algebra/strap/UPOLYC-.lsp +++ b/src/algebra/strap/UPOLYC-.lsp @@ -179,13 +179,13 @@ ((OR (SPADCALL |p| (|getShellEntry| $ 9)) (ZEROP (SPADCALL |p| (|getShellEntry| $ 11)))) NIL) - ('T (LIST (SPADCALL (|getShellEntry| $ 13)))))) + ('T (LIST (SPADCALL (|getShellEntry| $ 14)))))) (DEFUN |UPOLYC-;degree;SSaosNni;2| (|p| |v| $) (SPADCALL |p| (|getShellEntry| $ 11))) (DEFUN |UPOLYC-;totalDegree;SLNni;3| (|p| |lv| $) - (COND ((NULL |lv|) 0) ('T (SPADCALL |p| (|getShellEntry| $ 17))))) + (COND ((NULL |lv|) 0) ('T (SPADCALL |p| (|getShellEntry| $ 20))))) (DEFUN |UPOLYC-;degree;SLL;4| (|p| |lv| $) (COND @@ -199,10 +199,10 @@ (|error| "can only eval a univariate polynomial once")) ('T (SPADCALL |p| (|SPADfirst| |lv|) (|SPADfirst| |lq|) - (|getShellEntry| $ 21))))) + (|getShellEntry| $ 28))))) (DEFUN |UPOLYC-;eval;SSaos2S;6| (|p| |v| |q| $) - (SPADCALL |p| |q| (|getShellEntry| $ 24))) + (SPADCALL |p| |q| (|getShellEntry| $ 31))) (DEFUN |UPOLYC-;eval;SLLS;7| (|p| |lv| |lr| $) (COND @@ -211,11 +211,11 @@ (|error| "can only eval a univariate polynomial once")) ('T (SPADCALL |p| (|SPADfirst| |lv|) (|SPADfirst| |lr|) - (|getShellEntry| $ 26))))) + (|getShellEntry| $ 35))))) (DEFUN |UPOLYC-;eval;SSaosRS;8| (|p| |v| |r| $) - (SPADCALL (SPADCALL |p| |r| (|getShellEntry| $ 29)) - (|getShellEntry| $ 30))) + (SPADCALL (SPADCALL |p| |r| (|getShellEntry| $ 37)) + (|getShellEntry| $ 38))) (DEFUN |UPOLYC-;eval;SLS;9| (|p| |le| $) (COND @@ -226,86 +226,86 @@ (COND ((QEQCAR (SPADCALL (SPADCALL (|SPADfirst| |le|) - (|getShellEntry| $ 33)) - (|getShellEntry| $ 35)) + (|getShellEntry| $ 45)) + (|getShellEntry| $ 47)) 1) |p|) ('T (SPADCALL |p| - (SPADCALL (|SPADfirst| |le|) (|getShellEntry| $ 36)) - (|getShellEntry| $ 24))))))) + (SPADCALL (|SPADfirst| |le|) (|getShellEntry| $ 48)) + (|getShellEntry| $ 31))))))) (DEFUN |UPOLYC-;mainVariable;SU;10| (|p| $) (COND ((ZEROP (SPADCALL |p| (|getShellEntry| $ 11))) (CONS 1 "failed")) - ('T (CONS 0 (SPADCALL (|getShellEntry| $ 13)))))) + ('T (CONS 0 (SPADCALL (|getShellEntry| $ 14)))))) (DEFUN |UPOLYC-;minimumDegree;SSaosNni;11| (|p| |v| $) - (SPADCALL |p| (|getShellEntry| $ 41))) + (SPADCALL |p| (|getShellEntry| $ 53))) (DEFUN |UPOLYC-;minimumDegree;SLL;12| (|p| |lv| $) (COND ((NULL |lv|) NIL) - ('T (LIST (SPADCALL |p| (|getShellEntry| $ 41)))))) + ('T (LIST (SPADCALL |p| (|getShellEntry| $ 53)))))) (DEFUN |UPOLYC-;monomial;SSaosNniS;13| (|p| |v| |n| $) (SPADCALL (CONS #'|UPOLYC-;monomial;SSaosNniS;13!0| (VECTOR $ |n|)) - |p| (|getShellEntry| $ 46))) + |p| (|getShellEntry| $ 58))) (DEFUN |UPOLYC-;monomial;SSaosNniS;13!0| (|#1| $$) (SPADCALL |#1| (|getShellEntry| $$ 1) - (|getShellEntry| (|getShellEntry| $$ 0) 44))) + (|getShellEntry| (|getShellEntry| $$ 0) 56))) (DEFUN |UPOLYC-;coerce;SaosS;14| (|v| $) - (SPADCALL (|spadConstant| $ 49) 1 (|getShellEntry| $ 50))) + (SPADCALL (|spadConstant| $ 61) 1 (|getShellEntry| $ 63))) (DEFUN |UPOLYC-;makeSUP;SSup;15| (|p| $) (COND - ((SPADCALL |p| (|getShellEntry| $ 9)) (|spadConstant| $ 53)) + ((SPADCALL |p| (|getShellEntry| $ 9)) (|spadConstant| $ 66)) ('T (SPADCALL - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 54)) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 67)) (SPADCALL |p| (|getShellEntry| $ 11)) - (|getShellEntry| $ 55)) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 56)) - (|getShellEntry| $ 57)) - (|getShellEntry| $ 58))))) + (|getShellEntry| $ 68)) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 69)) + (|getShellEntry| $ 70)) + (|getShellEntry| $ 71))))) (DEFUN |UPOLYC-;unmakeSUP;SupS;16| (|sp| $) (COND - ((SPADCALL |sp| (|getShellEntry| $ 60)) (|spadConstant| $ 61)) + ((SPADCALL |sp| (|getShellEntry| $ 73)) (|spadConstant| $ 74)) ('T (SPADCALL - (SPADCALL (SPADCALL |sp| (|getShellEntry| $ 62)) - (SPADCALL |sp| (|getShellEntry| $ 63)) - (|getShellEntry| $ 50)) - (SPADCALL (SPADCALL |sp| (|getShellEntry| $ 64)) - (|getShellEntry| $ 65)) - (|getShellEntry| $ 66))))) + (SPADCALL (SPADCALL |sp| (|getShellEntry| $ 75)) + (SPADCALL |sp| (|getShellEntry| $ 76)) + (|getShellEntry| $ 63)) + (SPADCALL (SPADCALL |sp| (|getShellEntry| $ 77)) + (|getShellEntry| $ 78)) + (|getShellEntry| $ 79))))) (DEFUN |UPOLYC-;karatsubaDivide;SNniR;17| (|p| |n| $) (SPADCALL |p| - (SPADCALL (|spadConstant| $ 49) |n| (|getShellEntry| $ 50)) - (|getShellEntry| $ 69))) + (SPADCALL (|spadConstant| $ 61) |n| (|getShellEntry| $ 63)) + (|getShellEntry| $ 82))) (DEFUN |UPOLYC-;shiftRight;SNniS;18| (|p| |n| $) (QCAR (SPADCALL |p| - (SPADCALL (|spadConstant| $ 49) |n| (|getShellEntry| $ 50)) - (|getShellEntry| $ 69)))) + (SPADCALL (|spadConstant| $ 61) |n| (|getShellEntry| $ 63)) + (|getShellEntry| $ 82)))) (DEFUN |UPOLYC-;shiftLeft;SNniS;19| (|p| |n| $) (SPADCALL |p| - (SPADCALL (|spadConstant| $ 49) |n| (|getShellEntry| $ 50)) - (|getShellEntry| $ 72))) + (SPADCALL (|spadConstant| $ 61) |n| (|getShellEntry| $ 63)) + (|getShellEntry| $ 85))) (DEFUN |UPOLYC-;solveLinearPolynomialEquation;LSupU;20| (|lpp| |pp| $) - (SPADCALL |lpp| |pp| (|getShellEntry| $ 78))) + (SPADCALL |lpp| |pp| (|getShellEntry| $ 91))) (DEFUN |UPOLYC-;factorPolynomial;SupF;21| (|pp| $) - (SPADCALL |pp| (|getShellEntry| $ 84))) + (SPADCALL |pp| (|getShellEntry| $ 97))) (DEFUN |UPOLYC-;factorSquareFreePolynomial;SupF;22| (|pp| $) - (SPADCALL |pp| (|getShellEntry| $ 87))) + (SPADCALL |pp| (|getShellEntry| $ 100))) (DEFUN |UPOLYC-;factor;SF;23| (|p| $) (PROG (|ansR| #0=#:G1691 |w| #1=#:G1692) @@ -314,21 +314,21 @@ ((ZEROP (SPADCALL |p| (|getShellEntry| $ 11))) (SEQ (LETT |ansR| (SPADCALL - (SPADCALL |p| (|getShellEntry| $ 54)) - (|getShellEntry| $ 90)) + (SPADCALL |p| (|getShellEntry| $ 67)) + (|getShellEntry| $ 103)) |UPOLYC-;factor;SF;23|) (EXIT (SPADCALL (SPADCALL (SPADCALL |ansR| - (|getShellEntry| $ 92)) - (|getShellEntry| $ 30)) + (|getShellEntry| $ 105)) + (|getShellEntry| $ 38)) (PROGN (LETT #0# NIL |UPOLYC-;factor;SF;23|) (SEQ (LETT |w| NIL |UPOLYC-;factor;SF;23|) (LETT #1# (SPADCALL |ansR| - (|getShellEntry| $ 97)) + (|getShellEntry| $ 110)) |UPOLYC-;factor;SF;23|) G190 (COND @@ -344,7 +344,7 @@ (CONS (VECTOR (QVELT |w| 0) (SPADCALL (QVELT |w| 1) - (|getShellEntry| $ 30)) + (|getShellEntry| $ 38)) (QVELT |w| 2)) #0#) |UPOLYC-;factor;SF;23|))) @@ -352,12 +352,12 @@ |UPOLYC-;factor;SF;23|) (GO G190) G191 (EXIT (NREVERSE0 #0#)))) - (|getShellEntry| $ 101))))) + (|getShellEntry| $ 114))))) ('T - (SPADCALL (ELT $ 65) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 57)) - (|getShellEntry| $ 102)) - (|getShellEntry| $ 106)))))))) + (SPADCALL (ELT $ 78) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 70)) + (|getShellEntry| $ 115)) + (|getShellEntry| $ 119)))))))) (DEFUN |UPOLYC-;vectorise;SNniV;24| (|p| |n| $) (PROG (|v| |m| |i| #0=#:G1693 #1=#:G1522) @@ -365,12 +365,12 @@ (SEQ (LETT |m| (SPADCALL (LETT |v| - (SPADCALL |n| (|spadConstant| $ 108) - (|getShellEntry| $ 110)) + (SPADCALL |n| (|spadConstant| $ 121) + (|getShellEntry| $ 123)) |UPOLYC-;vectorise;SNniV;24|) - (|getShellEntry| $ 111)) + (|getShellEntry| $ 124)) |UPOLYC-;vectorise;SNniV;24|) - (SEQ (LETT |i| (SPADCALL |v| (|getShellEntry| $ 111)) + (SEQ (LETT |i| (SPADCALL |v| (|getShellEntry| $ 124)) |UPOLYC-;vectorise;SNniV;24|) (LETT #0# (QVSIZE |v|) |UPOLYC-;vectorise;SNniV;24|) G190 (COND ((> |i| #0#) (GO G191))) @@ -385,29 +385,29 @@ ('T 'T)) '(|NonNegativeInteger|) #1#)) - (|getShellEntry| $ 112)) - (|getShellEntry| $ 113)))) + (|getShellEntry| $ 127)) + (|getShellEntry| $ 128)))) (LETT |i| (+ |i| 1) |UPOLYC-;vectorise;SNniV;24|) (GO G190) G191 (EXIT NIL)) (EXIT |v|))))) (DEFUN |UPOLYC-;retract;SR;25| (|p| $) (COND - ((SPADCALL |p| (|getShellEntry| $ 9)) (|spadConstant| $ 108)) + ((SPADCALL |p| (|getShellEntry| $ 9)) (|spadConstant| $ 121)) ((ZEROP (SPADCALL |p| (|getShellEntry| $ 11))) - (SPADCALL |p| (|getShellEntry| $ 54))) + (SPADCALL |p| (|getShellEntry| $ 67))) ('T (|error| "Polynomial is not of degree 0")))) (DEFUN |UPOLYC-;retractIfCan;SU;26| (|p| $) (COND ((SPADCALL |p| (|getShellEntry| $ 9)) - (CONS 0 (|spadConstant| $ 108))) + (CONS 0 (|spadConstant| $ 121))) ((ZEROP (SPADCALL |p| (|getShellEntry| $ 11))) - (CONS 0 (SPADCALL |p| (|getShellEntry| $ 54)))) + (CONS 0 (SPADCALL |p| (|getShellEntry| $ 67)))) ('T (CONS 1 "failed")))) (DEFUN |UPOLYC-;init;S;27| ($) - (SPADCALL (|spadConstant| $ 118) (|getShellEntry| $ 30))) + (SPADCALL (|spadConstant| $ 133) (|getShellEntry| $ 38))) (DEFUN |UPOLYC-;nextItemInner| (|n| $) (PROG (|nn| |n1| |n2| #0=#:G1546 |n3|) @@ -417,27 +417,27 @@ (CONS 0 (SPADCALL (PROG2 (LETT #0# - (SPADCALL (|spadConstant| $ 108) - (|getShellEntry| $ 121)) + (SPADCALL (|spadConstant| $ 121) + (|getShellEntry| $ 136)) |UPOLYC-;nextItemInner|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 7) #0#)) - (|getShellEntry| $ 30)))) + (|getShellEntry| $ 38)))) ((ZEROP (SPADCALL |n| (|getShellEntry| $ 11))) (SEQ (LETT |nn| (SPADCALL - (SPADCALL |n| (|getShellEntry| $ 54)) - (|getShellEntry| $ 121)) + (SPADCALL |n| (|getShellEntry| $ 67)) + (|getShellEntry| $ 136)) |UPOLYC-;nextItemInner|) (EXIT (COND ((QEQCAR |nn| 1) (CONS 1 "failed")) ('T (CONS 0 (SPADCALL (QCDR |nn|) - (|getShellEntry| $ 30)))))))) + (|getShellEntry| $ 38)))))))) ('T - (SEQ (LETT |n1| (SPADCALL |n| (|getShellEntry| $ 56)) + (SEQ (LETT |n1| (SPADCALL |n| (|getShellEntry| $ 69)) |UPOLYC-;nextItemInner|) (LETT |n2| (|UPOLYC-;nextItemInner| |n1| $) |UPOLYC-;nextItemInner|) @@ -447,12 +447,12 @@ (SPADCALL (SPADCALL (SPADCALL |n| - (|getShellEntry| $ 54)) + (|getShellEntry| $ 67)) (SPADCALL |n| (|getShellEntry| $ 11)) - (|getShellEntry| $ 50)) + (|getShellEntry| $ 63)) (QCDR |n2|) - (|getShellEntry| $ 66)))) + (|getShellEntry| $ 79)))) ((< (+ 1 (SPADCALL |n1| (|getShellEntry| $ 11))) @@ -461,16 +461,16 @@ (SPADCALL (SPADCALL (SPADCALL |n| - (|getShellEntry| $ 54)) + (|getShellEntry| $ 67)) (SPADCALL |n| (|getShellEntry| $ 11)) - (|getShellEntry| $ 50)) + (|getShellEntry| $ 63)) (SPADCALL (PROG2 (LETT #0# (SPADCALL - (|spadConstant| $ 118) - (|getShellEntry| $ 121)) + (|spadConstant| $ 133) + (|getShellEntry| $ 136)) |UPOLYC-;nextItemInner|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -478,14 +478,14 @@ (+ 1 (SPADCALL |n1| (|getShellEntry| $ 11))) - (|getShellEntry| $ 50)) - (|getShellEntry| $ 66)))) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 79)))) ('T (SEQ (LETT |n3| (SPADCALL (SPADCALL |n| - (|getShellEntry| $ 54)) - (|getShellEntry| $ 121)) + (|getShellEntry| $ 67)) + (|getShellEntry| $ 136)) |UPOLYC-;nextItemInner|) (EXIT (COND ((QEQCAR |n3| 1) @@ -495,7 +495,7 @@ (SPADCALL (QCDR |n3|) (SPADCALL |n| (|getShellEntry| $ 11)) - (|getShellEntry| $ 50))))))))))))))))) + (|getShellEntry| $ 63))))))))))))))))) (DEFUN |UPOLYC-;nextItem;SU;29| (|n| $) (PROG (|n1| #0=#:G1559) @@ -507,20 +507,20 @@ (CONS 0 (SPADCALL (PROG2 (LETT #0# - (SPADCALL (|spadConstant| $ 118) - (|getShellEntry| $ 121)) + (SPADCALL (|spadConstant| $ 133) + (|getShellEntry| $ 136)) |UPOLYC-;nextItem;SU;29|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 7) #0#)) (+ 1 (SPADCALL |n| (|getShellEntry| $ 11))) - (|getShellEntry| $ 50)))) + (|getShellEntry| $ 63)))) ('T |n1|))))))) (DEFUN |UPOLYC-;content;SSaosS;30| (|p| |v| $) - (SPADCALL (SPADCALL |p| (|getShellEntry| $ 124)) - (|getShellEntry| $ 30))) + (SPADCALL (SPADCALL |p| (|getShellEntry| $ 140)) + (|getShellEntry| $ 38))) (DEFUN |UPOLYC-;primeFactor| (|p| |q| $) (PROG (#0=#:G1565 |p1|) @@ -529,15 +529,15 @@ (PROG2 (LETT #0# (SPADCALL |p| (SPADCALL |p| |q| - (|getShellEntry| $ 126)) - (|getShellEntry| $ 127)) + (|getShellEntry| $ 142)) + (|getShellEntry| $ 143)) |UPOLYC-;primeFactor|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) (|getShellEntry| $ 6) #0#)) |UPOLYC-;primeFactor|) (EXIT (COND - ((SPADCALL |p1| |p| (|getShellEntry| $ 128)) |p|) + ((SPADCALL |p1| |p| (|getShellEntry| $ 144)) |p|) ('T (|UPOLYC-;primeFactor| |p1| |q| $)))))))) (DEFUN |UPOLYC-;separate;2SR;32| (|p| |q| $) @@ -548,7 +548,7 @@ (EXIT (CONS |a| (PROG2 (LETT #0# (SPADCALL |p| |a| - (|getShellEntry| $ 127)) + (|getShellEntry| $ 143)) |UPOLYC-;separate;2SR;32|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -557,7 +557,7 @@ (DEFUN |UPOLYC-;differentiate;SM2S;33| (|x| |deriv| |x'| $) (PROG (|dg| |lc| #0=#:G1576 |d|) (RETURN - (SEQ (LETT |d| (|spadConstant| $ 61) + (SEQ (LETT |d| (|spadConstant| $ 74) |UPOLYC-;differentiate;SM2S;33|) (SEQ G190 (COND @@ -566,7 +566,7 @@ (SPADCALL |x| (|getShellEntry| $ 11)) |UPOLYC-;differentiate;SM2S;33|))) (GO G191))) - (SEQ (LETT |lc| (SPADCALL |x| (|getShellEntry| $ 54)) + (SEQ (LETT |lc| (SPADCALL |x| (|getShellEntry| $ 67)) |UPOLYC-;differentiate;SM2S;33|) (LETT |d| (SPADCALL @@ -574,7 +574,7 @@ (SPADCALL |x'| (SPADCALL (SPADCALL |dg| |lc| - (|getShellEntry| $ 132)) + (|getShellEntry| $ 149)) (PROG1 (LETT #0# (- |dg| 1) |UPOLYC-;differentiate;SM2S;33|) @@ -583,30 +583,30 @@ ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 50)) - (|getShellEntry| $ 72)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 85)) + (|getShellEntry| $ 79)) (SPADCALL (SPADCALL |lc| |deriv|) |dg| - (|getShellEntry| $ 50)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 79)) |UPOLYC-;differentiate;SM2S;33|) (EXIT (LETT |x| - (SPADCALL |x| (|getShellEntry| $ 56)) + (SPADCALL |x| (|getShellEntry| $ 69)) |UPOLYC-;differentiate;SM2S;33|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |d| (SPADCALL (SPADCALL - (SPADCALL |x| (|getShellEntry| $ 54)) + (SPADCALL |x| (|getShellEntry| $ 67)) |deriv|) - (|getShellEntry| $ 30)) - (|getShellEntry| $ 66))))))) + (|getShellEntry| $ 38)) + (|getShellEntry| $ 79))))))) (DEFUN |UPOLYC-;ncdiff| (|n| |x'| $) (PROG (#0=#:G1594 |n1|) (RETURN (COND - ((ZEROP |n|) (|spadConstant| $ 61)) + ((ZEROP |n|) (|spadConstant| $ 74)) ((ZEROP (LETT |n1| (PROG1 (LETT #0# (- |n| 1) |UPOLYC-;ncdiff|) (|check-subtype| @@ -617,19 +617,19 @@ ('T (SPADCALL (SPADCALL |x'| - (SPADCALL (|spadConstant| $ 49) |n1| - (|getShellEntry| $ 50)) - (|getShellEntry| $ 72)) + (SPADCALL (|spadConstant| $ 61) |n1| + (|getShellEntry| $ 63)) + (|getShellEntry| $ 85)) (SPADCALL - (SPADCALL (|spadConstant| $ 49) 1 - (|getShellEntry| $ 50)) - (|UPOLYC-;ncdiff| |n1| |x'| $) (|getShellEntry| $ 72)) - (|getShellEntry| $ 66))))))) + (SPADCALL (|spadConstant| $ 61) 1 + (|getShellEntry| $ 63)) + (|UPOLYC-;ncdiff| |n1| |x'| $) (|getShellEntry| $ 85)) + (|getShellEntry| $ 79))))))) (DEFUN |UPOLYC-;differentiate;SM2S;35| (|x| |deriv| |x'| $) (PROG (|dg| |lc| |d|) (RETURN - (SEQ (LETT |d| (|spadConstant| $ 61) + (SEQ (LETT |d| (|spadConstant| $ 74) |UPOLYC-;differentiate;SM2S;35|) (SEQ G190 (COND @@ -638,38 +638,38 @@ (SPADCALL |x| (|getShellEntry| $ 11)) |UPOLYC-;differentiate;SM2S;35|))) (GO G191))) - (SEQ (LETT |lc| (SPADCALL |x| (|getShellEntry| $ 54)) + (SEQ (LETT |lc| (SPADCALL |x| (|getShellEntry| $ 67)) |UPOLYC-;differentiate;SM2S;35|) (LETT |d| (SPADCALL (SPADCALL |d| (SPADCALL (SPADCALL |lc| |deriv|) - |dg| (|getShellEntry| $ 50)) - (|getShellEntry| $ 66)) + |dg| (|getShellEntry| $ 63)) + (|getShellEntry| $ 79)) (SPADCALL |lc| (|UPOLYC-;ncdiff| |dg| |x'| $) - (|getShellEntry| $ 135)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 154)) + (|getShellEntry| $ 79)) |UPOLYC-;differentiate;SM2S;35|) (EXIT (LETT |x| - (SPADCALL |x| (|getShellEntry| $ 56)) + (SPADCALL |x| (|getShellEntry| $ 69)) |UPOLYC-;differentiate;SM2S;35|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |d| (SPADCALL (SPADCALL - (SPADCALL |x| (|getShellEntry| $ 54)) + (SPADCALL |x| (|getShellEntry| $ 67)) |deriv|) - (|getShellEntry| $ 30)) - (|getShellEntry| $ 66))))))) + (|getShellEntry| $ 38)) + (|getShellEntry| $ 79))))))) (DEFUN |UPOLYC-;differentiate;SMS;36| (|x| |deriv| $) - (SPADCALL |x| |deriv| (|spadConstant| $ 48) (|getShellEntry| $ 136))) + (SPADCALL |x| |deriv| (|spadConstant| $ 60) (|getShellEntry| $ 155))) (DEFUN |UPOLYC-;differentiate;2S;37| (|x| $) (PROG (|dg| #0=#:G1603 |d|) (RETURN - (SEQ (LETT |d| (|spadConstant| $ 61) + (SEQ (LETT |d| (|spadConstant| $ 74) |UPOLYC-;differentiate;2S;37|) (SEQ G190 (COND @@ -683,33 +683,33 @@ (SPADCALL (SPADCALL |dg| (SPADCALL |x| - (|getShellEntry| $ 54)) - (|getShellEntry| $ 132)) + (|getShellEntry| $ 67)) + (|getShellEntry| $ 149)) (PROG1 (LETT #0# (- |dg| 1) |UPOLYC-;differentiate;2S;37|) (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 50)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 79)) |UPOLYC-;differentiate;2S;37|) (EXIT (LETT |x| - (SPADCALL |x| (|getShellEntry| $ 56)) + (SPADCALL |x| (|getShellEntry| $ 69)) |UPOLYC-;differentiate;2S;37|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |d|))))) (DEFUN |UPOLYC-;differentiate;SSaosS;38| (|x| |v| $) - (SPADCALL |x| (|getShellEntry| $ 139))) + (SPADCALL |x| (|getShellEntry| $ 158))) (DEFUN |UPOLYC-;elt;3F;39| (|g| |f| $) (SPADCALL - (SPADCALL (SPADCALL |g| (|getShellEntry| $ 142)) |f| - (|getShellEntry| $ 144)) - (SPADCALL (SPADCALL |g| (|getShellEntry| $ 145)) |f| - (|getShellEntry| $ 144)) - (|getShellEntry| $ 146))) + (SPADCALL (SPADCALL |g| (|getShellEntry| $ 161)) |f| + (|getShellEntry| $ 163)) + (SPADCALL (SPADCALL |g| (|getShellEntry| $ 164)) |f| + (|getShellEntry| $ 163)) + (|getShellEntry| $ 165))) (DEFUN |UPOLYC-;pseudoQuotient;3S;40| (|p| |q| $) (PROG (|n| #0=#:G1611) @@ -720,7 +720,7 @@ 1) |UPOLYC-;pseudoQuotient;3S;40|) (EXIT (COND - ((< |n| 1) (|spadConstant| $ 61)) + ((< |n| 1) (|spadConstant| $ 74)) ('T (PROG2 (LETT #0# (SPADCALL @@ -728,19 +728,19 @@ (SPADCALL (SPADCALL (SPADCALL |q| - (|getShellEntry| $ 54)) + (|getShellEntry| $ 67)) (PROG1 |n| (|check-subtype| (COND ((< |n| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |n|)) - (|getShellEntry| $ 148)) - |p| (|getShellEntry| $ 135)) + (|getShellEntry| $ 169)) + |p| (|getShellEntry| $ 154)) (SPADCALL |p| |q| - (|getShellEntry| $ 149)) - (|getShellEntry| $ 150)) - |q| (|getShellEntry| $ 127)) + (|getShellEntry| $ 170)) + (|getShellEntry| $ 171)) + |q| (|getShellEntry| $ 143)) |UPOLYC-;pseudoQuotient;3S;40|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -756,22 +756,22 @@ |UPOLYC-;pseudoDivide;2SR;41|) (EXIT (COND ((< |n| 1) - (VECTOR (|spadConstant| $ 49) (|spadConstant| $ 61) + (VECTOR (|spadConstant| $ 61) (|spadConstant| $ 74) |p|)) ('T (SEQ (LETT |prem| (SPADCALL |p| |q| - (|getShellEntry| $ 149)) + (|getShellEntry| $ 170)) |UPOLYC-;pseudoDivide;2SR;41|) (LETT |lc| (SPADCALL (SPADCALL |q| - (|getShellEntry| $ 54)) + (|getShellEntry| $ 67)) (PROG1 |n| (|check-subtype| (COND ((< |n| 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) |n|)) - (|getShellEntry| $ 148)) + (|getShellEntry| $ 169)) |UPOLYC-;pseudoDivide;2SR;41|) (EXIT (VECTOR |lc| (PROG2 @@ -779,10 +779,10 @@ (SPADCALL (SPADCALL (SPADCALL |lc| |p| - (|getShellEntry| $ 135)) + (|getShellEntry| $ 154)) |prem| - (|getShellEntry| $ 150)) - |q| (|getShellEntry| $ 127)) + (|getShellEntry| $ 171)) + |q| (|getShellEntry| $ 143)) |UPOLYC-;pseudoDivide;2SR;41|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) @@ -793,8 +793,8 @@ (PROG (|n| |d|) (RETURN (SEQ (LETT |n| - (SPADCALL (SPADCALL |f| (|getShellEntry| $ 142)) |q| - (|getShellEntry| $ 154)) + (SPADCALL (SPADCALL |f| (|getShellEntry| $ 161)) |q| + (|getShellEntry| $ 175)) |UPOLYC-;composite;FSU;42|) (EXIT (COND ((QEQCAR |n| 1) (CONS 1 "failed")) @@ -802,33 +802,33 @@ (SEQ (LETT |d| (SPADCALL (SPADCALL |f| - (|getShellEntry| $ 145)) - |q| (|getShellEntry| $ 154)) + (|getShellEntry| $ 164)) + |q| (|getShellEntry| $ 175)) |UPOLYC-;composite;FSU;42|) (EXIT (COND ((QEQCAR |d| 1) (CONS 1 "failed")) ('T (CONS 0 (SPADCALL (QCDR |n|) (QCDR |d|) - (|getShellEntry| $ 155)))))))))))))) + (|getShellEntry| $ 176)))))))))))))) (DEFUN |UPOLYC-;composite;2SU;43| (|p| |q| $) (PROG (|cqr| |v| |u| |w| #0=#:G1643) (RETURN (SEQ (COND - ((SPADCALL |p| (|getShellEntry| $ 158)) (CONS 0 |p|)) + ((SPADCALL |p| (|getShellEntry| $ 179)) (CONS 0 |p|)) ('T (SEQ (EXIT (SEQ (LETT |cqr| (SPADCALL |p| |q| - (|getShellEntry| $ 159)) + (|getShellEntry| $ 180)) |UPOLYC-;composite;2SU;43|) (COND ((SPADCALL (QVELT |cqr| 2) - (|getShellEntry| $ 158)) + (|getShellEntry| $ 179)) (SEQ (LETT |v| (SPADCALL (QVELT |cqr| 2) (QVELT |cqr| 0) - (|getShellEntry| $ 160)) + (|getShellEntry| $ 181)) |UPOLYC-;composite;2SU;43|) (EXIT (COND @@ -837,7 +837,7 @@ (LETT |u| (SPADCALL (QVELT |cqr| 1) |q| - (|getShellEntry| $ 154)) + (|getShellEntry| $ 175)) |UPOLYC-;composite;2SU;43|) (EXIT (COND @@ -847,7 +847,7 @@ (SPADCALL (QCDR |u|) (QVELT |cqr| 0) (|getShellEntry| $ - 160)) + 181)) |UPOLYC-;composite;2SU;43|) (EXIT (COND @@ -860,15 +860,15 @@ (SPADCALL (SPADCALL (|spadConstant| - $ 49) + $ 61) 1 (|getShellEntry| - $ 50)) + $ 63)) (QCDR |w|) (|getShellEntry| - $ 72)) + $ 85)) (|getShellEntry| - $ 66))) + $ 79))) |UPOLYC-;composite;2SU;43|) (GO #0#)))))))))))))))) (EXIT (CONS 1 "failed")))) @@ -879,14 +879,14 @@ (RETURN (SEQ (COND ((SPADCALL |p| (|getShellEntry| $ 9)) - (|spadConstant| $ 162)) + (|spadConstant| $ 183)) ('T (SEQ (LETT |ans| (SPADCALL (SPADCALL - (SPADCALL |p| (|getShellEntry| $ 54)) - (|getShellEntry| $ 30)) - (|getShellEntry| $ 163)) + (SPADCALL |p| (|getShellEntry| $ 67)) + (|getShellEntry| $ 38)) + (|getShellEntry| $ 184)) |UPOLYC-;elt;S2F;44|) (LETT |n| (SPADCALL |p| (|getShellEntry| $ 11)) |UPOLYC-;elt;S2F;44|) @@ -895,7 +895,7 @@ ((NULL (NOT (SPADCALL (LETT |p| (SPADCALL |p| - (|getShellEntry| $ 56)) + (|getShellEntry| $ 69)) |UPOLYC-;elt;S2F;44|) (|getShellEntry| $ 9)))) (GO G191))) @@ -916,15 +916,15 @@ ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 164)) - (|getShellEntry| $ 165)) + (|getShellEntry| $ 185)) + (|getShellEntry| $ 186)) (SPADCALL (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 54)) - (|getShellEntry| $ 30)) - (|getShellEntry| $ 163)) - (|getShellEntry| $ 166)) + (|getShellEntry| $ 67)) + (|getShellEntry| $ 38)) + (|getShellEntry| $ 184)) + (|getShellEntry| $ 187)) |UPOLYC-;elt;S2F;44|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (COND @@ -932,8 +932,8 @@ ('T (SPADCALL |ans| (SPADCALL |f| |n| - (|getShellEntry| $ 167)) - (|getShellEntry| $ 165)))))))))))) + (|getShellEntry| $ 188)) + (|getShellEntry| $ 186)))))))))))) (DEFUN |UPOLYC-;order;2SNni;45| (|p| |q| $) (PROG (|u| #0=#:G1663 |ans|) @@ -949,7 +949,7 @@ (SEQ (LETT |u| (SPADCALL |p| |q| - (|getShellEntry| $ 127)) + (|getShellEntry| $ 143)) |UPOLYC-;order;2SNni;45|) (EXIT (COND @@ -969,41 +969,41 @@ #0# (EXIT #0#))))) (DEFUN |UPOLYC-;squareFree;SF;46| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 171))) + (SPADCALL |p| (|getShellEntry| $ 192))) (DEFUN |UPOLYC-;squareFreePart;2S;47| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 173))) + (SPADCALL |p| (|getShellEntry| $ 194))) (DEFUN |UPOLYC-;gcdPolynomial;3Sup;48| (|pp| |qq| $) (COND - ((SPADCALL |pp| (|getShellEntry| $ 175)) - (SPADCALL |qq| (|getShellEntry| $ 176))) - ((SPADCALL |qq| (|getShellEntry| $ 175)) - (SPADCALL |pp| (|getShellEntry| $ 176))) + ((SPADCALL |pp| (|getShellEntry| $ 196)) + (SPADCALL |qq| (|getShellEntry| $ 197))) + ((SPADCALL |qq| (|getShellEntry| $ 196)) + (SPADCALL |pp| (|getShellEntry| $ 197))) ('T (SPADCALL (SPADCALL - (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 177)) - (SPADCALL |qq| (|getShellEntry| $ 177)) - (|getShellEntry| $ 126)) + (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 198)) + (SPADCALL |qq| (|getShellEntry| $ 198)) + (|getShellEntry| $ 142)) (SPADCALL - (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 178)) - (SPADCALL |qq| (|getShellEntry| $ 178)) - (|getShellEntry| $ 179)) - (|getShellEntry| $ 178)) - (|getShellEntry| $ 180)) - (|getShellEntry| $ 176))))) + (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 199)) + (SPADCALL |qq| (|getShellEntry| $ 199)) + (|getShellEntry| $ 200)) + (|getShellEntry| $ 199)) + (|getShellEntry| $ 201)) + (|getShellEntry| $ 197))))) (DEFUN |UPOLYC-;squareFreePolynomial;SupF;49| (|pp| $) - (SPADCALL |pp| (|getShellEntry| $ 183))) + (SPADCALL |pp| (|getShellEntry| $ 204))) (DEFUN |UPOLYC-;elt;F2R;50| (|f| |r| $) (SPADCALL - (SPADCALL (SPADCALL |f| (|getShellEntry| $ 142)) |r| - (|getShellEntry| $ 29)) - (SPADCALL (SPADCALL |f| (|getShellEntry| $ 145)) |r| - (|getShellEntry| $ 29)) - (|getShellEntry| $ 185))) + (SPADCALL (SPADCALL |f| (|getShellEntry| $ 161)) |r| + (|getShellEntry| $ 37)) + (SPADCALL (SPADCALL |f| (|getShellEntry| $ 164)) |r| + (|getShellEntry| $ 37)) + (|getShellEntry| $ 206))) (DEFUN |UPOLYC-;euclideanSize;SNni;51| (|x| $) (COND @@ -1018,12 +1018,12 @@ ((SPADCALL |y| (|getShellEntry| $ 9)) (|error| "division by 0 in Univariate Polynomials")) ('T - (SEQ (LETT |quot| (|spadConstant| $ 61) + (SEQ (LETT |quot| (|spadConstant| $ 74) |UPOLYC-;divide;2SR;52|) (LETT |lc| (SPADCALL - (SPADCALL |y| (|getShellEntry| $ 54)) - (|getShellEntry| $ 188)) + (SPADCALL |y| (|getShellEntry| $ 67)) + (|getShellEntry| $ 209)) |UPOLYC-;divide;2SR;52|) (SEQ G190 (COND @@ -1042,8 +1042,8 @@ (SEQ (LETT |f| (SPADCALL |lc| (SPADCALL |x| - (|getShellEntry| $ 54)) - (|getShellEntry| $ 189)) + (|getShellEntry| $ 67)) + (|getShellEntry| $ 211)) |UPOLYC-;divide;2SR;52|) (LETT |n| (PROG1 @@ -1061,16 +1061,16 @@ (LETT |quot| (SPADCALL |quot| (SPADCALL |f| |n| - (|getShellEntry| $ 50)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 79)) |UPOLYC-;divide;2SR;52|) (EXIT (LETT |x| (SPADCALL |x| (SPADCALL (SPADCALL |f| |n| - (|getShellEntry| $ 50)) - |y| (|getShellEntry| $ 72)) - (|getShellEntry| $ 150)) + (|getShellEntry| $ 63)) + |y| (|getShellEntry| $ 85)) + (|getShellEntry| $ 171)) |UPOLYC-;divide;2SR;52|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT (CONS |quot| |x|))))))))) @@ -1078,13 +1078,13 @@ (DEFUN |UPOLYC-;integrate;2S;53| (|p| $) (PROG (|l| |d| |ans|) (RETURN - (SEQ (LETT |ans| (|spadConstant| $ 61) |UPOLYC-;integrate;2S;53|) + (SEQ (LETT |ans| (|spadConstant| $ 74) |UPOLYC-;integrate;2S;53|) (SEQ G190 (COND - ((NULL (SPADCALL |p| (|spadConstant| $ 61) - (|getShellEntry| $ 191))) + ((NULL (SPADCALL |p| (|spadConstant| $ 74) + (|getShellEntry| $ 213))) (GO G191))) - (SEQ (LETT |l| (SPADCALL |p| (|getShellEntry| $ 54)) + (SEQ (LETT |l| (SPADCALL |p| (|getShellEntry| $ 67)) |UPOLYC-;integrate;2S;53|) (LETT |d| (+ 1 (SPADCALL |p| (|getShellEntry| $ 11))) @@ -1094,15 +1094,15 @@ (SPADCALL (SPADCALL (SPADCALL |d| - (|getShellEntry| $ 193)) - (|getShellEntry| $ 194)) + (|getShellEntry| $ 215)) + (|getShellEntry| $ 216)) (SPADCALL |l| |d| - (|getShellEntry| $ 50)) - (|getShellEntry| $ 195)) - (|getShellEntry| $ 66)) + (|getShellEntry| $ 63)) + (|getShellEntry| $ 217)) + (|getShellEntry| $ 79)) |UPOLYC-;integrate;2S;53|) (EXIT (LETT |p| - (SPADCALL |p| (|getShellEntry| $ 56)) + (SPADCALL |p| (|getShellEntry| $ 69)) |UPOLYC-;integrate;2S;53|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |ans|))))) @@ -1116,7 +1116,7 @@ (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|UnivariatePolynomialCategory&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 202) . #0#) + (LETT $ (|newShell| 224) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -1134,279 +1134,292 @@ (COND ((|HasCategory| |#2| '(|PolynomialFactorizationExplicit|)) (PROGN - (|setShellEntry| $ 82 + (|setShellEntry| $ 95 (CONS (|dispatchFunction| |UPOLYC-;solveLinearPolynomialEquation;LSupU;20|) $)) - (|setShellEntry| $ 86 + (|setShellEntry| $ 99 (CONS (|dispatchFunction| |UPOLYC-;factorPolynomial;SupF;21|) $)) - (|setShellEntry| $ 88 + (|setShellEntry| $ 101 (CONS (|dispatchFunction| |UPOLYC-;factorSquareFreePolynomial;SupF;22|) $)) - (|setShellEntry| $ 107 + (|setShellEntry| $ 120 (CONS (|dispatchFunction| |UPOLYC-;factor;SF;23|) $))))) (COND ((|testBitVector| |pv$| 6) (PROGN - (|setShellEntry| $ 119 + (|setShellEntry| $ 134 (CONS (|dispatchFunction| |UPOLYC-;init;S;27|) $)) NIL - (|setShellEntry| $ 123 + (|setShellEntry| $ 139 (CONS (|dispatchFunction| |UPOLYC-;nextItem;SU;29|) $))))) (COND ((|testBitVector| |pv$| 3) (PROGN - (|setShellEntry| $ 125 + (|setShellEntry| $ 141 (CONS (|dispatchFunction| |UPOLYC-;content;SSaosS;30|) $)) NIL - (|setShellEntry| $ 130 + (|setShellEntry| $ 146 (CONS (|dispatchFunction| |UPOLYC-;separate;2SR;32|) $))))) (COND ((|testBitVector| |pv$| 5) - (|setShellEntry| $ 134 + (|setShellEntry| $ 151 (CONS (|dispatchFunction| |UPOLYC-;differentiate;SM2S;33|) $))) ('T (PROGN - (|setShellEntry| $ 134 + (|setShellEntry| $ 151 (CONS (|dispatchFunction| |UPOLYC-;differentiate;SM2S;35|) $))))) (COND ((|testBitVector| |pv$| 4) (PROGN - (|setShellEntry| $ 147 + (|setShellEntry| $ 166 (CONS (|dispatchFunction| |UPOLYC-;elt;3F;39|) $)) - (|setShellEntry| $ 151 + (|setShellEntry| $ 172 (CONS (|dispatchFunction| |UPOLYC-;pseudoQuotient;3S;40|) $)) - (|setShellEntry| $ 153 + (|setShellEntry| $ 174 (CONS (|dispatchFunction| |UPOLYC-;pseudoDivide;2SR;41|) $)) - (|setShellEntry| $ 157 + (|setShellEntry| $ 178 (CONS (|dispatchFunction| |UPOLYC-;composite;FSU;42|) $)) - (|setShellEntry| $ 161 + (|setShellEntry| $ 182 (CONS (|dispatchFunction| |UPOLYC-;composite;2SU;43|) $)) - (|setShellEntry| $ 168 + (|setShellEntry| $ 189 (CONS (|dispatchFunction| |UPOLYC-;elt;S2F;44|) $)) - (|setShellEntry| $ 169 + (|setShellEntry| $ 190 (CONS (|dispatchFunction| |UPOLYC-;order;2SNni;45|) $))))) (COND ((|testBitVector| |pv$| 3) (PROGN - (|setShellEntry| $ 172 + (|setShellEntry| $ 193 (CONS (|dispatchFunction| |UPOLYC-;squareFree;SF;46|) $)) - (|setShellEntry| $ 174 + (|setShellEntry| $ 195 (CONS (|dispatchFunction| |UPOLYC-;squareFreePart;2S;47|) $))))) (COND ((|HasCategory| |#2| '(|PolynomialFactorizationExplicit|)) (PROGN - (|setShellEntry| $ 181 + (|setShellEntry| $ 202 (CONS (|dispatchFunction| |UPOLYC-;gcdPolynomial;3Sup;48|) $)) - (|setShellEntry| $ 184 + (|setShellEntry| $ 205 (CONS (|dispatchFunction| |UPOLYC-;squareFreePolynomial;SupF;49|) $))))) (COND ((|testBitVector| |pv$| 2) (PROGN - (|setShellEntry| $ 186 + (|setShellEntry| $ 207 (CONS (|dispatchFunction| |UPOLYC-;elt;F2R;50|) $)) - (|setShellEntry| $ 187 + (|setShellEntry| $ 208 (CONS (|dispatchFunction| |UPOLYC-;euclideanSize;SNni;51|) $)) - (|setShellEntry| $ 190 + (|setShellEntry| $ 212 (CONS (|dispatchFunction| |UPOLYC-;divide;2SR;52|) $))))) (COND ((|testBitVector| |pv$| 1) - (|setShellEntry| $ 196 + (|setShellEntry| $ 218 (CONS (|dispatchFunction| |UPOLYC-;integrate;2S;53|) $)))) $)))) (MAKEPROP '|UnivariatePolynomialCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|local| |#2|) (|Boolean|) (0 . |zero?|) (|NonNegativeInteger|) - (5 . |degree|) (|SingletonAsOrderedSet|) (10 . |create|) - (|List| 12) |UPOLYC-;variables;SL;1| - |UPOLYC-;degree;SSaosNni;2| (14 . |totalDegree|) - |UPOLYC-;totalDegree;SLNni;3| (|List| 10) - |UPOLYC-;degree;SLL;4| (19 . |eval|) (|List| $) - |UPOLYC-;eval;SLLS;5| (26 . |elt|) - |UPOLYC-;eval;SSaos2S;6| (32 . |eval|) (|List| 7) - |UPOLYC-;eval;SLLS;7| (39 . |elt|) (45 . |coerce|) - |UPOLYC-;eval;SSaosRS;8| (|Equation| 6) (50 . |lhs|) - (|Union| 12 '"failed") (55 . |mainVariable|) (60 . |rhs|) - (|Equation| $) (|List| 37) |UPOLYC-;eval;SLS;9| - |UPOLYC-;mainVariable;SU;10| (65 . |minimumDegree|) + (5 . |degree|) (10 . |zero?|) (|SingletonAsOrderedSet|) + (15 . |create|) (|List| 13) |UPOLYC-;variables;SL;1| + |UPOLYC-;degree;SSaosNni;2| (19 . |empty?|) (24 . |Zero|) + (28 . |totalDegree|) |UPOLYC-;totalDegree;SLNni;3| + (|List| 10) |UPOLYC-;degree;SLL;4| (33 . |rest|) + (38 . |first|) (|List| 6) (43 . |first|) (48 . |eval|) + (|List| $) |UPOLYC-;eval;SLLS;5| (55 . |elt|) + |UPOLYC-;eval;SSaos2S;6| (|List| 7) (61 . |first|) + (66 . |eval|) |UPOLYC-;eval;SLLS;7| (73 . |elt|) + (79 . |coerce|) |UPOLYC-;eval;SSaosRS;8| (|Equation| 6) + (|List| 40) (84 . |empty?|) (89 . |rest|) (94 . |first|) + (99 . |lhs|) (|Union| 13 '"failed") (104 . |mainVariable|) + (109 . |rhs|) (|Equation| $) (|List| 49) + |UPOLYC-;eval;SLS;9| |UPOLYC-;mainVariable;SU;10| + (114 . |minimumDegree|) |UPOLYC-;minimumDegree;SSaosNni;11| - |UPOLYC-;minimumDegree;SLL;12| (70 . +) (|Mapping| 10 10) - (76 . |mapExponents|) |UPOLYC-;monomial;SSaosNniS;13| - (82 . |One|) (86 . |One|) (90 . |monomial|) - |UPOLYC-;coerce;SaosS;14| (|SparseUnivariatePolynomial| 7) - (96 . |Zero|) (100 . |leadingCoefficient|) - (105 . |monomial|) (111 . |reductum|) (116 . |makeSUP|) - (121 . +) |UPOLYC-;makeSUP;SSup;15| (127 . |zero?|) - (132 . |Zero|) (136 . |leadingCoefficient|) - (141 . |degree|) (146 . |reductum|) (151 . |unmakeSUP|) - (156 . +) |UPOLYC-;unmakeSUP;SupS;16| + |UPOLYC-;minimumDegree;SLL;12| (119 . +) (|Mapping| 10 10) + (125 . |mapExponents|) |UPOLYC-;monomial;SSaosNniS;13| + (131 . |One|) (135 . |One|) (139 . |One|) + (143 . |monomial|) |UPOLYC-;coerce;SaosS;14| + (|SparseUnivariatePolynomial| 7) (149 . |Zero|) + (153 . |leadingCoefficient|) (158 . |monomial|) + (164 . |reductum|) (169 . |makeSUP|) (174 . +) + |UPOLYC-;makeSUP;SSup;15| (180 . |zero?|) (185 . |Zero|) + (189 . |leadingCoefficient|) (194 . |degree|) + (199 . |reductum|) (204 . |unmakeSUP|) (209 . +) + |UPOLYC-;unmakeSUP;SupS;16| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - (162 . |monicDivide|) |UPOLYC-;karatsubaDivide;SNniR;17| - |UPOLYC-;shiftRight;SNniS;18| (168 . *) + (215 . |monicDivide|) |UPOLYC-;karatsubaDivide;SNniR;17| + |UPOLYC-;shiftRight;SNniS;18| (221 . *) |UPOLYC-;shiftLeft;SNniS;19| - (|SparseUnivariatePolynomial| 6) (|List| 74) - (|Union| 75 '"failed") + (|SparseUnivariatePolynomial| 6) (|List| 87) + (|Union| 88 '"failed") (|PolynomialFactorizationByRecursionUnivariate| 7 6) - (174 . |solveLinearPolynomialEquationByRecursion|) - (|SparseUnivariatePolynomial| $) (|List| 79) - (|Union| 80 '"failed") - (180 . |solveLinearPolynomialEquation|) (|Factored| 74) - (186 . |factorByRecursion|) (|Factored| 79) - (191 . |factorPolynomial|) - (196 . |factorSquareFreeByRecursion|) - (201 . |factorSquareFreePolynomial|) (|Factored| $) - (206 . |factor|) (|Factored| 7) (211 . |unit|) + (227 . |solveLinearPolynomialEquationByRecursion|) + (|SparseUnivariatePolynomial| $) (|List| 92) + (|Union| 93 '"failed") + (233 . |solveLinearPolynomialEquation|) (|Factored| 87) + (239 . |factorByRecursion|) (|Factored| 92) + (244 . |factorPolynomial|) + (249 . |factorSquareFreeByRecursion|) + (254 . |factorSquareFreePolynomial|) (|Factored| $) + (259 . |factor|) (|Factored| 7) (264 . |unit|) (|Union| '"nil" '"sqfr" '"irred" '"prime") (|Integer|) - (|Record| (|:| |flg| 93) (|:| |fctr| 7) (|:| |xpnt| 94)) - (|List| 95) (216 . |factorList|) - (|Record| (|:| |flg| 93) (|:| |fctr| 6) (|:| |xpnt| 94)) - (|List| 98) (|Factored| 6) (221 . |makeFR|) - (227 . |factorPolynomial|) (|Mapping| 6 52) - (|Factored| 52) (|FactoredFunctions2| 52 6) (232 . |map|) - (238 . |factor|) (243 . |Zero|) (|Vector| 7) (247 . |new|) - (253 . |minIndex|) (258 . |coefficient|) - (264 . |qsetelt!|) |UPOLYC-;vectorise;SNniV;24| - |UPOLYC-;retract;SR;25| (|Union| 7 '"failed") - |UPOLYC-;retractIfCan;SU;26| (271 . |init|) (275 . |init|) - (|Union| $ '"failed") (279 . |nextItem|) (284 . |One|) - (288 . |nextItem|) (293 . |content|) (298 . |content|) - (304 . |gcd|) (310 . |exquo|) (316 . =) + (|Record| (|:| |flg| 106) (|:| |fctr| 7) (|:| |xpnt| 107)) + (|List| 108) (269 . |factorList|) + (|Record| (|:| |flg| 106) (|:| |fctr| 6) (|:| |xpnt| 107)) + (|List| 111) (|Factored| 6) (274 . |makeFR|) + (280 . |factorPolynomial|) (|Mapping| 6 65) + (|Factored| 65) (|FactoredFunctions2| 65 6) (285 . |map|) + (291 . |factor|) (296 . |Zero|) (|Vector| 7) (300 . |new|) + (306 . |minIndex|) (311 . |maxIndex|) (316 . -) + (322 . |coefficient|) (328 . |qsetelt!|) + |UPOLYC-;vectorise;SNniV;24| |UPOLYC-;retract;SR;25| + (|Union| 7 '"failed") |UPOLYC-;retractIfCan;SU;26| + (335 . |init|) (339 . |init|) (|Union| $ '"failed") + (343 . |nextItem|) (348 . |One|) (352 . <) + (358 . |nextItem|) (363 . |content|) (368 . |content|) + (374 . |gcd|) (380 . |exquo|) (386 . =) (|Record| (|:| |primePart| $) (|:| |commonPart| $)) - (322 . |separate|) (328 . |Zero|) (332 . *) - (|Mapping| 7 7) (338 . |differentiate|) (345 . *) - (351 . |differentiate|) |UPOLYC-;differentiate;SMS;36| - |UPOLYC-;differentiate;2S;37| (358 . |differentiate|) + (392 . |separate|) (398 . |Zero|) (402 . |Zero|) (406 . *) + (|Mapping| 7 7) (412 . |differentiate|) + (|PositiveInteger|) (419 . |One|) (423 . *) + (429 . |differentiate|) |UPOLYC-;differentiate;SMS;36| + |UPOLYC-;differentiate;2S;37| (436 . |differentiate|) |UPOLYC-;differentiate;SSaosS;38| (|Fraction| 6) - (363 . |numer|) (|Fraction| $) (368 . |elt|) - (374 . |denom|) (379 . /) (385 . |elt|) (391 . **) - (397 . |pseudoRemainder|) (403 . -) - (409 . |pseudoQuotient|) + (441 . |numer|) (|Fraction| $) (446 . |elt|) + (452 . |denom|) (457 . /) (463 . |elt|) (469 . +) + (475 . <) (481 . **) (487 . |pseudoRemainder|) (493 . -) + (499 . |pseudoQuotient|) (|Record| (|:| |coef| 7) (|:| |quotient| $) (|:| |remainder| $)) - (415 . |pseudoDivide|) (421 . |composite|) (427 . /) - (|Union| 143 '"failed") (433 . |composite|) - (439 . |ground?|) (444 . |pseudoDivide|) (450 . |exquo|) - (456 . |composite|) (462 . |Zero|) (466 . |coerce|) - (471 . **) (477 . *) (483 . +) (489 . **) (495 . |elt|) - (501 . |order|) (|UnivariatePolynomialSquareFree| 7 6) - (507 . |squareFree|) (512 . |squareFree|) - (517 . |squareFreePart|) (522 . |squareFreePart|) - (527 . |zero?|) (532 . |unitCanonical|) (537 . |content|) - (542 . |primitivePart|) (547 . |subResultantGcd|) - (553 . *) (559 . |gcdPolynomial|) - (|UnivariatePolynomialSquareFree| 6 74) - (565 . |squareFree|) (570 . |squareFreePolynomial|) - (575 . /) (581 . |elt|) (587 . |euclideanSize|) - (592 . |inv|) (597 . *) (603 . |divide|) (609 . ~=) - (|Fraction| 94) (615 . |coerce|) (620 . |inv|) (625 . *) - (631 . |integrate|) (|Symbol|) (|List| 197) - (|Union| 94 '"failed") (|Union| 192 '"failed") + (505 . |pseudoDivide|) (511 . |composite|) (517 . /) + (|Union| 162 '"failed") (523 . |composite|) + (529 . |ground?|) (534 . |pseudoDivide|) (540 . |exquo|) + (546 . |composite|) (552 . |Zero|) (556 . |coerce|) + (561 . **) (567 . *) (573 . +) (579 . **) (585 . |elt|) + (591 . |order|) (|UnivariatePolynomialSquareFree| 7 6) + (597 . |squareFree|) (602 . |squareFree|) + (607 . |squareFreePart|) (612 . |squareFreePart|) + (617 . |zero?|) (622 . |unitCanonical|) (627 . |content|) + (632 . |primitivePart|) (637 . |subResultantGcd|) + (643 . *) (649 . |gcdPolynomial|) + (|UnivariatePolynomialSquareFree| 6 87) + (655 . |squareFree|) (660 . |squareFreePolynomial|) + (665 . /) (671 . |elt|) (677 . |euclideanSize|) + (682 . |inv|) (687 . |false|) (691 . *) (697 . |divide|) + (703 . ~=) (|Fraction| 107) (709 . |coerce|) (714 . |inv|) + (719 . *) (725 . |integrate|) (|Symbol|) (|List| 219) + (|Union| 107 '"failed") (|Union| 214 '"failed") (|OutputForm|)) - '#(|vectorise| 636 |variables| 642 |unmakeSUP| 647 - |totalDegree| 652 |squareFreePolynomial| 658 - |squareFreePart| 663 |squareFree| 668 - |solveLinearPolynomialEquation| 673 |shiftRight| 679 - |shiftLeft| 685 |separate| 691 |retractIfCan| 697 - |retract| 702 |pseudoQuotient| 707 |pseudoDivide| 713 - |order| 719 |nextItem| 725 |monomial| 730 |minimumDegree| - 737 |makeSUP| 749 |mainVariable| 754 |karatsubaDivide| 759 - |integrate| 765 |init| 770 |gcdPolynomial| 774 - |factorSquareFreePolynomial| 780 |factorPolynomial| 785 - |factor| 790 |eval| 795 |euclideanSize| 829 |elt| 834 - |divide| 852 |differentiate| 858 |degree| 882 |content| - 894 |composite| 900 |coerce| 912) + '#(|vectorise| 730 |variables| 736 |unmakeSUP| 741 + |totalDegree| 746 |squareFreePolynomial| 752 + |squareFreePart| 757 |squareFree| 762 + |solveLinearPolynomialEquation| 767 |shiftRight| 773 + |shiftLeft| 779 |separate| 785 |retractIfCan| 791 + |retract| 796 |pseudoQuotient| 801 |pseudoDivide| 807 + |order| 813 |nextItem| 819 |monomial| 824 |minimumDegree| + 831 |makeSUP| 843 |mainVariable| 848 |karatsubaDivide| 853 + |integrate| 859 |init| 864 |gcdPolynomial| 868 + |factorSquareFreePolynomial| 874 |factorPolynomial| 879 + |factor| 884 |eval| 889 |euclideanSize| 923 |elt| 928 + |divide| 946 |differentiate| 952 |degree| 976 |content| + 988 |composite| 994 |coerce| 1006) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 196 - '(1 6 8 0 9 1 6 10 0 11 0 12 0 13 1 6 - 10 0 17 3 6 0 0 12 0 21 2 6 0 0 0 24 - 3 6 0 0 12 7 26 2 6 7 0 7 29 1 6 0 7 - 30 1 32 6 0 33 1 6 34 0 35 1 32 6 0 - 36 1 6 10 0 41 2 10 0 0 0 44 2 6 0 45 - 0 46 0 6 0 48 0 7 0 49 2 6 0 7 10 50 - 0 52 0 53 1 6 7 0 54 2 52 0 7 10 55 1 - 6 0 0 56 1 6 52 0 57 2 52 0 0 0 58 1 - 52 8 0 60 0 6 0 61 1 52 7 0 62 1 52 - 10 0 63 1 52 0 0 64 1 6 0 52 65 2 6 0 - 0 0 66 2 6 68 0 0 69 2 6 0 0 0 72 2 - 77 76 75 74 78 2 0 81 80 79 82 1 77 - 83 74 84 1 0 85 79 86 1 77 83 74 87 1 - 0 85 79 88 1 7 89 0 90 1 91 7 0 92 1 - 91 96 0 97 2 100 0 6 99 101 1 7 85 79 - 102 2 105 100 103 104 106 1 0 89 0 - 107 0 7 0 108 2 109 0 10 7 110 1 109 - 94 0 111 2 6 7 0 10 112 3 109 7 0 94 - 7 113 0 7 0 118 0 0 0 119 1 7 120 0 - 121 0 74 0 122 1 0 120 0 123 1 6 7 0 - 124 2 0 0 0 12 125 2 6 0 0 0 126 2 6 - 120 0 0 127 2 6 8 0 0 128 2 0 129 0 0 - 130 0 74 0 131 2 7 0 10 0 132 3 0 0 0 - 133 0 134 2 6 0 7 0 135 3 6 0 0 133 0 - 136 1 6 0 0 139 1 141 6 0 142 2 6 143 - 0 143 144 1 141 6 0 145 2 141 0 0 0 - 146 2 0 143 143 143 147 2 7 0 0 10 - 148 2 6 0 0 0 149 2 6 0 0 0 150 2 0 0 - 0 0 151 2 0 152 0 0 153 2 6 120 0 0 - 154 2 141 0 6 6 155 2 0 156 143 0 157 - 1 6 8 0 158 2 6 152 0 0 159 2 6 120 0 - 7 160 2 0 120 0 0 161 0 141 0 162 1 - 141 0 6 163 2 141 0 0 94 164 2 141 0 - 0 0 165 2 141 0 0 0 166 2 141 0 0 10 - 167 2 0 143 0 143 168 2 0 10 0 0 169 - 1 170 100 6 171 1 0 89 0 172 1 170 6 - 6 173 1 0 0 0 174 1 74 8 0 175 1 74 0 - 0 176 1 74 6 0 177 1 74 0 0 178 2 74 - 0 0 0 179 2 74 0 6 0 180 2 0 79 79 79 - 181 1 182 83 74 183 1 0 85 79 184 2 7 - 0 0 0 185 2 0 7 143 7 186 1 0 10 0 - 187 1 7 0 0 188 2 7 0 0 0 189 2 0 68 - 0 0 190 2 6 8 0 0 191 1 192 0 94 193 - 1 192 0 0 194 2 6 0 192 0 195 1 0 0 0 - 196 2 0 109 0 10 114 1 0 14 0 15 1 0 - 0 52 67 2 0 10 0 14 18 1 0 85 79 184 - 1 0 0 0 174 1 0 89 0 172 2 0 81 80 79 - 82 2 0 0 0 10 71 2 0 0 0 10 73 2 0 - 129 0 0 130 1 0 116 0 117 1 0 7 0 115 - 2 0 0 0 0 151 2 0 152 0 0 153 2 0 10 - 0 0 169 1 0 120 0 123 3 0 0 0 12 10 - 47 2 0 19 0 14 43 2 0 10 0 12 42 1 0 - 52 0 59 1 0 34 0 40 2 0 68 0 10 70 1 - 0 0 0 196 0 0 0 119 2 0 79 79 79 181 - 1 0 85 79 88 1 0 85 79 86 1 0 89 0 - 107 3 0 0 0 12 0 25 3 0 0 0 14 22 23 - 3 0 0 0 14 27 28 3 0 0 0 12 7 31 2 0 - 0 0 38 39 1 0 10 0 187 2 0 143 0 143 - 168 2 0 7 143 7 186 2 0 143 143 143 - 147 2 0 68 0 0 190 3 0 0 0 133 0 134 - 2 0 0 0 133 137 1 0 0 0 138 2 0 0 0 - 12 140 2 0 10 0 12 16 2 0 19 0 14 20 - 2 0 0 0 12 125 2 0 120 0 0 161 2 0 - 156 143 0 157 1 0 0 12 51))))) + (|makeByteWordVec2| 218 + '(1 6 8 0 9 1 6 10 0 11 1 10 8 0 12 0 + 13 0 14 1 15 8 0 18 0 10 0 19 1 6 10 + 0 20 1 15 0 0 24 1 15 13 0 25 1 26 6 + 0 27 3 6 0 0 13 0 28 2 6 0 0 0 31 1 + 33 7 0 34 3 6 0 0 13 7 35 2 6 7 0 7 + 37 1 6 0 7 38 1 41 8 0 42 1 41 0 0 43 + 1 41 40 0 44 1 40 6 0 45 1 6 46 0 47 + 1 40 6 0 48 1 6 10 0 53 2 10 0 0 0 56 + 2 6 0 57 0 58 0 6 0 60 0 7 0 61 0 10 + 0 62 2 6 0 7 10 63 0 65 0 66 1 6 7 0 + 67 2 65 0 7 10 68 1 6 0 0 69 1 6 65 0 + 70 2 65 0 0 0 71 1 65 8 0 73 0 6 0 74 + 1 65 7 0 75 1 65 10 0 76 1 65 0 0 77 + 1 6 0 65 78 2 6 0 0 0 79 2 6 81 0 0 + 82 2 6 0 0 0 85 2 90 89 88 87 91 2 0 + 94 93 92 95 1 90 96 87 97 1 0 98 92 + 99 1 90 96 87 100 1 0 98 92 101 1 7 + 102 0 103 1 104 7 0 105 1 104 109 0 + 110 2 113 0 6 112 114 1 7 98 92 115 2 + 118 113 116 117 119 1 0 102 0 120 0 7 + 0 121 2 122 0 10 7 123 1 122 107 0 + 124 1 122 107 0 125 2 107 0 0 0 126 2 + 6 7 0 10 127 3 122 7 0 107 7 128 0 7 + 0 133 0 0 0 134 1 7 135 0 136 0 87 0 + 137 2 10 8 0 0 138 1 0 135 0 139 1 6 + 7 0 140 2 0 0 0 13 141 2 6 0 0 0 142 + 2 6 135 0 0 143 2 6 8 0 0 144 2 0 145 + 0 0 146 0 87 0 147 0 107 0 148 2 7 0 + 10 0 149 3 0 0 0 150 0 151 0 152 0 + 153 2 6 0 7 0 154 3 6 0 0 150 0 155 1 + 6 0 0 158 1 160 6 0 161 2 6 162 0 162 + 163 1 160 6 0 164 2 160 0 0 0 165 2 0 + 162 162 162 166 2 107 0 0 0 167 2 107 + 8 0 0 168 2 7 0 0 10 169 2 6 0 0 0 + 170 2 6 0 0 0 171 2 0 0 0 0 172 2 0 + 173 0 0 174 2 6 135 0 0 175 2 160 0 6 + 6 176 2 0 177 162 0 178 1 6 8 0 179 2 + 6 173 0 0 180 2 6 135 0 7 181 2 0 135 + 0 0 182 0 160 0 183 1 160 0 6 184 2 + 160 0 0 107 185 2 160 0 0 0 186 2 160 + 0 0 0 187 2 160 0 0 10 188 2 0 162 0 + 162 189 2 0 10 0 0 190 1 191 113 6 + 192 1 0 102 0 193 1 191 6 6 194 1 0 0 + 0 195 1 87 8 0 196 1 87 0 0 197 1 87 + 6 0 198 1 87 0 0 199 2 87 0 0 0 200 2 + 87 0 6 0 201 2 0 92 92 92 202 1 203 + 96 87 204 1 0 98 92 205 2 7 0 0 0 206 + 2 0 7 162 7 207 1 0 10 0 208 1 7 0 0 + 209 0 8 0 210 2 7 0 0 0 211 2 0 81 0 + 0 212 2 6 8 0 0 213 1 214 0 107 215 1 + 214 0 0 216 2 6 0 214 0 217 1 0 0 0 + 218 2 0 122 0 10 129 1 0 15 0 16 1 0 + 0 65 80 2 0 10 0 15 21 1 0 98 92 205 + 1 0 0 0 195 1 0 102 0 193 2 0 94 93 + 92 95 2 0 0 0 10 84 2 0 0 0 10 86 2 0 + 145 0 0 146 1 0 131 0 132 1 0 7 0 130 + 2 0 0 0 0 172 2 0 173 0 0 174 2 0 10 + 0 0 190 1 0 135 0 139 3 0 0 0 13 10 + 59 2 0 22 0 15 55 2 0 10 0 13 54 1 0 + 65 0 72 1 0 46 0 52 2 0 81 0 10 83 1 + 0 0 0 218 0 0 0 134 2 0 92 92 92 202 + 1 0 98 92 101 1 0 98 92 99 1 0 102 0 + 120 3 0 0 0 13 0 32 3 0 0 0 15 29 30 + 3 0 0 0 15 33 36 3 0 0 0 13 7 39 2 0 + 0 0 50 51 1 0 10 0 208 2 0 162 0 162 + 189 2 0 7 162 7 207 2 0 162 162 162 + 166 2 0 81 0 0 212 3 0 0 0 150 0 151 + 2 0 0 0 150 156 1 0 0 0 157 2 0 0 0 + 13 159 2 0 10 0 13 17 2 0 22 0 15 23 + 2 0 0 0 13 141 2 0 135 0 0 182 2 0 + 177 162 0 178 1 0 0 13 64))))) '|lookupComplete|)) diff --git a/src/algebra/strap/URAGG-.lsp b/src/algebra/strap/URAGG-.lsp index 023dd8a0..50039169 100644 --- a/src/algebra/strap/URAGG-.lsp +++ b/src/algebra/strap/URAGG-.lsp @@ -134,7 +134,7 @@ (NOT (SPADCALL (|URAGG-;findCycle| |x| $) (|getShellEntry| $ 20)))))) (DEFUN |URAGG-;last;AS;7| (|x| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 22)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 23)) (|getShellEntry| $ 8))) (DEFUN |URAGG-;nodes;AL;8| (|x| $) @@ -235,7 +235,7 @@ (SEQ (COND ((EQL |k| 1000) (COND - ((SPADCALL |x| (|getShellEntry| $ 33)) + ((SPADCALL |x| (|getShellEntry| $ 49)) (EXIT (|error| "cyclic list")))))) (EXIT (LETT |x| (SPADCALL |x| (|getShellEntry| $ 14)) @@ -262,7 +262,7 @@ ((EQL |k| 1000) (COND ((SPADCALL |x| - (|getShellEntry| $ 33)) + (|getShellEntry| $ 49)) (EXIT (|error| "cyclic list")))))) (EXIT (LETT |y| (SPADCALL @@ -286,7 +286,7 @@ (GO G191))) (SEQ (COND ((SPADCALL |x| |y| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 52)) (PROGN (LETT #0# |x| |URAGG-;findCycle|) (GO #0#)))) @@ -306,7 +306,7 @@ (GO #0#)))) (COND ((SPADCALL |x| |y| - (|getShellEntry| $ 36)) + (|getShellEntry| $ 52)) (PROGN (LETT #0# |y| |URAGG-;findCycle|) (GO #0#)))) @@ -324,7 +324,7 @@ (SEQ (COND ((SPADCALL (LETT |y| - (LETT |x| (SPADCALL |x| (|getShellEntry| $ 37)) + (LETT |x| (SPADCALL |x| (|getShellEntry| $ 53)) |URAGG-;cycleTail;2A;18|) |URAGG-;cycleTail;2A;18|) (|getShellEntry| $ 20)) @@ -335,7 +335,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| |z| - (|getShellEntry| $ 36)))) + (|getShellEntry| $ 52)))) (GO G191))) (SEQ (LETT |y| |z| |URAGG-;cycleTail;2A;18|) (EXIT (LETT |z| @@ -361,7 +361,7 @@ (SEQ (LETT |l| 1 |URAGG-;cycleEntry;2A;19|) G190 (COND ((NULL (NOT (SPADCALL |y| |z| - (|getShellEntry| $ 36)))) + (|getShellEntry| $ 52)))) (GO G191))) (SEQ (EXIT (LETT |z| (SPADCALL |z| @@ -383,7 +383,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |x| |y| - (|getShellEntry| $ 36)))) + (|getShellEntry| $ 52)))) (GO G191))) (SEQ (LETT |x| (SPADCALL |x| @@ -412,7 +412,7 @@ (SEQ (LETT |k| 1 |URAGG-;cycleLength;ANni;20|) G190 (COND ((NULL (NOT (SPADCALL |x| |y| - (|getShellEntry| $ 36)))) + (|getShellEntry| $ 52)))) (GO G191))) (SEQ (EXIT (LETT |y| (SPADCALL |y| @@ -443,7 +443,7 @@ (DEFUN |URAGG-;last;ANniA;22| (|x| |n| $) (PROG (|m| #0=#:G1499) (RETURN - (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 42)) + (SEQ (LETT |m| (SPADCALL |x| (|getShellEntry| $ 59)) |URAGG-;last;ANniA;22|) (EXIT (COND ((< |m| |n|) (|error| "index out of range")) @@ -455,14 +455,14 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 43)) - (|getShellEntry| $ 44))))))))) + (|getShellEntry| $ 61)) + (|getShellEntry| $ 62))))))))) (DEFUN |URAGG-;=;2AB;23| (|x| |y| $) (PROG (|k| #0=#:G1509) (RETURN (SEQ (EXIT (COND - ((SPADCALL |x| |y| (|getShellEntry| $ 36)) 'T) + ((SPADCALL |x| |y| (|getShellEntry| $ 52)) 'T) ('T (SEQ (SEQ (LETT |k| 0 |URAGG-;=;2AB;23|) G190 (COND @@ -479,7 +479,7 @@ ((EQL |k| 1000) (COND ((SPADCALL |x| - (|getShellEntry| $ 33)) + (|getShellEntry| $ 49)) (EXIT (|error| "cyclic list")))))) (EXIT (COND @@ -488,7 +488,7 @@ (|getShellEntry| $ 8)) (SPADCALL |y| (|getShellEntry| $ 8)) - (|getShellEntry| $ 46)) + (|getShellEntry| $ 65)) (PROGN (LETT #0# 'NIL |URAGG-;=;2AB;23|) @@ -523,7 +523,7 @@ (GO G191))) (SEQ (EXIT (COND ((SPADCALL |u| |v| - (|getShellEntry| $ 48)) + (|getShellEntry| $ 67)) (PROGN (LETT #0# 'T |URAGG-;node?;2AB;24|) @@ -534,7 +534,7 @@ ((EQL |k| 1000) (COND ((SPADCALL |v| - (|getShellEntry| $ 33)) + (|getShellEntry| $ 49)) (EXIT (|error| "cyclic list")))))) @@ -546,39 +546,39 @@ (LETT |k| (QSADD1 |k|) |URAGG-;node?;2AB;24|) (GO G190) G191 (EXIT NIL)) - (EXIT (SPADCALL |u| |v| (|getShellEntry| $ 48))))) + (EXIT (SPADCALL |u| |v| (|getShellEntry| $ 67))))) #0# (EXIT #0#))))) (DEFUN |URAGG-;setelt;Afirst2S;25| (|x| T3 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 50))) + (SPADCALL |x| |a| (|getShellEntry| $ 69))) (DEFUN |URAGG-;setelt;Alast2S;26| (|x| T4 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 52))) + (SPADCALL |x| |a| (|getShellEntry| $ 71))) (DEFUN |URAGG-;setelt;Arest2A;27| (|x| T5 |a| $) - (SPADCALL |x| |a| (|getShellEntry| $ 54))) + (SPADCALL |x| |a| (|getShellEntry| $ 73))) (DEFUN |URAGG-;concat;3A;28| (|x| |y| $) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 44)) |y| - (|getShellEntry| $ 56))) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 62)) |y| + (|getShellEntry| $ 75))) (DEFUN |URAGG-;setlast!;A2S;29| (|x| |s| $) (SEQ (COND ((SPADCALL |x| (|getShellEntry| $ 20)) (|error| "setlast: empty list")) ('T - (SEQ (SPADCALL (SPADCALL |x| (|getShellEntry| $ 22)) |s| - (|getShellEntry| $ 50)) + (SEQ (SPADCALL (SPADCALL |x| (|getShellEntry| $ 23)) |s| + (|getShellEntry| $ 69)) (EXIT |s|)))))) (DEFUN |URAGG-;setchildren!;ALA;30| (|u| |lv| $) (COND ((EQL (LENGTH |lv|) 1) - (SPADCALL |u| (|SPADfirst| |lv|) (|getShellEntry| $ 54))) + (SPADCALL |u| (|SPADfirst| |lv|) (|getShellEntry| $ 73))) ('T (|error| "wrong number of children specified")))) (DEFUN |URAGG-;setvalue!;A2S;31| (|u| |s| $) - (SPADCALL |u| |s| (|getShellEntry| $ 50))) + (SPADCALL |u| |s| (|getShellEntry| $ 69))) (DEFUN |URAGG-;split!;AIA;32| (|p| |n| $) (PROG (#0=#:G1525 |q|) @@ -593,12 +593,12 @@ (|check-subtype| (COND ((< #0# 0) 'NIL) ('T 'T)) '(|NonNegativeInteger|) #0#)) - (|getShellEntry| $ 43)) + (|getShellEntry| $ 61)) |URAGG-;split!;AIA;32|) (LETT |q| (SPADCALL |p| (|getShellEntry| $ 14)) |URAGG-;split!;AIA;32|) - (SPADCALL |p| (SPADCALL (|getShellEntry| $ 61)) - (|getShellEntry| $ 54)) + (SPADCALL |p| (SPADCALL (|getShellEntry| $ 82)) + (|getShellEntry| $ 73)) (EXIT |q|)))))))) (DEFUN |URAGG-;cycleSplit!;2A;33| (|x| $) @@ -606,10 +606,10 @@ (RETURN (SEQ (COND ((OR (SPADCALL - (LETT |y| (SPADCALL |x| (|getShellEntry| $ 37)) + (LETT |y| (SPADCALL |x| (|getShellEntry| $ 53)) |URAGG-;cycleSplit!;2A;33|) (|getShellEntry| $ 20)) - (SPADCALL |x| |y| (|getShellEntry| $ 36))) + (SPADCALL |x| |y| (|getShellEntry| $ 52))) |y|) ('T (SEQ (LETT |z| (SPADCALL |x| (|getShellEntry| $ 14)) @@ -617,7 +617,7 @@ (SEQ G190 (COND ((NULL (NOT (SPADCALL |z| |y| - (|getShellEntry| $ 36)))) + (|getShellEntry| $ 52)))) (GO G191))) (SEQ (LETT |x| |z| |URAGG-;cycleSplit!;2A;33|) (EXIT (LETT |z| @@ -625,8 +625,8 @@ (|getShellEntry| $ 14)) |URAGG-;cycleSplit!;2A;33|))) NIL (GO G190) G191 (EXIT NIL)) - (SPADCALL |x| (SPADCALL (|getShellEntry| $ 61)) - (|getShellEntry| $ 54)) + (SPADCALL |x| (SPADCALL (|getShellEntry| $ 82)) + (|getShellEntry| $ 73)) (EXIT |y|)))))))) (DEFUN |UnaryRecursiveAggregate&| (|#1| |#2|) @@ -638,7 +638,7 @@ (LETT |dv$2| (|devaluate| |#2|) . #0#) (LETT |dv$| (LIST '|UnaryRecursiveAggregate&| |dv$1| |dv$2|) . #0#) - (LETT $ (|newShell| 66) . #0#) + (LETT $ (|newShell| 86) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -649,41 +649,41 @@ (|setShellEntry| $ 7 |#2|) (COND ((|HasAttribute| |#1| '|finiteAggregate|) - (|setShellEntry| $ 45 + (|setShellEntry| $ 63 (CONS (|dispatchFunction| |URAGG-;last;ANniA;22|) $)))) (COND ((|HasCategory| |#2| '(|SetCategory|)) (PROGN - (|setShellEntry| $ 47 + (|setShellEntry| $ 66 (CONS (|dispatchFunction| |URAGG-;=;2AB;23|) $)) - (|setShellEntry| $ 49 + (|setShellEntry| $ 68 (CONS (|dispatchFunction| |URAGG-;node?;2AB;24|) $))))) (COND ((|testBitVector| |pv$| 1) (PROGN - (|setShellEntry| $ 51 + (|setShellEntry| $ 70 (CONS (|dispatchFunction| |URAGG-;setelt;Afirst2S;25|) $)) - (|setShellEntry| $ 53 + (|setShellEntry| $ 72 (CONS (|dispatchFunction| |URAGG-;setelt;Alast2S;26|) $)) - (|setShellEntry| $ 55 + (|setShellEntry| $ 74 (CONS (|dispatchFunction| |URAGG-;setelt;Arest2A;27|) $)) - (|setShellEntry| $ 57 + (|setShellEntry| $ 76 (CONS (|dispatchFunction| |URAGG-;concat;3A;28|) $)) - (|setShellEntry| $ 58 + (|setShellEntry| $ 77 (CONS (|dispatchFunction| |URAGG-;setlast!;A2S;29|) $)) - (|setShellEntry| $ 59 + (|setShellEntry| $ 80 (CONS (|dispatchFunction| |URAGG-;setchildren!;ALA;30|) $)) - (|setShellEntry| $ 60 + (|setShellEntry| $ 81 (CONS (|dispatchFunction| |URAGG-;setvalue!;A2S;31|) $)) - (|setShellEntry| $ 63 + (|setShellEntry| $ 83 (CONS (|dispatchFunction| |URAGG-;split!;AIA;32|) $)) - (|setShellEntry| $ 64 + (|setShellEntry| $ 84 (CONS (|dispatchFunction| |URAGG-;cycleSplit!;2A;33|) $))))) $)))) @@ -694,54 +694,66 @@ '"last" |URAGG-;elt;AlastS;2| (10 . |rest|) '"rest" |URAGG-;elt;ArestA;3| |URAGG-;second;AS;4| |URAGG-;third;AS;5| (|Boolean|) (15 . |empty?|) - |URAGG-;cyclic?;AB;6| (20 . |tail|) |URAGG-;last;AS;7| - (|List| $) |URAGG-;nodes;AL;8| |URAGG-;children;AL;9| + (20 . |false|) |URAGG-;cyclic?;AB;6| (24 . |tail|) + |URAGG-;last;AS;7| (|List| 6) (29 . |empty|) + (33 . |concat|) (39 . |reverse!|) (|List| $) + |URAGG-;nodes;AL;8| |URAGG-;children;AL;9| |URAGG-;leaf?;AB;10| |URAGG-;value;AS;11| - (|NonNegativeInteger|) |URAGG-;less?;ANniB;12| + (|NonNegativeInteger|) (44 . |Zero|) (|Integer|) + (48 . |Zero|) (52 . <) (58 . |One|) (62 . |One|) (66 . -) + |URAGG-;less?;ANniB;12| (72 . |zero?|) |URAGG-;more?;ANniB;13| |URAGG-;size?;ANniB;14| - (25 . |cyclic?|) |URAGG-;#;ANni;15| |URAGG-;tail;2A;16| - (30 . |eq?|) (36 . |cycleEntry|) |URAGG-;cycleTail;2A;18| + (|SingleInteger|) (77 . |Zero|) (81 . =) (87 . |cyclic?|) + |URAGG-;#;ANni;15| |URAGG-;tail;2A;16| (92 . |eq?|) + (98 . |cycleEntry|) |URAGG-;cycleTail;2A;18| (103 . |One|) |URAGG-;cycleEntry;2A;19| |URAGG-;cycleLength;ANni;20| - |URAGG-;rest;ANniA;21| (41 . |#|) (46 . |rest|) - (52 . |copy|) (57 . |last|) (63 . ~=) (69 . =) (75 . =) - (81 . |node?|) (87 . |setfirst!|) (93 . |setelt|) - (100 . |setlast!|) (106 . |setelt|) (113 . |setrest!|) - (119 . |setelt|) (126 . |concat!|) (132 . |concat|) - (138 . |setlast!|) (144 . |setchildren!|) - (150 . |setvalue!|) (156 . |empty|) (|Integer|) - (160 . |split!|) (166 . |cycleSplit!|) '"value") - '#(|value| 171 |third| 176 |tail| 181 |split!| 186 |size?| - 192 |setvalue!| 198 |setlast!| 204 |setelt| 210 - |setchildren!| 231 |second| 237 |rest| 242 |nodes| 248 - |node?| 253 |more?| 259 |less?| 265 |leaf?| 271 |last| 276 - |elt| 287 |cyclic?| 305 |cycleTail| 310 |cycleSplit!| 315 - |cycleLength| 320 |cycleEntry| 325 |concat| 330 |children| - 336 = 341 |#| 347) + |URAGG-;rest;ANniA;21| (107 . |#|) (112 . <) + (118 . |rest|) (124 . |copy|) (129 . |last|) + (135 . |true|) (139 . ~=) (145 . =) (151 . =) + (157 . |node?|) (163 . |setfirst!|) (169 . |setelt|) + (176 . |setlast!|) (182 . |setelt|) (189 . |setrest!|) + (195 . |setelt|) (202 . |concat!|) (208 . |concat|) + (214 . |setlast!|) (220 . |#|) (225 . |first|) + (230 . |setchildren!|) (236 . |setvalue!|) (242 . |empty|) + (246 . |split!|) (252 . |cycleSplit!|) '"value") + '#(|value| 257 |third| 262 |tail| 267 |split!| 272 |size?| + 278 |setvalue!| 284 |setlast!| 290 |setelt| 296 + |setchildren!| 317 |second| 323 |rest| 328 |nodes| 334 + |node?| 339 |more?| 345 |less?| 351 |leaf?| 357 |last| 362 + |elt| 373 |cyclic?| 391 |cycleTail| 396 |cycleSplit!| 401 + |cycleLength| 406 |cycleEntry| 411 |concat| 416 |children| + 422 = 427 |#| 433) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() - (|makeByteWordVec2| 64 + (|makeByteWordVec2| 84 '(1 6 7 0 8 1 6 7 0 11 1 6 0 0 14 1 6 - 19 0 20 1 6 0 0 22 1 6 19 0 33 2 6 19 - 0 0 36 1 6 0 0 37 1 6 29 0 42 2 6 0 0 - 29 43 1 6 0 0 44 2 0 0 0 29 45 2 7 19 - 0 0 46 2 0 19 0 0 47 2 6 19 0 0 48 2 - 0 19 0 0 49 2 6 7 0 7 50 3 0 7 0 9 7 - 51 2 6 7 0 7 52 3 0 7 0 12 7 53 2 6 0 - 0 0 54 3 0 0 0 15 0 55 2 6 0 0 0 56 2 - 0 0 0 0 57 2 0 7 0 7 58 2 0 0 0 24 59 - 2 0 7 0 7 60 0 6 0 61 2 0 0 0 62 63 1 - 0 0 0 64 1 0 7 0 28 1 0 7 0 18 1 0 0 - 0 35 2 0 0 0 62 63 2 0 19 0 29 32 2 0 - 7 0 7 60 2 0 7 0 7 58 3 0 7 0 12 7 53 - 3 0 0 0 15 0 55 3 0 7 0 9 7 51 2 0 0 - 0 24 59 1 0 7 0 17 2 0 0 0 29 41 1 0 - 24 0 25 2 0 19 0 0 49 2 0 19 0 29 31 - 2 0 19 0 29 30 1 0 19 0 27 2 0 0 0 29 - 45 1 0 7 0 23 2 0 7 0 12 13 2 0 0 0 - 15 16 2 0 7 0 9 10 1 0 19 0 21 1 0 0 - 0 38 1 0 0 0 64 1 0 29 0 40 1 0 0 0 - 39 2 0 0 0 0 57 1 0 24 0 26 2 0 19 0 - 0 47 1 0 29 0 34))))) + 19 0 20 0 19 0 21 1 6 0 0 23 0 25 0 + 26 2 25 0 6 0 27 1 25 0 0 28 0 34 0 + 35 0 36 0 37 2 36 19 0 0 38 0 34 0 39 + 0 36 0 40 2 36 0 0 0 41 1 36 19 0 43 + 0 46 0 47 2 34 19 0 0 48 1 6 19 0 49 + 2 6 19 0 0 52 1 6 0 0 53 0 46 0 55 1 + 6 34 0 59 2 34 19 0 0 60 2 6 0 0 34 + 61 1 6 0 0 62 2 0 0 0 34 63 0 19 0 64 + 2 7 19 0 0 65 2 0 19 0 0 66 2 6 19 0 + 0 67 2 0 19 0 0 68 2 6 7 0 7 69 3 0 7 + 0 9 7 70 2 6 7 0 7 71 3 0 7 0 12 7 72 + 2 6 0 0 0 73 3 0 0 0 15 0 74 2 6 0 0 + 0 75 2 0 0 0 0 76 2 0 7 0 7 77 1 25 + 34 0 78 1 25 6 0 79 2 0 0 0 29 80 2 0 + 7 0 7 81 0 6 0 82 2 0 0 0 36 83 1 0 0 + 0 84 1 0 7 0 33 1 0 7 0 18 1 0 0 0 51 + 2 0 0 0 36 83 2 0 19 0 34 45 2 0 7 0 + 7 81 2 0 7 0 7 77 3 0 7 0 12 7 72 3 0 + 0 0 15 0 74 3 0 7 0 9 7 70 2 0 0 0 29 + 80 1 0 7 0 17 2 0 0 0 34 58 1 0 29 0 + 30 2 0 19 0 0 68 2 0 19 0 34 44 2 0 + 19 0 34 42 1 0 19 0 32 2 0 0 0 34 63 + 1 0 7 0 24 2 0 7 0 12 13 2 0 0 0 15 + 16 2 0 7 0 9 10 1 0 19 0 22 1 0 0 0 + 54 1 0 0 0 84 1 0 34 0 57 1 0 0 0 56 + 2 0 0 0 0 76 1 0 29 0 31 2 0 19 0 0 + 66 1 0 34 0 50))))) '|lookupComplete|)) diff --git a/src/algebra/strap/VECTOR.lsp b/src/algebra/strap/VECTOR.lsp index f7ad2d7f..50609410 100644 --- a/src/algebra/strap/VECTOR.lsp +++ b/src/algebra/strap/VECTOR.lsp @@ -8,14 +8,14 @@ |VECTOR;convert;$If;2|)) (DEFUN |VECTOR;vector;L$;1| (|l| $) - (SPADCALL |l| (|getShellEntry| $ 8))) + (SPADCALL |l| (|getShellEntry| $ 10))) (DEFUN |VECTOR;convert;$If;2| (|x| $) (SPADCALL - (LIST (SPADCALL '|vector| (|getShellEntry| $ 12)) - (SPADCALL (SPADCALL |x| (|getShellEntry| $ 13)) - (|getShellEntry| $ 14))) - (|getShellEntry| $ 16))) + (LIST (SPADCALL '|vector| (|getShellEntry| $ 14)) + (SPADCALL (SPADCALL |x| (|getShellEntry| $ 15)) + (|getShellEntry| $ 16))) + (|getShellEntry| $ 18))) (DEFUN |Vector| (#0=#:G1408) (PROG () @@ -40,7 +40,7 @@ (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|Vector|)) (LETT |dv$| (LIST '|Vector| |dv$1|) . #0#) - (LETT $ (|newShell| 35) . #0#) + (LETT $ (|newShell| 36) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| @@ -89,23 +89,23 @@ (|setShellEntry| $ 6 |#1|) (COND ((|testBitVector| |pv$| 3) - (|setShellEntry| $ 17 + (|setShellEntry| $ 19 (CONS (|dispatchFunction| |VECTOR;convert;$If;2|) $)))) $)))) (MAKEPROP '|Vector| '|infovec| (LIST '#(NIL NIL NIL NIL NIL (|IndexedVector| 6 (NRTEVAL 1)) - (|local| |#1|) (|List| 6) (0 . |construct|) - |VECTOR;vector;L$;1| (|Symbol|) (|InputForm|) - (5 . |convert|) (10 . |parts|) (15 . |convert|) (|List| $) - (20 . |convert|) (25 . |convert|) (|Mapping| 6 6 6) - (|Boolean|) (|NonNegativeInteger|) (|Equation| 6) - (|List| 21) (|Integer|) (|Mapping| 19 6) - (|Mapping| 19 6 6) (|UniversalSegment| 23) (|Void|) - (|Mapping| 6 6) (|OutputForm|) (|Matrix| 6) + (|local| |#1|) (|Integer|) (0 . |One|) (|List| 6) + (4 . |construct|) |VECTOR;vector;L$;1| (|Symbol|) + (|InputForm|) (9 . |convert|) (14 . |parts|) + (19 . |convert|) (|List| $) (24 . |convert|) + (29 . |convert|) (|Mapping| 6 6 6) (|Boolean|) + (|NonNegativeInteger|) (|Equation| 6) (|List| 23) + (|Mapping| 21 6) (|Mapping| 21 6 6) (|UniversalSegment| 7) + (|Void|) (|Mapping| 6 6) (|OutputForm|) (|Matrix| 6) (|SingleInteger|) (|String|) (|Union| 6 '"failed") - (|List| 23)) - '#(|vector| 30 |parts| 35 |convert| 40 |construct| 45) + (|List| 7)) + '#(|vector| 34 |parts| 39 |convert| 44 |construct| 49) '((|shallowlyMutable| . 0) (|finiteAggregate| . 0)) (CONS (|makeByteWordVec2| 5 '(0 0 0 0 0 0 0 5 0 0 1 4 0 0 1 2 3 4)) @@ -121,18 +121,17 @@ (|OneDimensionalArrayAggregate| 6) (|FiniteLinearAggregate| 6) (|LinearAggregate| 6) - (|IndexedAggregate| 23 6) + (|IndexedAggregate| 7 6) (|Collection| 6) (|HomogeneousAggregate| 6) (|OrderedSet|) (|Aggregate|) - (|EltableAggregate| 23 6) (|Evalable| 6) - (|SetCategory|) (|Type|) - (|Eltable| 23 6) (|InnerEvalable| 6 6) - (|CoercibleTo| 29) (|ConvertibleTo| 11) - (|BasicType|)) - (|makeByteWordVec2| 17 - '(1 0 0 7 8 1 11 0 10 12 1 0 7 0 13 1 7 - 11 0 14 1 11 0 15 16 1 0 11 0 17 1 0 - 0 7 9 1 0 7 0 13 1 3 11 0 17 1 0 0 7 - 8))))) + (|EltableAggregate| 7 6) (|Evalable| 6) + (|SetCategory|) (|Type|) (|Eltable| 7 6) + (|InnerEvalable| 6 6) (|CoercibleTo| 30) + (|ConvertibleTo| 13) (|BasicType|)) + (|makeByteWordVec2| 19 + '(0 7 0 8 1 0 0 9 10 1 13 0 12 14 1 0 9 + 0 15 1 9 13 0 16 1 13 0 17 18 1 0 13 + 0 19 1 0 0 9 11 1 0 9 0 15 1 3 13 0 + 19 1 0 0 9 10))))) '|lookupIncomplete|)) diff --git a/src/interp/nruncomp.boot b/src/interp/nruncomp.boot index 72d88b88..b4094c98 100644 --- a/src/interp/nruncomp.boot +++ b/src/interp/nruncomp.boot @@ -192,13 +192,13 @@ genDeltaEntry opMmPair == if eltOrConst = 'Subsumed then eltOrConst := 'ELT if atom dc then dc = "$" => nsig := sig - if NUMBERP nsig then nsig := MSUBST('$,dc,substitute("$$","$",sig)) - newimp := optDeltaEntry(op,nsig,dc,eltOrConst) => newimp + if NUMBERP nsig then nsig := MSUBST("$",dc,substitute("$$","$",sig)) setDifference(listOfBoundVars dc,$functorLocalParameters) ^= [] => ['applyFun,['compiledLookupCheck,MKQ op, mkList consSig(nsig,dc),consDomainForm(dc,nil)]] odc := dc - if not atom dc then dc := substitute("$$",'$,dc) + if not atom dc then + dc := substitute("$$","$",dc) opModemapPair := [op,[dc,:[NRTgetLocalIndex x for x in nsig]],["T",cform]] -- force pred to T if null NRTassocIndex dc and @@ -217,6 +217,7 @@ genDeltaEntry opMmPair == $NRTdeltaListComp:=[nil,:$NRTdeltaListComp] $NRTdeltaLength := $NRTdeltaLength+1 0 + impl := optDeltaEntry(op,nsig,odc,eltOrConst) => impl u ++ Return the slot number (within the template vector of the functor diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ae573563..475a0ed8 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2281224 . 3444026013) +(2282896 . 3444870410) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,10 +56,10 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3485) +(-32 R -2036) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) +((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -88,14 +88,14 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3485 UP UPUP -2999) +(-40 -2036 UP UPUP -1646) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-350))) (-3943 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-350)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-3943 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-350)))) (-3943 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-350))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-546)))) (-3943 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -3485) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2811 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2811 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2811 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-2811 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -2036) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -421) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,24 +106,24 @@ NIL ((|HasCategory| |#1| (QUOTE (-307)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4405 |has| |#1| (-556)) (-4403 . T) (-4402 . T)) -((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . T)) +((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4408 . T) (-4409 . T)) -((-3943 (-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-846)))) (-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))))) +((-2811 (-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|))))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-546))))) +((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL @@ -132,19 +132,19 @@ NIL ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) ((-4405 . T)) NIL -(-51) -((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) +(-51 S) +((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) NIL NIL -(-52 S) -((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) +(-52) +((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL (-53 R M P) ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3485) +(-54 |Base| R -2036) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -160,131 +160,131 @@ NIL ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) ((-4408 . T) (-4409 . T)) NIL -(-58 S) -((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-59 A B) +(-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL +(-59 S) +((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) +((-4409 . T) (-4408 . T)) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-61 -3956) -((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) -NIL -NIL -(-62 -3956) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-61 -3359) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -3956) +(-62 -3359) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-64 -3956) +(-63 -3359) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -3956) +(-64 -3359) +((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +NIL +NIL +(-65 -3359) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3956) +(-66 -3359) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3956) +(-67 -3359) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3956) +(-68 -3359) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3956) +(-69 -3359) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3956) +(-70 -3359) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3956) +(-71 -3359) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3956) +(-72 -3359) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3956) +(-73 -3359) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3956) +(-74 -3359) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3956) -((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) -NIL -NIL -(-76 |nameOne| |nameTwo| |nameThree|) +(-75 |nameOne| |nameTwo| |nameThree|) ((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE FCN(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=Y(2) F(2)=Y(3) F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) RETURN END SUBROUTINE JACOBF(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N,N),X,Y(N) INTEGER N F(1,1)=0.0D0 F(1,2)=1.0D0 F(1,3)=0.0D0 F(2,1)=0.0D0 F(2,2)=0.0D0 F(2,3)=1.0D0 F(3,1)=-1.0D0*Y(3) F(3,2)=4.0D0*EPS*Y(2) F(3,3)=-1.0D0*Y(1) RETURN END SUBROUTINE JACEPS(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=0.0D0 F(2)=0.0D0 F(3)=2.0D0*Y(2)**2-2.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 |nameOne| |nameTwo| |nameThree|) +(-76 |nameOne| |nameTwo| |nameThree|) ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3956) +(-77 -3359) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3956) +(-78 -3359) +((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +NIL +NIL +(-79 -3359) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3956) +(-80 -3359) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3956) +(-81 -3359) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3956) -((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) -NIL -NIL -(-83 -3956) +(-82 -3359) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3956) +(-83 -3359) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3956) +(-84 -3359) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3956) +(-85 -3359) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3956) -((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) +(-86 -3359) +((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3956) +(-87 -3359) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-89 -3956) +(-88 -3359) +((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) +NIL +NIL +(-89 -3359) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-546) (QUOTE (-906))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-546) (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-147))) (|HasCategory| (-546) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-546) (QUOTE (-1016))) (|HasCategory| (-546) (QUOTE (-816))) (-3943 (|HasCategory| (-546) (QUOTE (-816))) (|HasCategory| (-546) (QUOTE (-846)))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-1144))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-546) (QUOTE (-233))) (|HasCategory| (-546) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-546) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -309) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -286) (QUOTE (-546)) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-307))) (|HasCategory| (-546) (QUOTE (-545))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-546) (LIST (QUOTE -636) (QUOTE (-546)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (|HasCategory| (-546) (QUOTE (-145))))) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-2811 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -371,7 +371,7 @@ NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-858))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) ((-4403 . T) (-4402 . T)) @@ -380,15 +380,15 @@ NIL ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-113) -((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) -NIL -NIL -(-114 A) +(-113 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL ((|HasCategory| |#1| (QUOTE (-846)))) -(-115 -3485 UP) +(-114) +((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) +NIL +NIL +(-115 -2036 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (QUOTE (-1016))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-3943 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-116 |#1|) (QUOTE (-1144))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2811 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-1144))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,19 +435,19 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-128) +((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) +((-4409 . T) (-4408 . T)) +((-2811 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2811 (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +(-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL -(-129) -((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| (-128) (QUOTE (-846))) (|HasCategory| (-128) (LIST (QUOTE -309) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1094))) (|HasCategory| (-128) (LIST (QUOTE -309) (QUOTE (-128)))))) (-3943 (-12 (|HasCategory| (-128) (QUOTE (-1094))) (|HasCategory| (-128) (LIST (QUOTE -309) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-128) (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| (-128) (QUOTE (-846))) (|HasCategory| (-128) (QUOTE (-1094)))) (|HasCategory| (-128) (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-128) (QUOTE (-1094))) (|HasCategory| (-128) (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| (-128) (QUOTE (-1094))) (|HasCategory| (-128) (LIST (QUOTE -309) (QUOTE (-128)))))) (-130) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -468,12 +468,12 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4410 "*") . T)) NIL -(-135 |minix| -3006 R) -((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) +(-135 |minix| -3807 S T$) +((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3006 S T$) -((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) +(-136 |minix| -3807 R) +((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL (-137) @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4408 . T) (-4398 . T) (-4409 . T)) -((-3943 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2811 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4405 . T)) NIL -(-148 -3485 UP UPUP) +(-148 -2036 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -531,7 +531,7 @@ NIL (-150 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4408))) +((|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasAttribute| |#1| (QUOTE -4408))) (-151 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -3485) +(-158 R -2036) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -573,11 +573,11 @@ NIL NIL NIL (-161) -((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) +((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) NIL NIL (-162) -((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) +((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) NIL NIL (-163) @@ -591,23 +591,23 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-846)))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-846)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4401 -3943 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1453 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-4401 -2811 (|has| |#1| (-555)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1786 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) NIL NIL -(-168 R) -((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4401 -3943 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1453 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-350))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-350)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-350)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-350)))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-350)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-1193)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-556)))) 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(-3943 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-906)))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-906))))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-556)))) (-3943 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-350)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4407)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-350))))) -(-169 R S) +(-168 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,{}u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL NIL +(-169 R) +((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) +((-4401 -2811 (|has| |#1| (-555)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4407 |has| |#1| (-6 -4407)) (-1786 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-846)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1193)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4407)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -643,7 +643,7 @@ NIL (-178 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-942 |#2|) (LIST (QUOTE -882) (|devaluate| |#1|)))) +((|HasCategory| (-948 |#2|) (LIST (QUOTE -882) (|devaluate| |#1|)))) (-179 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -661,26 +661,26 @@ NIL NIL NIL (-183) -((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) +((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") (((|Constructor|) $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) NIL NIL -(-184) -((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") (((|Constructor|) $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) +(-184 S) +((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL -(-185 S) +(-185) ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) NIL NIL (-186) -((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) +((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL (-187) -((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) +((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3485) +(-188 R -2036) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,28 +788,28 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-215 -3485 UP UPUP R) +(-215 -2036 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-216 -3485 FP) +(-216 -2036 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-546) (QUOTE (-906))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-546) (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-147))) (|HasCategory| (-546) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-546) (QUOTE (-1016))) (|HasCategory| (-546) (QUOTE (-816))) (-3943 (|HasCategory| (-546) (QUOTE (-816))) (|HasCategory| (-546) (QUOTE (-846)))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-1144))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-546) (QUOTE (-233))) (|HasCategory| (-546) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-546) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -309) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -286) (QUOTE (-546)) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-307))) (|HasCategory| (-546) (QUOTE (-545))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-546) (LIST (QUOTE -636) (QUOTE (-546)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (|HasCategory| (-546) (QUOTE (-145))))) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-2811 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3485) -((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +(-219 R -2036) +((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-220 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL (-221 R1 R2) @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4405 . T)) NIL -(-224 R -3485) +(-224 R -2036) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4184 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-1775 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -3006 R) +(-237 S -3807 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4405)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -3006 R) +((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4405)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1093)))) +(-238 -3807 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4402 |has| |#2| (-1045)) (-4403 |has| |#2| (-1045)) (-4405 |has| |#2| (-6 -4405)) ((-4410 "*") |has| |#2| (-172)) (-4408 . T)) NIL -(-239 -3006 R) -((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4402 |has| |#2| (-1045)) (-4403 |has| |#2| (-1045)) (-4405 |has| |#2| (-6 -4405)) ((-4410 "*") |has| |#2| (-172)) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-363))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-789))) (-3943 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-172))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (-3943 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -911,15 +911,15 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-556)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-722)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-789)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-844)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1093))))) (-2811 (-12 (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (|HasCategory| |#3| (QUOTE (-722))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169)))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-2811 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1093)))) (-2811 (|HasAttribute| |#3| (QUOTE -4405)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-233)))) (-253 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-254 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) ((-4408 . T) (-4409 . T)) NIL -(-255 |Ex|) -((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) -NIL -NIL -(-256) +(-255) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-257 R |Ex|) +(-256 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-258) +(-257) ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-259 R) +(-258 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL NIL +(-259 |Ex|) +((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) +NIL +NIL (-260) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL (-261) -((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) -NIL -NIL -(-262) ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL NIL -(-263 S) +(-262 S) ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL +(-263) +((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) +NIL +NIL (-264 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . 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T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#3| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1032,11 +1032,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-276 R -3485) +(-276 R -2036) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-277 R -3485) +(-277 R -2036) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1055,7 +1055,7 @@ NIL (-281 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093)))) (-282 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) ((-4409 . T)) @@ -1084,7 +1084,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-289 S R |Mod| -2194 -3924 |exactQuo|) +(-289 S R |Mod| -2299 -2383 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL @@ -1100,58 +1100,58 @@ NIL ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-293 S) -((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4405 -3943 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-1045)) (-4403 |has| |#1| (-1045))) -((|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-3943 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-3943 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-298))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-3943 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) -(-294 S R) +(-293 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL +(-294 S) +((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) +((-4405 -2811 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-1045)) (-4403 |has| |#1| (-1045))) +((|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-1093)))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-302))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) (-295 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-296) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-297 S) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) -NIL -((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1045)))) -(-298) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) -NIL -NIL -(-299 -3485 S) +(-297 -2036 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-300 E -3485) +(-298 E -2036) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL -(-301) -((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) +(-299 A B) +((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) NIL NIL -(-302 A B) -((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) +(-300) +((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) NIL NIL -(-303) -((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) +(-301 S) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-1045)))) +(-302) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-304 R1) +(-303 R1) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) NIL NIL -(-305 R1 R2) +(-304 R1 R2) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) NIL NIL +(-305) +((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) +NIL +NIL (-306 S) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL @@ -1168,35 +1168,35 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-310 -3485) +(-310 -2036) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL (-311) -((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) +((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) NIL NIL (-312) -((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) +((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL (-313 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1016))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-3943 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1144))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-906)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))))) -(-314 R) -((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4405 -3943 (-3247 (|has| |#1| (-1045)) (|has| |#1| (-636 (-546)))) (-12 (|has| |#1| (-556)) (-3943 (-3247 (|has| |#1| (-1045)) (|has| |#1| (-636 (-546)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-556)) (-4401 |has| |#1| (-556)) (-4406 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(|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-25)))) (-3943 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-546))))) -(-315 R S) +((|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2811 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1144))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2811 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +(-314 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL NIL -(-316 R FE) +(-315 R FE) ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-317 R -3485) +(-316 R) +((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) +((-4405 -2811 (-3743 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (-12 (|has| |#1| (-555)) (-2811 (-3743 (|has| |#1| (-1045)) (|has| |#1| (-636 (-563)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-555)) (-4400 |has| |#1| (-555))) +((-2811 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-2811 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1105)))) (-2811 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))))) (-2811 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) +(-317 R -2036) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1206,8 +1206,8 @@ NIL NIL (-319 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-546)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-320 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1219,7 +1219,7 @@ NIL (-322 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) ((-4403 . T) (-4402 . T)) -((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-788)))) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-788)))) (-323 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1231,20 +1231,20 @@ NIL (-325 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172)))) (-326 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-327 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -3485) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -2036) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-368)))) -(-329 -3485) +(-329 -2036) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL @@ -1260,22 +1260,22 @@ NIL ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}"))) NIL NIL -(-333 -3485 UP UPUP R) -((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) -NIL -NIL -(-334 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-333 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-335 S -3485 UP UPUP R) +(-334 S -2036 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-336 -3485 UP UPUP R) +(-335 -2036 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL +(-336 -2036 UP UPUP R) +((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) +NIL +NIL (-337 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL @@ -1287,87 +1287,87 @@ NIL (-339 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-546))))) -(-340 |p| |n|) -((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| (-902 |#1|) (QUOTE (-145))) (|HasCategory| (-902 |#1|) (QUOTE (-368)))) (|HasCategory| (-902 |#1|) (QUOTE (-147))) (|HasCategory| (-902 |#1|) (QUOTE (-368))) (|HasCategory| (-902 |#1|) (QUOTE (-145)))) -(-341 S -3485 UP UPUP) +((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) +(-340 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) +NIL +NIL +(-341 S -2036 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -3485 UP UPUP) +(-342 -2036 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-343 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) -((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) -NIL -NIL -(-344 |p| |extdeg|) +(-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| (-902 |#1|) (QUOTE (-145))) (|HasCategory| (-902 |#1|) (QUOTE (-368)))) (|HasCategory| (-902 |#1|) (QUOTE (-147))) (|HasCategory| (-902 |#1|) (QUOTE (-368))) (|HasCategory| (-902 |#1|) (QUOTE (-145)))) -(-345 GF |defpol|) +((-2811 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +(-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-346 GF |extdeg|) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-347 GF) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL NIL -(-348 F1 GF F2) +(-347 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-349 S) +(-348 S) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) NIL NIL -(-350) +(-349) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-351 R UP -3485) +(-350 R UP -2036) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-352 |p| |extdeg|) +(-351 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| (-902 |#1|) (QUOTE (-145))) (|HasCategory| (-902 |#1|) (QUOTE (-368)))) (|HasCategory| (-902 |#1|) (QUOTE (-147))) (|HasCategory| (-902 |#1|) (QUOTE (-368))) (|HasCategory| (-902 |#1|) (QUOTE (-145)))) -(-353 GF |uni|) +((-2811 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +(-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-354 GF |extdeg|) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-354 |p| |n|) +((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-2811 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 GF) -((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2036 GF) +((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-357 -3485 GF) -((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) +(-357 GF) +((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-358 -3485 FP FPP) +(-358 -2036 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2811 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1384,21 +1384,21 @@ NIL ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-364 S) -((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) +(-364 |Name| S) +((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL -(-365 |Name| S) -((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) +(-365 S) +((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL (-366 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-556)))) +((|HasCategory| |#2| (QUOTE (-555)))) (-367 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4405 |has| |#1| (-556)) (-4403 . T) (-4402 . T)) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . T)) NIL (-368) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1412,18 +1412,18 @@ NIL ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) ((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-371 A S) +(-371 S A R B) +((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) +NIL +NIL +(-372 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) -(-372 S) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093)))) +(-373 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) ((-4408 . T)) NIL -(-373 S A R B) -((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) -NIL -NIL (-374 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) ((|JacobiIdentity| . T) (|NullSquare| . T) (-4403 . T) (-4402 . T)) @@ -1435,43 +1435,43 @@ NIL (-376 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546))))) +((|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-377 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) ((-4405 . T)) NIL -(-378) -((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4391 . T) (-4399 . T) (-4184 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -NIL -(-379 |Par|) +(-378 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL NIL +(-379) +((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-4391 . T) (-4399 . T) (-1775 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) NIL NIL (-381 R S) -((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4403 . T) (-4402 . T)) -((|HasCategory| |#1| (QUOTE (-172)))) -(-382 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) ((-4403 . T) (-4402 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) +(-382 R |Basis|) +((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) +((-4403 . T) (-4402 . T)) +NIL (-383) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) NIL NIL -(-384 R |Basis|) -((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4403 . T) (-4402 . T)) -NIL -(-385) +(-384) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL +(-385 R S) +((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) +((-4403 . T) (-4402 . T)) +((|HasCategory| |#1| (QUOTE (-172)))) (-386 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL @@ -1496,35 +1496,35 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-392 -3485 UP UPUP R) +(-392 -2036 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-393) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) +(-393 S) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) NIL NIL -(-394 S) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) +(-394) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL (-395) -((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) +((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) NIL NIL (-396) -((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) +((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL (-397) -((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-398 -3956 |returnType| -1497 |symbols|) +(-398 -3359 |returnType| -3975 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-399 -3485 UP) +(-399 -2036 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,121 +1546,121 @@ NIL ((|HasAttribute| |#1| (QUOTE -4391)) (|HasAttribute| |#1| (QUOTE -4399))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-4184 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-1775 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-405 R) -((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1212))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) -(-406 R S) +(-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL -(-407 S) -((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4395 -12 (|has| |#1| (-6 -4406)) (|has| |#1| (-452)) (|has| |#1| (-6 -4395))) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-816))) (-3943 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-817)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4395)) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-408 A B) +(-406 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL NIL -(-409 S R UP) +(-407 S) +((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) +((-4395 -12 (|has| |#1| (-6 -4406)) (|has| |#1| (-452)) (|has| |#1| (-6 -4395))) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2811 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4406)) (|HasAttribute| |#1| (QUOTE -4395)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL -(-410 R UP) +(-409 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) ((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-411 A S) +(-410 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546))))) -(-412 S) +((|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) +(-411 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-413 R -3485 UP A) -((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) -((-4405 . T)) -NIL -(-414 R1 F1 U1 A1 R2 F2 U2 A2) +(-412 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-415 R -3485 UP A |ibasis|) +(-413 R -2036 UP A) +((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) +((-4405 . T)) +NIL +(-414 R -2036 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1034) (|devaluate| |#2|)))) -(-416 AR R AS S) +(-415 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-417 S R) +(-416 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) -(-418 R) +(-417 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4405 |has| |#1| (-556)) (-4403 . T) (-4402 . T)) +((-4405 |has| |#1| (-555)) (-4403 . T) (-4402 . T)) NIL +(-418 R) +((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) +((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1212))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL NIL -(-420 S R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +(-420 R FE |x| |cen|) +((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535))))) -(-421 R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4405 -3943 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-556)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-556)) (-4400 |has| |#1| (-556))) NIL -(-422 R A S B) +(-421 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-423 R FE |x| |cen|) -((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) +(-422 R FE |Expon| UPS TRAN |x|) +((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) NIL NIL -(-424 R FE |Expon| UPS TRAN |x|) -((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) +(-423 S A R B) +((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-425 A S) +(-424 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL ((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) -(-426 S) +(-425 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4408 . T) (-4398 . T) (-4409 . T)) NIL -(-427 S A R B) -((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) -NIL -NIL -(-428 R -3485) +(-426 R -2036) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL -(-429 R E) +(-427 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4395 -12 (|has| |#1| (-6 -4395)) (|has| |#2| (-6 -4395))) (-4402 . T) (-4403 . T) (-4405 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4395)) (|HasAttribute| |#2| (QUOTE -4395)))) -(-430 R -3485) +(-428 R -2036) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-431 R -3485) +(-429 S R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +NIL +((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) +(-430 R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +((-4405 -2811 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-555)) (-4400 |has| |#1| (-555))) +NIL +(-431 R -2036) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-432 R -3485) +(-432 R -2036) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-433 R -3485) +(-433 R -2036) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1668,16 +1668,16 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-435 R -3485 UP) +(-435 R -2036 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-48))))) (-436) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) +((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL NIL (-437) -((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL NIL (-438 |f|) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-443 R UP -3485) +(-443 R UP -2036) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1717,21 +1717,21 @@ NIL NIL NIL (-447 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) -NIL -((|HasCategory| |#1| (QUOTE (-363)))) -(-448 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL -(-449 |Dom| |Expon| |VarSet| |Dpol|) +(-448 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL NIL -(-450 |Dom| |Expon| |VarSet| |Dpol|) +(-449 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL NIL +(-450 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) +NIL +((|HasCategory| |#1| (QUOTE (-363)))) (-451 S) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL @@ -1742,12 +1742,12 @@ NIL NIL (-453 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4405 |has| (-407 (-942 |#1|)) (-556)) (-4403 . T) (-4402 . T)) -((|HasCategory| (-407 (-942 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-407 (-942 |#1|)) (QUOTE (-556)))) +((-4405 |has| (-407 (-948 |#1|)) (-555)) (-4403 . T) (-4402 . T)) +((|HasCategory| (-407 (-948 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-407 (-948 |#1|)) (QUOTE (-555)))) (-454 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-556)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1783,7 +1783,7 @@ NIL (-463 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-464 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -3485 R) +(-471 |lv| -2036 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1826,16 +1826,16 @@ NIL NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . 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The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-477) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-481 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-2811 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1867,8 +1867,8 @@ NIL (-484 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-485 -3485 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-485 -2036 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1879,11 +1879,11 @@ NIL (-487) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-546) (QUOTE (-906))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-546) (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-147))) (|HasCategory| (-546) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-546) (QUOTE (-1016))) (|HasCategory| (-546) (QUOTE (-816))) (-3943 (|HasCategory| (-546) (QUOTE (-816))) (|HasCategory| (-546) (QUOTE (-846)))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-1144))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-546) (QUOTE (-233))) (|HasCategory| (-546) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-546) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -309) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -286) (QUOTE (-546)) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-307))) (|HasCategory| (-546) (QUOTE (-545))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-546) (LIST (QUOTE -636) (QUOTE (-546)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (|HasCategory| (-546) (QUOTE (-145))))) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-2811 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) (-488 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) +((|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (-489 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,34 +1904,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -3485 UP |AlExt| |AlPol|) +(-494 -2036 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-495) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-546))))) +((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563))))) (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-498 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-499 R UP -3485) +(-499 R UP -2036) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-500 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-858))))) (-501 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -3485 |Expon| |VarSet| |DPoly|) +(-504 -2036 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-1169))))) @@ -1969,15 +1969,15 @@ NIL NIL NIL (-510 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL NIL (-511 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL NIL (-512 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL (-513 S A B) @@ -1995,7 +1995,7 @@ NIL (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2003,15 +2003,15 @@ NIL (-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((-3943 (|HasCategory| (-580 |#1|) (QUOTE (-145))) (|HasCategory| (-580 |#1|) (QUOTE (-368)))) (|HasCategory| (-580 |#1|) (QUOTE (-147))) (|HasCategory| (-580 |#1|) (QUOTE (-368))) (|HasCategory| (-580 |#1|) (QUOTE (-145)))) +((-2811 (|HasCategory| (-580 |#1|) (QUOTE (-145))) (|HasCategory| (-580 |#1|) (QUOTE (-368)))) (|HasCategory| (-580 |#1|) (QUOTE (-147))) (|HasCategory| (-580 |#1|) (QUOTE (-368))) (|HasCategory| (-580 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-520 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2023,7 +2023,7 @@ NIL (-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2056,7 +2056,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-532 K -3485 |Par|) +(-532 K -2036 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2068,19 +2068,19 @@ NIL ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-535) -((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) +(-535 R) +((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-536 R) -((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) +(-536) +((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL (-537 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-538 K -3485 |Par|) +(-538 K -2036 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2101,7 +2101,7 @@ NIL NIL NIL (-543 R UP) -((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) +((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) NIL NIL (-544 S) @@ -2113,90 +2113,90 @@ NIL ((-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-546) -((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4390 . T) (-4396 . T) (-4400 . T) (-4395 . T) (-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -NIL -(-547) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) NIL NIL -(-548) +(-547) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) NIL NIL -(-549) +(-548) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) NIL NIL -(-550 |Key| |Entry| |addDom|) +(-549 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859))))) -(-551 R -3485) +((-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) +(-550 R -2036) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-552 R0 -3485 UP UPUP R) +(-551 R0 -2036 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL -(-553) +(-552) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-554 R) +(-553 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4184 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-1775 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-555 S) +(-554 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL -(-556) +(-555) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-557 R -3485) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) +(-556 R -2036) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL -(-558 I) +(-557 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-559) -((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) +(-558) +((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-560 R -3485 L) -((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) +(-559 R -2036 L) +((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -653) (|devaluate| |#2|)))) -(-561) +((|HasCategory| |#3| (LIST (QUOTE -651) (|devaluate| |#2|)))) +(-560) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-562 -3485 UP UPUP R) +(-561 -2036 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-563 -3485 UP) +(-562 -2036 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL +(-563) +((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) +((-4390 . T) (-4396 . T) (-4400 . T) (-4395 . T) (-4406 . T) (-4407 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +NIL (-564) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-565 R -3485 L) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) +(-565 R -2036 L) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -653) (|devaluate| |#2|)))) -(-566 R -3485) +((|HasCategory| |#3| (LIST (QUOTE -651) (|devaluate| |#2|)))) +(-566 R -2036) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-567 -3485 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-626))))) +(-567 -2036 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2204,27 +2204,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-569 -3485) +(-569 -2036) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-570 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-4184 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-1775 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-571) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-572 R -3485) +(-572 R -2036) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-573 -3485 UP) -((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-626))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-555)))) +(-573 -2036 UP) +((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-574 R -3485) +(-574 R -2036) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2256,18 +2256,18 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-582 -3485) -((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4403 . T) (-4402 . T)) -((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169))))) -(-583 E -3485) -((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) +(-582 R -2036) +((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-584 R -3485) -((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) +(-583 E -2036) +((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL +(-584 -2036) +((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) +((-4403 . T) (-4402 . T)) +((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-585 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2295,19 +2295,19 @@ NIL (-591 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-3943 (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2811 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2811 (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-592 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-593 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-546)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-546)) (|devaluate| |#1|)))) (|HasCategory| (-546) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-546)))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|)))) (|HasCategory| (-563) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563)))))) (-594 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4403 |has| |#1| (-556)) (-4402 |has| |#1| (-556)) ((-4410 "*") |has| |#1| (-556)) (-4401 |has| |#1| (-556)) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-556)))) +((-4403 |has| |#1| (-555)) (-4402 |has| |#1| (-555)) ((-4410 "*") |has| |#1| (-555)) (-4401 |has| |#1| (-555)) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-555)))) (-595 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL @@ -2316,7 +2316,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-597 R -3485 FG) +(-597 R -2036 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2327,11 +2327,11 @@ NIL (-599 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-600 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-1093)))) (-601 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2346,12 +2346,12 @@ NIL NIL (-604 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4405 -3943 (-3247 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-418 |#1|)) (|has| |#1| (-556)))) (-4403 . T) (-4402 . T)) -((-3943 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4405 -2811 (-3743 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4403 . T) (-4402 . T)) +((-2811 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-605 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-606 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2360,14 +2360,14 @@ NIL ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) ((-4409 . T)) NIL -(-608 S) -((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) -NIL -((|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) -(-609 R S) +(-608 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL +(-609 S) +((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-610 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2376,7 +2376,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-612 -3485 UP) +(-612 -2036 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2392,26 +2392,26 @@ NIL ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL -(-616 A R S) -((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-844)))) -(-617 S R) +(-616 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-618 R) +(-617 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4405 . T)) NIL -(-619 R -3485) +(-618 A R S) +((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-844)))) +(-619 R -2036) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) NIL NIL (-620 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) ((-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4401 . T) (-4405 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-621 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2432,66 +2432,66 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) NIL NIL -(-626 R -3485) -((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) +(-626) +((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-627) -((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) +(-627 R -2036) +((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-628 |lv| -3485) +(-628 |lv| -2036) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-629) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2233) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -309) (QUOTE (-51))))) (|HasCategory| (-1151) (QUOTE (-846))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 (-51))) (QUOTE (-1094)))) -(-630 R A) -((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4405 -3943 (-3247 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-418 |#1|)) (|has| |#1| (-556)))) (-4403 . T) (-4402 . T)) -((-3943 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -418) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) -(-631 S R) +((-12 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -3704) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1151) (QUOTE (-846))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 (-52))) (QUOTE (-1093)))) +(-630 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) -(-632 R) +(-631 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) ((|JacobiIdentity| . T) (|NullSquare| . T) (-4403 . T) (-4402 . T)) NIL +(-632 R A) +((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) +((-4405 -2811 (-3743 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4403 . T) (-4402 . T)) +((-2811 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-633 R FE) -((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) +((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL NIL (-634 R) -((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) +((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL (-635 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-3733 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-3730 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-636 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4405 . T)) NIL -(-637 S) -((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-638 A B) -((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) +(-637 A B) +((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-639 A B) -((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) +(-638 A B) +((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL NIL -(-640 A B C) +(-639 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL +(-640 S) +((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) +((-4409 . T) (-4408 . T)) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-641 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2499,7 +2499,7 @@ NIL (-642 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-643 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2516,50 +2516,50 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-647 M R S) -((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4403 . T) (-4402 . T)) -((|HasCategory| |#1| (QUOTE (-787)))) -(-648 R -3485 L) +(-647 R -2036 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-649 A -2799) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-650 A) +(-648 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-651 A M) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) +(-649 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-652 S A) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) +(-650 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) -(-653 A) +(-651 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-654 -3485 UP) +(-652 -2036 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-655 A L) +(-653 A -2312) +((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) +((-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) +(-654 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-656 S) +(-655 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-657) +(-656) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL +(-657 M R S) +((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4403 . T) (-4402 . T)) +((|HasCategory| |#1| (QUOTE (-787)))) (-658 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL @@ -2576,12 +2576,12 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4409 . T) (-4408 . T)) NIL -(-662 -3485 |Row| |Col| M) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-662 -2036) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-663 -3485) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +(-663 -2036 |Row| |Col| M) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL (-664 R E OV P) @@ -2591,7 +2591,7 @@ NIL (-665 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4405 . T) (-4408 . T) (-4402 . T) (-4403 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-3943 (|HasAttribute| |#2| (QUOTE (-4410 #1#))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555))) (-2811 (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-666) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2611,7 +2611,7 @@ NIL (-670 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-671) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2648,26 +2648,26 @@ NIL ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-680 S R |Row| |Col|) +(-680 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) +NIL +NIL +(-681 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) -(-681 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555)))) +(-682 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) ((-4408 . T) (-4409 . T)) NIL -(-682 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) -((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) -NIL -NIL (-683 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556)))) +((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555)))) (-684 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4408 . T) (-4409 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4410 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-685 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2676,7 +2676,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-687 S -3485 FLAF FLAS) +(-687 S -2036 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2686,8 +2686,8 @@ NIL NIL (-689) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4401 . T) (-4406 |has| (-694) (-363)) (-4400 |has| (-694) (-363)) (-1453 . T) (-4407 |has| (-694) (-6 -4407)) (-4404 |has| (-694) (-6 -4404)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-694) (QUOTE (-147))) (|HasCategory| (-694) (QUOTE (-145))) (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-694) (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-363))) (-3943 (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-233))) (-3943 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-350)))) (|HasCategory| (-694) (QUOTE (-350))) (|HasCategory| (-694) (LIST (QUOTE -286) (QUOTE (-694)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -309) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (-3943 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-350)))) (|HasCategory| (-694) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-694) (QUOTE (-1016))) (|HasCategory| (-694) (QUOTE (-1193))) (-12 (|HasCategory| (-694) (QUOTE (-998))) (|HasCategory| (-694) (QUOTE (-1193)))) (-3943 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (-12 (|HasCategory| (-694) (QUOTE (-350))) (|HasCategory| (-694) (QUOTE (-906)))) (|HasCategory| (-694) (QUOTE (-363)))) (-3943 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (-12 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-906)))) (-12 (|HasCategory| (-694) (QUOTE (-350))) (|HasCategory| (-694) (QUOTE (-906))))) (|HasCategory| (-694) (QUOTE (-545))) (-12 (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-1193)))) (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906))) (-3943 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (|HasCategory| (-694) (QUOTE (-363)))) (-3943 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (|HasCategory| (-694) (QUOTE (-556)))) (-12 (|HasCategory| (-694) (QUOTE (-233))) (|HasCategory| (-694) (QUOTE (-363)))) (-12 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169))))) (|HasCategory| (-694) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-694) (QUOTE (-846))) (|HasCategory| (-694) (QUOTE (-556))) (|HasAttribute| (-694) (QUOTE -4407)) (|HasAttribute| (-694) (QUOTE -4404)) (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (|HasCategory| (-694) (QUOTE (-145)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-906)))) (|HasCategory| (-694) (QUOTE (-350))))) +((-4401 . T) (-4406 |has| (-694) (-363)) (-4400 |has| (-694) (-363)) (-1786 . T) (-4407 |has| (-694) (-6 -4407)) (-4404 |has| (-694) (-6 -4404)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-694) (QUOTE (-147))) (|HasCategory| (-694) (QUOTE (-145))) (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-363))) (-2811 (|HasCategory| (-694) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-233))) (-2811 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (LIST (QUOTE -286) (QUOTE (-694)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -309) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-694) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-694) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (-2811 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-349)))) (|HasCategory| (-694) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-694) (QUOTE (-1018))) (|HasCategory| (-694) (QUOTE (-1193))) (-12 (|HasCategory| (-694) (QUOTE (-998))) (|HasCategory| (-694) (QUOTE (-1193)))) (-2811 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (-2811 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-363))) (|HasCategory| (-694) (QUOTE (-905)))) (-12 (|HasCategory| (-694) (QUOTE (-349))) (|HasCategory| (-694) (QUOTE (-905))))) (|HasCategory| (-694) (QUOTE (-545))) (-12 (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-1193)))) (|HasCategory| (-694) (QUOTE (-1054))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905))) (-2811 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-363)))) (-2811 (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-555)))) (-12 (|HasCategory| (-694) (QUOTE (-233))) (|HasCategory| (-694) (QUOTE (-363)))) (-12 (|HasCategory| (-694) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-694) (QUOTE (-363)))) (|HasCategory| (-694) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-694) (QUOTE (-846))) (|HasCategory| (-694) (QUOTE (-555))) (|HasAttribute| (-694) (QUOTE -4407)) (|HasAttribute| (-694) (QUOTE -4404)) (-12 (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-145)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-694) (QUOTE (-307))) (|HasCategory| (-694) (QUOTE (-905)))) (|HasCategory| (-694) (QUOTE (-349))))) (-690 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4409 . T)) @@ -2697,16 +2697,16 @@ NIL NIL NIL (-692) -((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) +((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-693 OV E -3485 PG) +(-693 OV E -2036 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-694) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-4184 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((-1775 . T) (-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-695 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-702 S -3058 I) +(-702 S -4191 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2756,14 +2756,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-707 R |Mod| -2194 -3924 |exactQuo|) +(-707 R |Mod| -2299 -2383 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-709 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -2194 -3924 |exactQuo|) +(-711 R |Mod| -2299 -2383 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4405 . T)) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4403 . T) (-4402 . T)) NIL -(-714 -3485) +(-714 -2036) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) ((-4405 . T)) NIL @@ -2807,7 +2807,7 @@ NIL (-719 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-350))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368)))) (-720 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) ((-4401 |has| |#1| (-363)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-723 -3485 UP) +(-723 -2036 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2838,8 +2838,8 @@ NIL NIL (-727 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-556)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-728 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2857,13 +2857,13 @@ NIL ((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-846)))) (-732 S) -((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4408 . T) (-4398 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-733 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) ((-4398 . T) (-4409 . T)) NIL +(-733 S) +((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) +((-4408 . T) (-4398 . T) (-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-734) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2874,7 +2874,7 @@ NIL NIL (-736 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4403 . T) (-4402 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-737 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2972,11 +2972,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-761 -3485) +(-761 -2036) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-762 P -3485) +(-762 P -2036) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -3485) +(-764 UP -2036) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3000,16 +3000,16 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4410 "*") . T)) NIL -(-768 R -3485) +(-768 R -2036) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL -(-769) -((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) +(-769 S) +((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-770 S) -((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) +(-770) +((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL (-771 R |PolR| E |PolE|) @@ -3020,7 +3020,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-773 -3485 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2036 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3034,20 +3034,20 @@ NIL NIL (-776 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169))))) (-3943 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))))) (-3943 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3733 (|HasCategory| |#1| (QUOTE (-545)))) (-3733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3733 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-546))))) (-3733 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3733 (|HasCategory| |#1| (LIST (QUOTE -987) (QUOTE (-546))))))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-777 R) -((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-778 R S) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3730 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3730 (|HasCategory| |#1| (QUOTE (-545)))) (-3730 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3730 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-563))))) (-3730 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-1169)))) (-3730 (|HasCategory| |#1| (LIST (QUOTE -988) (QUOTE (-563))))))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-777 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL +(-778 R) +((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-779 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-780 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) ((-4409 . T) (-4408 . T)) @@ -3055,7 +3055,7 @@ NIL (-781 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-172)))) +((-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-172)))) (-782) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -3092,43 +3092,43 @@ NIL ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-791 S R) +(-791) +((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) +NIL +NIL +(-792 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) -(-792 R) +((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) +(-793 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-793) -((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) +(-794 -2811 R OS S) +((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-794 R) +(-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-3943 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) -(-795 -3943 R OS S) -((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) -NIL -NIL +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2811 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (-796) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-797 R -3485 L) +(-797 R -2036 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-798 R -3485) -((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) +(-798 R -2036) +((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL (-799) ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-800 R -3485) +(-800 R -2036) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3136,11 +3136,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-802 -3485 UP UPUP R) +(-802 -2036 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-803 -3485 UP L LQ) +(-803 -2036 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3148,38 +3148,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-805 -3485 UP L LQ) +(-805 -2036 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-806 -3485 UP) -((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) +(-806 -2036 UP) +((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-807 -3485 L UP A LO) +(-807 -2036 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-808 -3485 UP) +(-808 -2036 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-809 -3485 LO) +(-809 -2036 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-810 -3485 LODO) +(-810 -2036 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-811 -3006 S |f|) +(-811 -3807 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4402 |has| |#2| (-1045)) (-4403 |has| |#2| (-1045)) (-4405 |has| |#2| (-6 -4405)) ((-4410 "*") |has| |#2| (-172)) (-4408 . 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(QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-2811 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-812 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-813 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4410 "*") |has| |#2| (-363)) (-4401 |has| |#2| (-363)) (-4406 |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 . T) (-4403 . T) (-4402 . T)) @@ -3197,37 +3197,37 @@ NIL ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-817) -((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) +((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL (-818) -((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) +((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL (-819) -((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) +((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL (-820) -((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) +((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL (-821) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-822) -((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) -NIL -NIL -(-823 R) +(-822 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-824 P R) +(-823 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) ((-4402 . T) (-4403 . T) (-4405 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) +(-824) +((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) +NIL +NIL (-825) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL @@ -3240,26 +3240,26 @@ NIL ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) NIL NIL -(-828 R) -((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4405 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) -(-829 R S) +(-828 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-830 R) -((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-831 A S) +(-829 R) +((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) +((-4405 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-2811 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +(-830 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL NIL -(-832 S) +(-831 S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL NIL +(-832 R) +((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) +((-4403 |has| |#1| (-172)) (-4402 |has| |#1| (-172)) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-833) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) NIL @@ -3280,19 +3280,19 @@ NIL ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-838 R) -((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4405 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-3943 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) -(-839 R S) +(-838 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL +(-839 R) +((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) +((-4405 |has| |#1| (-844))) +((|HasCategory| |#1| (QUOTE (-844))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-2811 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -3006 S) +(-841 -3807 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3319,7 +3319,7 @@ NIL (-847 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172)))) (-848 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) ((-4402 . T) (-4403 . T) (-4405 . T)) @@ -3327,19 +3327,19 @@ NIL (-849 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL -((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -3652) +((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) +(-850 R |sigma| -2016) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-851 |x| R |sigma| -3652) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) +(-851 |x| R |sigma| -2016) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) (-852 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-853) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL @@ -3348,24 +3348,24 @@ NIL ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-855) -((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) +(-855 S) +((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-856 S) +(-856) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL (-857) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) +((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL (-858) -((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) +((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL (-859) -((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) +((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL (-860 |VariableList|) @@ -3389,25 +3389,25 @@ NIL NIL NIL (-865 |p|) -((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) +((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-866 |p|) -((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) +((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-867 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-865 |#1|) (QUOTE (-906))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-865 |#1|) (QUOTE (-145))) (|HasCategory| (-865 |#1|) (QUOTE (-147))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-865 |#1|) (QUOTE (-1016))) (|HasCategory| (-865 |#1|) (QUOTE (-816))) (-3943 (|HasCategory| (-865 |#1|) (QUOTE (-816))) (|HasCategory| (-865 |#1|) (QUOTE (-846)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-865 |#1|) (QUOTE (-1144))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| (-865 |#1|) (QUOTE (-233))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -865) (|devaluate| |#1|)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (QUOTE (-307))) (|HasCategory| (-865 |#1|) (QUOTE (-545))) (|HasCategory| (-865 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-865 |#1|) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-865 |#1|) (QUOTE (-906)))) (|HasCategory| (-865 |#1|) (QUOTE (-145))))) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2811 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-1144))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) (-868 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-816))) (-3943 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2811 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-869 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-3943 (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) (-870) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3463,27 +3463,27 @@ NIL (-883 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-3733 (|HasCategory| |#2| (QUOTE (-1045)))) (-3733 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-3733 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) -(-884 R S) -((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) -NIL -NIL -(-885 R A B) +((-12 (-3730 (|HasCategory| |#2| (QUOTE (-1045)))) (-3730 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-3730 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) +(-884 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-886 R) -((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) +(-885 R S) +((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-887 R -3058) +(-886 R -4191) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL -(-888 R S) +(-887 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL +(-888 R) +((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) +NIL +NIL (-889 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL @@ -3496,7 +3496,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-892 UP -3485) +(-892 UP -2036) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3519,44 +3519,44 @@ NIL (-897 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-898 S) -((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4405 . T)) -((-3943 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) -(-899 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-898 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-900 S) +(-899 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) ((-4405 . T)) NIL -(-901 S) +(-900 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-902 |p|) -((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-903 R E |VarSet| S) +(-901 S) +((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) +((-4405 . T)) +((-2811 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +(-902 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-904 R S) +(-903 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-905 S) +(-904 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-145)))) -(-906) +(-905) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-907 R0 -3485 UP UPUP R) +(-906 |p|) +((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) +((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) +(-907 R0 -2036 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3584,63 +3584,63 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-914 -3485) +(-914 -2036) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL -(-915) -((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4410 "*") . T)) -NIL -(-916 R) +(-915 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-917) +(-916) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-918 |xx| -3485) -((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) -NIL +(-917) +((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) +(((-4410 "*") . T)) NIL -(-919 -3485 P) +(-918 -2036 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL +(-919 |xx| -2036) +((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) +NIL +NIL (-920 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-921) -((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) +(-921 S) +((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-922 S) -((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) +(-922) +((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL (-923) -((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) +((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL (-924) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) +(-925 R -2036) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-926 R -3485) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) +(-926) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL (-927 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-928 S R -3485) +(-928 S R -2036) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3660,12 +3660,12 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|)))) -(-933 -3058) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) +(-933 R -2036 -4191) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-934 R -3485 -3058) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) +(-934 -4191) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL (-935 S R Q) @@ -3687,7 +3687,7 @@ NIL (-939 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-940 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3696,35 +3696,35 @@ NIL ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-844)))) -(-942 R) -((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1169) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-943 R S) +(-942 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-944 |x| R) +(-943 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-945 S R E |VarSet|) +(-944 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-906))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-846)))) -(-946 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-905))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846)))) +(-945 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL -(-947 E V R P -3485) +(-946 E V R P -2036) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-948 E |Vars| R P S) +(-947 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-949 E V R P -3485) +(-948 R) +((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-949 E V R P -2036) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3736,42 +3736,42 @@ NIL ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-952 R E) -((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4406))) -(-953 R L) +(-952 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-954 S) -((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-955 A B) +(-953 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL -(-956) +(-954 S) +((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) +((-4409 . T) (-4408 . T)) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-955) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-957 -3485) +(-956 -2036) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-958 I) +(-957 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-959) +(-958) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL +(-959 R E) +((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4406))) (-960 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4405 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-961) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3806,7 +3806,7 @@ NIL NIL (-969 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-970) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3815,7 +3815,7 @@ NIL (-971 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-556)))) +((|HasCategory| |#2| (QUOTE (-555)))) (-972 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) ((-4408 . T)) @@ -3852,18 +3852,18 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-981 K R UP -3485) +(-981 K R UP -2036) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-982 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) -NIL -((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307))))) -(-983 |vl| |nv|) +(-982 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL +(-983 R |Var| |Expon| |Dpoly|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +NIL +((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307))))) (-984 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL @@ -3872,18 +3872,18 @@ NIL ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-986 A S) +(-986 A B R S) +((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) +NIL +NIL +(-987 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1144)))) -(-987 S) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144)))) +(-988 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-988 A B R S) -((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) -NIL -NIL (-989 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL @@ -3896,26 +3896,26 @@ NIL ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) ((-4408 . T) (-4409 . T)) NIL -(-992 R) -((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((-4401 |has| |#1| (-290)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) -(-993 S R) +(-992 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-290)))) -(-994 R) +((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-290)))) +(-993 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) ((-4401 |has| |#1| (-290)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-995 QR R QS S) +(-994 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL +(-995 R) +((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) +((-4401 |has| |#1| (-290)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) (-996 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-997 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3924,14 +3924,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-999 -3485 UP UPUP |radicnd| |n|) +(-999 -2036 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4401 |has| (-407 |#2|) (-363)) (-4406 |has| (-407 |#2|) (-363)) (-4400 |has| (-407 |#2|) (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-350))) (-3943 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-350)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-3943 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-350)))) (-3943 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-350))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-546)))) (-3943 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2811 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2811 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2811 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-2811 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1000 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-546) (QUOTE (-906))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-546) (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-147))) (|HasCategory| (-546) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-546) (QUOTE (-1016))) (|HasCategory| (-546) (QUOTE (-816))) (-3943 (|HasCategory| (-546) (QUOTE (-816))) (|HasCategory| (-546) (QUOTE (-846)))) (|HasCategory| (-546) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-1144))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-546) (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-546) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-546) (QUOTE (-233))) (|HasCategory| (-546) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-546) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -309) (QUOTE (-546)))) (|HasCategory| (-546) (LIST (QUOTE -286) (QUOTE (-546)) (QUOTE (-546)))) (|HasCategory| (-546) (QUOTE (-307))) (|HasCategory| (-546) (QUOTE (-545))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-546) (LIST (QUOTE -636) (QUOTE (-546)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-546) (QUOTE (-906)))) (|HasCategory| (-546) (QUOTE (-145))))) +((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-2811 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145))))) (-1001) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3951,7 +3951,7 @@ NIL (-1005 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-1093)))) (-1006 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -3964,19 +3964,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4401 . T) (-4406 . T) (-4400 . T) (-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4405 . T)) NIL -(-1009 R -3485) +(-1009 R -2036) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1010 R -3485) +(-1010 R -2036) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1011 -3485 UP) +(-1011 -2036 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1012 -3485 UP) +(-1012 -2036 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -3992,16 +3992,16 @@ NIL ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-1016) -((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) +(-1016 |Pol|) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL (-1017 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1018 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +(-1018) +((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL (-1019) @@ -4011,35 +4011,35 @@ NIL (-1020 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4401 . T) (-4406 . T) (-4400 . T) (-4403 . T) (-4402 . T) ((-4410 "*") . T) (-4405 . T)) -((-3943 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-407 (-546)) (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-407 (-546)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-407 (-546)) (LIST (QUOTE -1034) (QUOTE (-546))))) -(-1021 -3485 L) +((-2811 (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563))))) +(-1021 -2036 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL (-1022 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1094)))) +((|HasCategory| |#1| (QUOTE (-1093)))) (-1023 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-859))))) -(-1024) -((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) -NIL -NIL -(-1025 R) +((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) +(-1024 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL ((|HasAttribute| |#1| (QUOTE (-4410 "*")))) -(-1026 R) +(-1025 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307)))) -(-1027 S) +(-1026 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL +(-1027) +((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) +NIL +NIL (-1028 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL @@ -4048,14 +4048,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1030 -3485 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2036 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1031) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2233) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -309) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-51) (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -3704) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4072,22 +4072,22 @@ NIL ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1036 R) -((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) -NIL -NIL -(-1037) +(-1036) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1038 UP) +(-1037 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1039 R) +(-1038 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL +(-1039 R) +((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) +NIL +NIL (-1040 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL @@ -4099,7 +4099,7 @@ NIL (-1042 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -776) (|devaluate| |#1|) (LIST (QUOTE -860) (|devaluate| |#2|)))))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -776) (|devaluate| |#1|) (LIST (QUOTE -860) (|devaluate| |#2|)))))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-1043) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL @@ -4112,14 +4112,14 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4405 . T)) NIL -(-1046 |xx| -3485) +(-1046 |xx| -2036) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL (-1047 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL -((|HasCategory| |#4| (QUOTE (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-556))) (|HasCategory| |#4| (QUOTE (-172)))) +((|HasCategory| |#4| (QUOTE (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-555))) (|HasCategory| |#4| (QUOTE (-172)))) (-1048 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) ((-4408 . T) (-4403 . T) (-4402 . T)) @@ -4127,7 +4127,7 @@ NIL (-1049 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4408 . T) (-4403 . T) (-4402 . T)) -((-3943 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-859))))) +((-2811 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858))))) (-1050 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4159,14 +4159,14 @@ NIL (-1057) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2233) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| (-51) (QUOTE (-1094))) (|HasCategory| (-51) (LIST (QUOTE -309) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (QUOTE (-1094))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-51) (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-51) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1169)) (|:| -2233 (-51))) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -3704) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1169)) (|:| -3704 (-52))) (LIST (QUOTE -610) (QUOTE (-858))))) (-1058 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -987) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-1169))))) +((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -988) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-1169))))) (-1059 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-1060) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4200,15 +4200,15 @@ NIL ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1068 |Base| R -3485) -((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) +(-1068 |f|) +((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1069 |f|) -((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) +(-1069 |Base| R -2036) +((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1070 |Base| R -3485) +(-1070 |Base| R -2036) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL @@ -4216,14 +4216,14 @@ NIL ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1072 R UP M) -((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((-4401 |has| |#1| (-363)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-350))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-350)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-350)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) -(-1073 UP SAE UPA) +(-1072 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL +(-1073 R UP M) +((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) +((-4401 |has| |#1| (-363)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1074 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4250,36 +4250,36 @@ NIL NIL (-1080 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1081 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1082 S) -((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) -NIL -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1094)))) -(-1083 R S) +(-1082 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-844)))) -(-1084) +(-1083) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL +(-1084 R S) +((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) +NIL +NIL (-1085 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1094)))) -(-1086 R S) -((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) +((|HasCategory| |#1| (QUOTE (-1093)))) +(-1086 S) +((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL (-1087 S) -((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -NIL +((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1093)))) (-1088 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) NIL @@ -4288,36 +4288,36 @@ NIL ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1090 S) -((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4408 . T) (-4398 . T) (-4409 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-1091 A S) +(-1090 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1092 S) +(-1091 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) ((-4398 . T)) NIL -(-1093 S) +(-1092 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1094) +(-1093) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1095 |m| |n|) -((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) +(-1094 |m| |n|) +((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1096) -((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) +(-1095 S) +((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) +((-4408 . T) (-4398 . T) (-4409 . T)) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-1096 |Str| |Sym| |Int| |Flt| |Expr|) +((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1097 |Str| |Sym| |Int| |Flt| |Expr|) -((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) +(-1097) +((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL (-1098 |Str| |Sym| |Int| |Flt| |Expr|) @@ -4355,25 +4355,25 @@ NIL (-1106 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4402 |has| |#3| (-1045)) (-4403 |has| |#3| (-1045)) (-4405 |has| |#3| (-6 -4405)) ((-4410 "*") |has| |#3| (-172)) (-4408 . 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(QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169))))) (-2811 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1093)))) (|HasAttribute| |#3| (QUOTE -4405)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1107 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-452)))) (-1108) -((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) +((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1109) -((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) +(-1109 R -2036) +((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1110 R -3485) -((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1110 R) +((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1111 R) -((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1111) +((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL (-1112) @@ -4402,17 +4402,17 @@ NIL NIL (-1118 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-905))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1119 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) (-1120 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4409 . T) (-4408 . T)) NIL -(-1121 UP -3485) +(-1121 UP -2036) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4467,11 +4467,11 @@ NIL (-1134 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1094))) (-3943 (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))) (-2811 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858))))) (-1135 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4405 . T) (-4397 |has| |#2| (-6 (-4410 "*"))) (-4408 . T) (-4402 . T) (-4403 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-3943 (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (-2811 (|HasAttribute| |#2| (QUOTE (-4410 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1136 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4487,11 +4487,11 @@ NIL (-1139 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-1140 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1141 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4503,7 +4503,7 @@ NIL (-1143 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093)))) (-1144) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4513,21 +4513,21 @@ NIL NIL NIL (-1146 S) -((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4409 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-1147 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1148 A B) +(-1147 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1149 A B C) +(-1148 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL +(-1149 S) +((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) +((-4409 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1150) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4409 . T) (-4408 . T)) @@ -4535,21 +4535,21 @@ NIL (-1151) NIL ((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2811 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1152 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094)))) (-3943 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 (-1151)) (|:| -2233 |#1|)) (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#1|)))))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 (-1151)) (|:| -3704 |#1|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-1153 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546)))))) +((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-1154 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL (-1155 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 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"computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4580,26 +4580,26 @@ NIL ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1163 R) -((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1164 R S) +(-1163 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1165 E OV R P) +(-1164 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL +(-1165 R) +((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-546)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1167 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1168) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4614,10 +4614,10 @@ NIL NIL (-1171 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3943 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-967) (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4406))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-6 -4406)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasAttribute| |#1| (QUOTE -4406))) (-1172) -((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) +((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL (-1173) @@ -4648,14 +4648,14 @@ NIL ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1180 |Key| |Entry|) -((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4408 . T) (-4409 . T)) -((-12 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4275) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2233) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -611) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-3943 (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -4275 |#1|) (|:| -2233 |#2|)) (LIST (QUOTE -610) (QUOTE (-859))))) -(-1181 S) +(-1180 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL +(-1181 |Key| |Entry|) +((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) +((-4408 . T) (-4409 . T)) +((-12 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3320) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3704) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-2811 (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3320 |#1|) (|:| -3704 |#2|)) (LIST (QUOTE -610) (QUOTE (-858))))) (-1182 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4676,12 +4676,12 @@ NIL ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1187) -((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) +(-1187 S) +((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1188 S) -((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) +(-1188) +((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL (-1189) @@ -4707,7 +4707,7 @@ NIL (-1194 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (-1195 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4716,7 +4716,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1197 R -3485) +(-1197 R -2036) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4724,22 +4724,22 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1199 R -3485) +(-1199 R -2036) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -886) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) -(-1200 |Coef|) -((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) -(-1201 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) +(-1200 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-368)))) -(-1202 R E V P) +(-1201 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) ((-4409 . T) (-4408 . T)) NIL +(-1202 |Coef|) +((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363)))) (-1203 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4751,17 +4751,17 @@ NIL (-1205 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) -(-1206 -3485) +((|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) +(-1206 -2036) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL (-1207) -((|constructor| (NIL "The fundamental Type."))) +((|constructor| (NIL "This domain represents a type AST."))) 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(-1246 |#1| |#2| |#3|) (LIST (QUOTE -1034) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-906)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-816)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-906)))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-145)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1246 |#1| |#2| |#3|) (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1217 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1216 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1218 |Coef|) +(-1217 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-1219 S |Coef| UTS) +(-1218 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) -(-1220 |Coef| UTS) +(-1219 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . 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(LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1249 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1222 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1223 S) -((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) -NIL -((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1094)))) -(-1224 R S) +(-1223 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-844)))) -(-1225 |x| R) -((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-556)) (-4404 |has| |#2| (-363)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-378)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-378))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-546)))) (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-546))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-378)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546))))) (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -886) (QUOTE (-546)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-546)))) (-3943 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (-3943 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-3943 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-3943 (-12 (|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) -(-1226 |x| R |y| S) +(-1224 S) +((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) +NIL +((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1093)))) +(-1225 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1227 R Q UP) +(-1226 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1228 R UP) +(-1227 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1229 R UP) +(-1228 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1230 R U) +(-1229 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1231 S R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(-1230 |x| R) +((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) +(((-4410 "*") |has| |#2| (-172)) (-4401 |has| |#2| (-555)) (-4404 |has| |#2| (-363)) (-4406 |has| |#2| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-2811 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +(-1231 R PR S PS) +((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1144)))) -(-1232 R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL -(-1233 R PR S PS) -((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) +(-1232 S R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1144)))) +(-1233 R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4404 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL (-1234 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4361) (LIST (|devaluate| |#2|) (QUOTE (-1169)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2062) (LIST (|devaluate| |#2|) (QUOTE (-1169)))))) (-1235 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL (-1236 RC P) -((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) +((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1237 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-546)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1238 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1237 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1239 |Coef|) +(-1238 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-1240 S |Coef| ULS) +(-1239 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1241 |Coef| ULS) +(-1240 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-1242 |Coef| ULS) +(-1241 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-546)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-3943 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-546)))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546)))))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) +(-1242 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4406 |has| |#1| (-363)) (-4400 |has| |#1| (-363)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-2811 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1243 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) -(((-4410 "*") |has| (-1237 |#2| |#3| |#4|) (-172)) (-4401 |has| (-1237 |#2| |#3| |#4|) (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| (-1237 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-172))) (-3943 (|HasCategory| (-1237 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-1237 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546)))))) (|HasCategory| (-1237 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| (-1237 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-546)))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1237 |#2| |#3| |#4|) (QUOTE (-556)))) +(((-4410 "*") |has| (-1242 |#2| |#3| |#4|) (-172)) (-4401 |has| (-1242 |#2| |#3| |#4|) (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-172))) (-2811 (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-555)))) (-1244 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4912,30 +4912,30 @@ NIL ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1246 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-556))) (-3943 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -4361) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasSignature| |#1| (LIST (QUOTE -4227) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1247 |Coef1| |Coef2| UTS1 UTS2) +(-1246 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1248 S |Coef|) +(-1247 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-956))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasSignature| |#2| (LIST (QUOTE -3474) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4227) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasCategory| |#2| (QUOTE (-363)))) -(-1249 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1193))) (|HasSignature| |#2| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3204) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363)))) +(-1248 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-556)) (-4402 . T) (-4403 . T) (-4405 . T)) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) NIL +(-1249 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) +(((-4410 "*") |has| |#1| (-172)) (-4401 |has| |#1| (-555)) (-4402 . T) (-4403 . T) (-4405 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-2811 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1105))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2062) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3204) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2185) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|))))))) (-1250 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1251 -3485 UP L UTS) +(-1251 -2036 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL -((|HasCategory| |#1| (QUOTE (-556)))) +((|HasCategory| |#1| (QUOTE (-555)))) (-1252) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL @@ -4952,28 +4952,28 @@ NIL ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) ((-4409 . T) (-4408 . T)) NIL -(-1256 R) -((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4409 . T) (-4408 . T)) -((-3943 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-3943 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-535)))) (-3943 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-546) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-1257 A B) +(-1256 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL +(-1257 R) +((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) +((-4409 . T) (-4408 . T)) +((-2811 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-2811 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1258) -((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) +((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL (-1259) -((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) +((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL (-1260) -((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) +((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL (-1261) -((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) +((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL (-1262) @@ -4992,7 +4992,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1266 K R UP -3485) +(-1266 K R UP -2036) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5011,7 +5011,7 @@ NIL (-1270 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) ((-4409 . T) (-4408 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-859))))) +((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858))))) (-1271 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) ((-4402 . T) (-4403 . T) (-4405 . T)) @@ -5024,30 +5024,30 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1274 S -3485) +(-1274 |vl| R) +((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) +((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) +NIL +(-1275 S -2036) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1275 -3485) +(-1276 -2036) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4400 . T) (-4406 . T) (-4401 . T) ((-4410 "*") . T) (-4402 . T) (-4403 . T) (-4405 . T)) NIL -(-1276 |vl| R) -((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) -NIL (-1277 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) ((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-546))))) (|HasAttribute| |#2| (QUOTE -4401))) -(-1278 R) -((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4401 |has| |#1| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4401))) -(-1279 |vl| R) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasAttribute| |#2| (QUOTE -4401))) +(-1278 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) ((-4401 |has| |#2| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) NIL +(-1279 R) +((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) +((-4401 |has| |#1| (-6 -4401)) (-4403 . T) (-4402 . T) (-4405 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4401))) (-1280 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) ((-4405 . T) (-4406 |has| |#1| (-6 -4406)) (-4401 |has| |#1| (-6 -4401)) (-4403 . T) (-4402 . T)) @@ -5088,4 +5088,4 @@ NIL NIL NIL NIL -((-3 NIL 2281204 2281209 2281214 2281219) (-2 NIL 2281184 2281189 2281194 2281199) (-1 NIL 2281164 2281169 2281174 2281179) (0 NIL 2281144 2281149 2281154 2281159) (-1285 "ZMOD.spad" 2280953 2280966 2281082 2281139) (-1284 "ZLINDEP.spad" 2279997 2280008 2280943 2280948) (-1283 "ZDSOLVE.spad" 2269846 2269868 2279987 2279992) (-1282 "YSTREAM.spad" 2269339 2269350 2269836 2269841) (-1281 "XRPOLY.spad" 2268559 2268579 2269195 2269264) (-1280 "XPR.spad" 2266350 2266363 2268277 2268376) (-1279 "XPOLYC.spad" 2265667 2265683 2266276 2266345) (-1278 "XPOLY.spad" 2265222 2265233 2265523 2265592) (-1277 "XPBWPOLY.spad" 2263659 2263679 2265002 2265071) (-1276 "XFALG.spad" 2260683 2260699 2263585 2263654) (-1275 "XF.spad" 2259144 2259159 2260585 2260678) (-1274 "XF.spad" 2257585 2257602 2259028 2259033) (-1273 "XEXPPKG.spad" 2256836 2256862 2257575 2257580) (-1272 "XDPOLY.spad" 2256450 2256466 2256692 2256761) (-1271 "XALG.spad" 2256110 2256121 2256406 2256445) (-1270 "WUTSET.spad" 2251949 2251966 2255756 2255783) (-1269 "WP.spad" 2251148 2251192 2251807 2251874) (-1268 "WHILEAST.spad" 2250946 2250955 2251138 2251143) (-1267 "WHEREAST.spad" 2250617 2250626 2250936 2250941) (-1266 "WFFINTBS.spad" 2248180 2248202 2250607 2250612) (-1265 "WEIER.spad" 2246394 2246405 2248170 2248175) (-1264 "VSPACE.spad" 2246067 2246078 2246362 2246389) (-1263 "VSPACE.spad" 2245760 2245773 2246057 2246062) (-1262 "VOID.spad" 2245437 2245446 2245750 2245755) (-1261 "VIEWDEF.spad" 2240634 2240643 2245427 2245432) (-1260 "VIEW3D.spad" 2224469 2224478 2240624 2240629) (-1259 "VIEW2D.spad" 2212206 2212215 2224459 2224464) (-1258 "VIEW.spad" 2209828 2209837 2212196 2212201) (-1257 "VECTOR2.spad" 2208455 2208468 2209818 2209823) (-1256 "VECTOR.spad" 2207130 2207141 2207381 2207408) (-1255 "VECTCAT.spad" 2205030 2205041 2207098 2207125) (-1254 "VECTCAT.spad" 2202738 2202751 2204808 2204813) (-1253 "VARIABLE.spad" 2202518 2202533 2202728 2202733) (-1252 "UTYPE.spad" 2202162 2202171 2202508 2202513) (-1251 "UTSODETL.spad" 2201455 2201479 2202118 2202123) (-1250 "UTSODE.spad" 2199643 2199663 2201445 2201450) (-1249 "UTSCAT.spad" 2197094 2197110 2199541 2199638) (-1248 "UTSCAT.spad" 2194189 2194207 2196638 2196643) (-1247 "UTS2.spad" 2193782 2193817 2194179 2194184) (-1246 "UTS.spad" 2188571 2188599 2192249 2192346) (-1245 "URAGG.spad" 2183203 2183214 2188561 2188566) (-1244 "URAGG.spad" 2177799 2177812 2183159 2183164) (-1243 "UPXSSING.spad" 2175442 2175468 2176880 2177013) (-1242 "UPXSCONS.spad" 2173199 2173219 2173574 2173723) (-1241 "UPXSCCA.spad" 2171764 2171784 2173045 2173194) (-1240 "UPXSCCA.spad" 2170471 2170493 2171754 2171759) (-1239 "UPXSCAT.spad" 2169052 2169068 2170317 2170466) (-1238 "UPXS2.spad" 2168593 2168646 2169042 2169047) (-1237 "UPXS.spad" 2165741 2165769 2166725 2166874) (-1236 "UPSQFREE.spad" 2164154 2164168 2165731 2165736) (-1235 "UPSCAT.spad" 2161747 2161771 2164052 2164149) (-1234 "UPSCAT.spad" 2159046 2159072 2161353 2161358) (-1233 "UPOLYC2.spad" 2158515 2158534 2159036 2159041) (-1232 "UPOLYC.spad" 2153493 2153504 2158357 2158510) (-1231 "UPOLYC.spad" 2148363 2148376 2153229 2153234) (-1230 "UPMP.spad" 2147253 2147266 2148353 2148358) (-1229 "UPDIVP.spad" 2146816 2146830 2147243 2147248) (-1228 "UPDECOMP.spad" 2145053 2145067 2146806 2146811) (-1227 "UPCDEN.spad" 2144260 2144276 2145043 2145048) (-1226 "UP2.spad" 2143622 2143643 2144250 2144255) (-1225 "UP.spad" 2140779 2140794 2141172 2141325) (-1224 "UNISEG2.spad" 2140272 2140285 2140735 2140740) (-1223 "UNISEG.spad" 2139625 2139636 2140191 2140196) (-1222 "UNIFACT.spad" 2138726 2138738 2139615 2139620) (-1221 "ULSCONS.spad" 2131120 2131140 2131492 2131641) (-1220 "ULSCCAT.spad" 2128849 2128869 2130966 2131115) (-1219 "ULSCCAT.spad" 2126686 2126708 2128805 2128810) (-1218 "ULSCAT.spad" 2124902 2124918 2126532 2126681) (-1217 "ULS2.spad" 2124414 2124467 2124892 2124897) (-1216 "ULS.spad" 2114966 2114994 2116059 2116488) (-1215 "UINT8.spad" 2114843 2114852 2114956 2114961) (-1214 "UINT32.spad" 2114719 2114728 2114833 2114838) (-1213 "UINT16.spad" 2114595 2114604 2114709 2114714) (-1212 "UFD.spad" 2113660 2113669 2114521 2114590) (-1211 "UFD.spad" 2112787 2112798 2113650 2113655) (-1210 "UDVO.spad" 2111634 2111643 2112777 2112782) (-1209 "UDPO.spad" 2109061 2109072 2111590 2111595) (-1208 "TYPEAST.spad" 2108980 2108989 2109051 2109056) (-1207 "TYPE.spad" 2108912 2108921 2108970 2108975) (-1206 "TWOFACT.spad" 2107562 2107577 2108902 2108907) (-1205 "TUPLE.spad" 2107046 2107057 2107461 2107466) (-1204 "TUBETOOL.spad" 2103883 2103892 2107036 2107041) (-1203 "TUBE.spad" 2102524 2102541 2103873 2103878) (-1202 "TSETCAT.spad" 2089651 2089668 2102492 2102519) (-1201 "TSETCAT.spad" 2076764 2076783 2089607 2089612) (-1200 "TS.spad" 2075353 2075369 2076329 2076426) (-1199 "TRMANIP.spad" 2069719 2069736 2075059 2075064) (-1198 "TRIMAT.spad" 2068678 2068703 2069709 2069714) (-1197 "TRIGMNIP.spad" 2067195 2067212 2068668 2068673) (-1196 "TRIGCAT.spad" 2066707 2066716 2067185 2067190) (-1195 "TRIGCAT.spad" 2066217 2066228 2066697 2066702) (-1194 "TREE.spad" 2064788 2064799 2065824 2065851) (-1193 "TRANFUN.spad" 2064619 2064628 2064778 2064783) (-1192 "TRANFUN.spad" 2064448 2064459 2064609 2064614) (-1191 "TOPSP.spad" 2064122 2064131 2064438 2064443) (-1190 "TOOLSIGN.spad" 2063785 2063796 2064112 2064117) (-1189 "TEXTFILE.spad" 2062342 2062351 2063775 2063780) (-1188 "TEX1.spad" 2061898 2061909 2062332 2062337) (-1187 "TEX.spad" 2059030 2059039 2061888 2061893) (-1186 "TEMUTL.spad" 2058585 2058594 2059020 2059025) (-1185 "TBCMPPK.spad" 2056678 2056701 2058575 2058580) (-1184 "TBAGG.spad" 2055714 2055737 2056658 2056673) (-1183 "TBAGG.spad" 2054758 2054783 2055704 2055709) (-1182 "TANEXP.spad" 2054134 2054145 2054748 2054753) (-1181 "TABLEAU.spad" 2053615 2053626 2054124 2054129) (-1180 "TABLE.spad" 2052026 2052049 2052296 2052323) (-1179 "TABLBUMP.spad" 2048809 2048820 2052016 2052021) (-1178 "SYSTEM.spad" 2048037 2048046 2048799 2048804) (-1177 "SYSSOLP.spad" 2045510 2045521 2048027 2048032) (-1176 "SYSNNI.spad" 2044690 2044701 2045500 2045505) (-1175 "SYSINT.spad" 2044094 2044105 2044680 2044685) (-1174 "SYNTAX.spad" 2040364 2040373 2044084 2044089) (-1173 "SYMTAB.spad" 2038420 2038429 2040354 2040359) (-1172 "SYMS.spad" 2034411 2034420 2038410 2038415) (-1171 "SYMPOLY.spad" 2033418 2033429 2033500 2033627) (-1170 "SYMFUNC.spad" 2032893 2032904 2033408 2033413) (-1169 "SYMBOL.spad" 2030320 2030329 2032883 2032888) (-1168 "SWITCH.spad" 2027077 2027086 2030310 2030315) (-1167 "SUTS.spad" 2023976 2024004 2025544 2025641) (-1166 "SUPXS.spad" 2021111 2021139 2022108 2022257) (-1165 "SUPFRACF.spad" 2020216 2020234 2021101 2021106) (-1164 "SUP2.spad" 2019606 2019619 2020206 2020211) (-1163 "SUP.spad" 2016375 2016386 2017156 2017309) (-1162 "SUMRF.spad" 2015341 2015352 2016365 2016370) (-1161 "SUMFS.spad" 2014974 2014991 2015331 2015336) (-1160 "SULS.spad" 2005513 2005541 2006619 2007048) (-1159 "SUCHTAST.spad" 2005282 2005291 2005503 2005508) (-1158 "SUCH.spad" 2004962 2004977 2005272 2005277) (-1157 "SUBSPACE.spad" 1996969 1996984 2004952 2004957) (-1156 "SUBRESP.spad" 1996129 1996143 1996925 1996930) (-1155 "STTFNC.spad" 1992597 1992613 1996119 1996124) (-1154 "STTF.spad" 1988696 1988712 1992587 1992592) (-1153 "STTAYLOR.spad" 1981094 1981105 1988577 1988582) (-1152 "STRTBL.spad" 1979599 1979616 1979748 1979775) (-1151 "STRING.spad" 1979008 1979017 1979022 1979049) (-1150 "STRICAT.spad" 1978796 1978805 1978976 1979003) (-1149 "STREAM3.spad" 1978341 1978356 1978786 1978791) (-1148 "STREAM2.spad" 1977409 1977422 1978331 1978336) (-1147 "STREAM1.spad" 1977113 1977124 1977399 1977404) (-1146 "STREAM.spad" 1973971 1973982 1976638 1976653) (-1145 "STINPROD.spad" 1972877 1972893 1973961 1973966) (-1144 "STEP.spad" 1972078 1972087 1972867 1972872) (-1143 "STBL.spad" 1970604 1970632 1970771 1970786) (-1142 "STAGG.spad" 1969679 1969690 1970594 1970599) (-1141 "STAGG.spad" 1968752 1968765 1969669 1969674) (-1140 "STACK.spad" 1968103 1968114 1968359 1968386) (-1139 "SREGSET.spad" 1965807 1965824 1967749 1967776) (-1138 "SRDCMPK.spad" 1964352 1964372 1965797 1965802) (-1137 "SRAGG.spad" 1959449 1959458 1964320 1964347) (-1136 "SRAGG.spad" 1954566 1954577 1959439 1959444) (-1135 "SQMATRIX.spad" 1952182 1952200 1953098 1953185) (-1134 "SPLTREE.spad" 1946734 1946747 1951618 1951645) (-1133 "SPLNODE.spad" 1943322 1943335 1946724 1946729) (-1132 "SPFCAT.spad" 1942099 1942108 1943312 1943317) (-1131 "SPECOUT.spad" 1940649 1940658 1942089 1942094) (-1130 "SPADXPT.spad" 1932788 1932797 1940639 1940644) (-1129 "spad-parser.spad" 1932253 1932262 1932778 1932783) (-1128 "SPADAST.spad" 1931954 1931963 1932243 1932248) (-1127 "SPACEC.spad" 1915967 1915978 1931944 1931949) (-1126 "SPACE3.spad" 1915743 1915754 1915957 1915962) (-1125 "SORTPAK.spad" 1915288 1915301 1915699 1915704) (-1124 "SOLVETRA.spad" 1913045 1913056 1915278 1915283) (-1123 "SOLVESER.spad" 1911565 1911576 1913035 1913040) (-1122 "SOLVERAD.spad" 1907575 1907586 1911555 1911560) (-1121 "SOLVEFOR.spad" 1905995 1906013 1907565 1907570) (-1120 "SNTSCAT.spad" 1905595 1905612 1905963 1905990) (-1119 "SMTS.spad" 1903855 1903881 1905160 1905257) (-1118 "SMP.spad" 1901294 1901314 1901684 1901811) (-1117 "SMITH.spad" 1900137 1900162 1901284 1901289) (-1116 "SMATCAT.spad" 1898247 1898277 1900081 1900132) (-1115 "SMATCAT.spad" 1896289 1896321 1898125 1898130) (-1114 "SKAGG.spad" 1895250 1895261 1896257 1896284) (-1113 "SINT.spad" 1894076 1894085 1895116 1895245) (-1112 "SIMPAN.spad" 1893804 1893813 1894066 1894071) (-1111 "SIGNRF.spad" 1892919 1892930 1893794 1893799) (-1110 "SIGNEF.spad" 1892195 1892212 1892909 1892914) (-1109 "SIGAST.spad" 1891576 1891585 1892185 1892190) (-1108 "SIG.spad" 1890904 1890913 1891566 1891571) (-1107 "SHP.spad" 1888822 1888837 1890860 1890865) (-1106 "SHDP.spad" 1878533 1878560 1879042 1879173) (-1105 "SGROUP.spad" 1878141 1878150 1878523 1878528) (-1104 "SGROUP.spad" 1877747 1877758 1878131 1878136) (-1103 "SGCF.spad" 1870628 1870637 1877737 1877742) (-1102 "SFRTCAT.spad" 1869556 1869573 1870596 1870623) (-1101 "SFRGCD.spad" 1868619 1868639 1869546 1869551) (-1100 "SFQCMPK.spad" 1863256 1863276 1868609 1868614) (-1099 "SFORT.spad" 1862691 1862705 1863246 1863251) (-1098 "SEXOF.spad" 1862534 1862574 1862681 1862686) (-1097 "SEXCAT.spad" 1860085 1860125 1862524 1862529) (-1096 "SEX.spad" 1859977 1859986 1860075 1860080) (-1095 "SETMN.spad" 1858413 1858430 1859967 1859972) (-1094 "SETCAT.spad" 1857898 1857907 1858403 1858408) (-1093 "SETCAT.spad" 1857381 1857392 1857888 1857893) (-1092 "SETAGG.spad" 1853902 1853913 1857361 1857376) (-1091 "SETAGG.spad" 1850431 1850444 1853892 1853897) (-1090 "SET.spad" 1848731 1848742 1849852 1849891) (-1089 "SEQAST.spad" 1848434 1848443 1848721 1848726) (-1088 "SEGXCAT.spad" 1847556 1847569 1848424 1848429) (-1087 "SEGCAT.spad" 1846463 1846474 1847546 1847551) (-1086 "SEGBIND2.spad" 1846159 1846172 1846453 1846458) (-1085 "SEGBIND.spad" 1845231 1845242 1846114 1846119) (-1084 "SEGAST.spad" 1844945 1844954 1845221 1845226) (-1083 "SEG2.spad" 1844370 1844383 1844901 1844906) (-1082 "SEG.spad" 1844183 1844194 1844289 1844294) (-1081 "SDVAR.spad" 1843459 1843470 1844173 1844178) (-1080 "SDPOL.spad" 1840849 1840860 1841140 1841267) (-1079 "SCPKG.spad" 1838928 1838939 1840839 1840844) (-1078 "SCOPE.spad" 1838073 1838082 1838918 1838923) (-1077 "SCACHE.spad" 1836755 1836766 1838063 1838068) (-1076 "SASTCAT.spad" 1836664 1836673 1836745 1836750) (-1075 "SAOS.spad" 1836536 1836545 1836654 1836659) (-1074 "SAERFFC.spad" 1836249 1836269 1836526 1836531) (-1073 "SAEFACT.spad" 1835950 1835970 1836239 1836244) (-1072 "SAE.spad" 1834125 1834141 1834736 1834871) (-1071 "RURPK.spad" 1831766 1831782 1834115 1834120) (-1070 "RULESET.spad" 1831207 1831231 1831756 1831761) (-1069 "RULECOLD.spad" 1831059 1831072 1831197 1831202) (-1068 "RULE.spad" 1829263 1829287 1831049 1831054) (-1067 "RSTRCAST.spad" 1828980 1828989 1829253 1829258) (-1066 "RSETGCD.spad" 1825358 1825378 1828970 1828975) (-1065 "RSETCAT.spad" 1815142 1815159 1825326 1825353) (-1064 "RSETCAT.spad" 1804946 1804965 1815132 1815137) (-1063 "RSDCMPK.spad" 1803398 1803418 1804936 1804941) (-1062 "RRCC.spad" 1801782 1801812 1803388 1803393) (-1061 "RRCC.spad" 1800164 1800196 1801772 1801777) (-1060 "RPTAST.spad" 1799866 1799875 1800154 1800159) (-1059 "RPOLCAT.spad" 1779226 1779241 1799734 1799861) (-1058 "RPOLCAT.spad" 1758300 1758317 1778810 1778815) (-1057 "ROUTINE.spad" 1754163 1754172 1756947 1756974) (-1056 "ROMAN.spad" 1753491 1753500 1754029 1754158) (-1055 "ROIRC.spad" 1752571 1752603 1753481 1753486) (-1054 "RNS.spad" 1751474 1751483 1752473 1752566) (-1053 "RNS.spad" 1750463 1750474 1751464 1751469) (-1052 "RNG.spad" 1750198 1750207 1750453 1750458) (-1051 "RMODULE.spad" 1749836 1749847 1750188 1750193) (-1050 "RMCAT2.spad" 1749244 1749301 1749826 1749831) (-1049 "RMATRIX.spad" 1748068 1748087 1748411 1748450) (-1048 "RMATCAT.spad" 1743601 1743632 1748024 1748063) (-1047 "RMATCAT.spad" 1739024 1739057 1743449 1743454) (-1046 "RINTERP.spad" 1738912 1738932 1739014 1739019) (-1045 "RING.spad" 1738382 1738391 1738892 1738907) (-1044 "RING.spad" 1737860 1737871 1738372 1738377) (-1043 "RIDIST.spad" 1737244 1737253 1737850 1737855) (-1042 "RGCHAIN.spad" 1735823 1735839 1736729 1736756) (-1041 "RGBCSPC.spad" 1735604 1735616 1735813 1735818) (-1040 "RGBCMDL.spad" 1735134 1735146 1735594 1735599) (-1039 "RFFACTOR.spad" 1734596 1734607 1735124 1735129) (-1038 "RFFACT.spad" 1734331 1734343 1734586 1734591) (-1037 "RFDIST.spad" 1733319 1733328 1734321 1734326) (-1036 "RF.spad" 1730933 1730944 1733309 1733314) (-1035 "RETSOL.spad" 1730350 1730363 1730923 1730928) (-1034 "RETRACT.spad" 1729778 1729789 1730340 1730345) (-1033 "RETRACT.spad" 1729204 1729217 1729768 1729773) (-1032 "RETAST.spad" 1729016 1729025 1729194 1729199) (-1031 "RESULT.spad" 1727076 1727085 1727663 1727690) (-1030 "RESRING.spad" 1726423 1726470 1727014 1727071) (-1029 "RESLATC.spad" 1725747 1725758 1726413 1726418) (-1028 "REPSQ.spad" 1725476 1725487 1725737 1725742) (-1027 "REPDB.spad" 1725181 1725192 1725466 1725471) (-1026 "REP2.spad" 1714753 1714764 1725023 1725028) (-1025 "REP1.spad" 1708743 1708754 1714703 1714708) (-1024 "REP.spad" 1706295 1706304 1708733 1708738) (-1023 "REGSET.spad" 1704092 1704109 1705941 1705968) (-1022 "REF.spad" 1703421 1703432 1704047 1704052) (-1021 "REDORDER.spad" 1702597 1702614 1703411 1703416) (-1020 "RECLOS.spad" 1701380 1701400 1702084 1702177) (-1019 "REALSOLV.spad" 1700512 1700521 1701370 1701375) (-1018 "REAL0Q.spad" 1697794 1697809 1700502 1700507) (-1017 "REAL0.spad" 1694622 1694637 1697784 1697789) (-1016 "REAL.spad" 1694494 1694503 1694612 1694617) (-1015 "RDUCEAST.spad" 1694215 1694224 1694484 1694489) (-1014 "RDIV.spad" 1693866 1693891 1694205 1694210) (-1013 "RDIST.spad" 1693429 1693440 1693856 1693861) (-1012 "RDETRS.spad" 1692225 1692243 1693419 1693424) (-1011 "RDETR.spad" 1690332 1690350 1692215 1692220) (-1010 "RDEEFS.spad" 1689405 1689422 1690322 1690327) (-1009 "RDEEF.spad" 1688401 1688418 1689395 1689400) (-1008 "RCFIELD.spad" 1685587 1685596 1688303 1688396) (-1007 "RCFIELD.spad" 1682859 1682870 1685577 1685582) (-1006 "RCAGG.spad" 1680771 1680782 1682849 1682854) (-1005 "RCAGG.spad" 1678610 1678623 1680690 1680695) (-1004 "RATRET.spad" 1677970 1677981 1678600 1678605) (-1003 "RATFACT.spad" 1677662 1677674 1677960 1677965) (-1002 "RANDSRC.spad" 1676981 1676990 1677652 1677657) (-1001 "RADUTIL.spad" 1676735 1676744 1676971 1676976) (-1000 "RADIX.spad" 1673636 1673650 1675202 1675295) (-999 "RADFF.spad" 1672050 1672086 1672168 1672324) (-998 "RADCAT.spad" 1671644 1671652 1672040 1672045) (-997 "RADCAT.spad" 1671236 1671246 1671634 1671639) (-996 "QUEUE.spad" 1670579 1670589 1670843 1670870) (-995 "QUATCT2.spad" 1670198 1670216 1670569 1670574) (-994 "QUATCAT.spad" 1668363 1668373 1670128 1670193) (-993 "QUATCAT.spad" 1666279 1666291 1668046 1668051) (-992 "QUAT.spad" 1664861 1664871 1665203 1665268) (-991 "QUAGG.spad" 1663687 1663697 1664829 1664856) (-990 "QQUTAST.spad" 1663456 1663464 1663677 1663682) (-989 "QFORM.spad" 1662919 1662933 1663446 1663451) (-988 "QFCAT2.spad" 1662610 1662626 1662909 1662914) (-987 "QFCAT.spad" 1661313 1661323 1662512 1662605) (-986 "QFCAT.spad" 1659607 1659619 1660808 1660813) (-985 "QEQUAT.spad" 1659164 1659172 1659597 1659602) (-984 "QCMPACK.spad" 1653911 1653930 1659154 1659159) (-983 "QALGSET2.spad" 1651907 1651925 1653901 1653906) (-982 "QALGSET.spad" 1647984 1648016 1651821 1651826) (-981 "PWFFINTB.spad" 1645294 1645315 1647974 1647979) (-980 "PUSHVAR.spad" 1644623 1644642 1645284 1645289) (-979 "PTRANFN.spad" 1640749 1640759 1644613 1644618) (-978 "PTPACK.spad" 1637837 1637847 1640739 1640744) (-977 "PTFUNC2.spad" 1637658 1637672 1637827 1637832) (-976 "PTCAT.spad" 1636907 1636917 1637626 1637653) (-975 "PSQFR.spad" 1636214 1636238 1636897 1636902) (-974 "PSEUDLIN.spad" 1635072 1635082 1636204 1636209) (-973 "PSETPK.spad" 1620505 1620521 1634950 1634955) (-972 "PSETCAT.spad" 1614425 1614448 1620485 1620500) (-971 "PSETCAT.spad" 1608319 1608344 1614381 1614386) (-970 "PSCURVE.spad" 1607302 1607310 1608309 1608314) (-969 "PSCAT.spad" 1606069 1606098 1607200 1607297) (-968 "PSCAT.spad" 1604926 1604957 1606059 1606064) (-967 "PRTITION.spad" 1603871 1603879 1604916 1604921) (-966 "PRTDAST.spad" 1603590 1603598 1603861 1603866) (-965 "PRS.spad" 1593152 1593169 1603546 1603551) (-964 "PRQAGG.spad" 1592583 1592593 1593120 1593147) (-963 "PROPLOG.spad" 1591986 1591994 1592573 1592578) (-962 "PROPFRML.spad" 1589904 1589915 1591976 1591981) (-961 "PROPERTY.spad" 1589398 1589406 1589894 1589899) (-960 "PRODUCT.spad" 1587078 1587090 1587364 1587419) (-959 "PRINT.spad" 1586830 1586838 1587068 1587073) (-958 "PRIMES.spad" 1585081 1585091 1586820 1586825) (-957 "PRIMELT.spad" 1583062 1583076 1585071 1585076) (-956 "PRIMCAT.spad" 1582685 1582693 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561299) (-351 "FFINTBAS.spad" 557404 557423 559980 559985) (-350 "FFIELDC.spad" 554979 554987 557306 557399) (-349 "FFIELDC.spad" 552640 552650 554969 554974) (-348 "FFHOM.spad" 551388 551405 552630 552635) (-347 "FFF.spad" 548823 548834 551378 551383) (-346 "FFCGX.spad" 547670 547690 548539 548632) (-345 "FFCGP.spad" 546559 546579 547386 547479) (-344 "FFCG.spad" 545351 545372 546240 546333) (-343 "FFCAT2.spad" 545096 545136 545341 545346) (-342 "FFCAT.spad" 538123 538145 544935 545091) (-341 "FFCAT.spad" 531229 531253 538043 538048) (-340 "FF.spad" 530677 530693 530910 531003) (-339 "FEXPR.spad" 522386 522432 530433 530472) (-338 "FEVALAB.spad" 522092 522102 522376 522381) (-337 "FEVALAB.spad" 521583 521595 521869 521874) (-336 "FDIVCAT.spad" 519625 519649 521573 521578) (-335 "FDIVCAT.spad" 517665 517691 519615 519620) (-334 "FDIV2.spad" 517319 517359 517655 517660) (-333 "FDIV.spad" 516761 516785 517309 517314) (-332 "FCPAK1.spad" 515314 515322 516751 516756) (-331 "FCOMP.spad" 514693 514703 515304 515309) (-330 "FC.spad" 504608 504616 514683 514688) (-329 "FAXF.spad" 497543 497557 504510 504603) (-328 "FAXF.spad" 490530 490546 497499 497504) (-327 "FARRAY.spad" 488676 488686 489713 489740) (-326 "FAMR.spad" 486796 486808 488574 488671) (-325 "FAMR.spad" 484900 484914 486680 486685) (-324 "FAMONOID.spad" 484550 484560 484854 484859) (-323 "FAMONC.spad" 482772 482784 484540 484545) (-322 "FAGROUP.spad" 482378 482388 482668 482695) (-321 "FACUTIL.spad" 480574 480591 482368 482373) (-320 "FACTFUNC.spad" 479750 479760 480564 480569) (-319 "EXPUPXS.spad" 476583 476606 477882 478031) (-318 "EXPRTUBE.spad" 473811 473819 476573 476578) (-317 "EXPRODE.spad" 470683 470699 473801 473806) (-316 "EXPR2UPS.spad" 466775 466788 470673 470678) (-315 "EXPR2.spad" 466478 466490 466765 466770) (-314 "EXPR.spad" 461753 461763 462467 462874) (-313 "EXPEXPAN.spad" 458691 458716 459325 459418) (-312 "EXITAST.spad" 458427 458435 458681 458686) (-311 "EXIT.spad" 458098 458106 458417 458422) (-310 "EVALCYC.spad" 457556 457570 458088 458093) (-309 "EVALAB.spad" 457120 457130 457546 457551) (-308 "EVALAB.spad" 456682 456694 457110 457115) (-307 "EUCDOM.spad" 454224 454232 456608 456677) (-306 "EUCDOM.spad" 451828 451838 454214 454219) (-305 "ESTOOLS2.spad" 451429 451443 451818 451823) (-304 "ESTOOLS1.spad" 451114 451125 451419 451424) (-303 "ESTOOLS.spad" 442954 442962 451104 451109) (-302 "ESCONT1.spad" 442703 442715 442944 442949) (-301 "ESCONT.spad" 439476 439484 442693 442698) (-300 "ES2.spad" 438971 438987 439466 439471) (-299 "ES1.spad" 438537 438553 438961 438966) (-298 "ES.spad" 431084 431092 438527 438532) (-297 "ES.spad" 423537 423547 430982 430987) (-296 "ERROR.spad" 420858 420866 423527 423532) (-295 "EQTBL.spad" 419330 419352 419539 419566) (-294 "EQ2.spad" 419046 419058 419320 419325) (-293 "EQ.spad" 413920 413930 416719 416831) (-292 "EP.spad" 410234 410244 413910 413915) (-291 "ENV.spad" 408936 408944 410224 410229) (-290 "ENTIRER.spad" 408604 408612 408880 408931) (-289 "EMR.spad" 407805 407846 408530 408599) (-288 "ELTAGG.spad" 406045 406064 407795 407800) (-287 "ELTAGG.spad" 404249 404270 406001 406006) (-286 "ELTAB.spad" 403696 403714 404239 404244) (-285 "ELFUTS.spad" 403075 403094 403686 403691) (-284 "ELEMFUN.spad" 402764 402772 403065 403070) (-283 "ELEMFUN.spad" 402451 402461 402754 402759) (-282 "ELAGG.spad" 400394 400404 402431 402446) (-281 "ELAGG.spad" 398274 398286 400313 400318) (-280 "ELABEXPR.spad" 397205 397213 398264 398269) (-279 "EFUPXS.spad" 393981 394011 397161 397166) (-278 "EFULS.spad" 390817 390840 393937 393942) (-277 "EFSTRUC.spad" 388772 388788 390807 390812) (-276 "EF.spad" 383538 383554 388762 388767) (-275 "EAB.spad" 381814 381822 383528 383533) (-274 "E04UCFA.spad" 381350 381358 381804 381809) (-273 "E04NAFA.spad" 380927 380935 381340 381345) (-272 "E04MBFA.spad" 380507 380515 380917 380922) (-271 "E04JAFA.spad" 380043 380051 380497 380502) (-270 "E04GCFA.spad" 379579 379587 380033 380038) (-269 "E04FDFA.spad" 379115 379123 379569 379574) (-268 "E04DGFA.spad" 378651 378659 379105 379110) (-267 "E04AGNT.spad" 374493 374501 378641 378646) (-266 "DVARCAT.spad" 371178 371188 374483 374488) (-265 "DVARCAT.spad" 367861 367873 371168 371173) (-264 "DSMP.spad" 365292 365306 365597 365724) (-263 "DROPT1.spad" 364955 364965 365282 365287) (-262 "DROPT0.spad" 359782 359790 364945 364950) (-261 "DROPT.spad" 353727 353735 359772 359777) (-260 "DRAWPT.spad" 351882 351890 353717 353722) (-259 "DRAWHACK.spad" 351190 351200 351872 351877) (-258 "DRAWCX.spad" 348632 348640 351180 351185) (-257 "DRAWCURV.spad" 348169 348184 348622 348627) (-256 "DRAWCFUN.spad" 337341 337349 348159 348164) (-255 "DRAW.spad" 329941 329954 337331 337336) (-254 "DQAGG.spad" 328109 328119 329909 329936) (-253 "DPOLCAT.spad" 323450 323466 327977 328104) (-252 "DPOLCAT.spad" 318877 318895 323406 323411) (-251 "DPMO.spad" 311103 311119 311241 311542) (-250 "DPMM.spad" 303342 303360 303467 303768) (-249 "DOMCTOR.spad" 303234 303242 303332 303337) (-248 "DOMAIN.spad" 302365 302373 303224 303229) (-247 "DMP.spad" 299587 299602 300159 300286) (-246 "DLP.spad" 298935 298945 299577 299582) (-245 "DLIST.spad" 297514 297524 298118 298145) (-244 "DLAGG.spad" 295925 295935 297504 297509) (-243 "DIVRING.spad" 295467 295475 295869 295920) (-242 "DIVRING.spad" 295053 295063 295457 295462) (-241 "DISPLAY.spad" 293233 293241 295043 295048) (-240 "DIRPROD2.spad" 292041 292059 293223 293228) (-239 "DIRPROD.spad" 281621 281637 282261 282392) (-238 "DIRPCAT.spad" 280563 280579 281485 281616) (-237 "DIRPCAT.spad" 279234 279252 280158 280163) (-236 "DIOSP.spad" 278059 278067 279224 279229) (-235 "DIOPS.spad" 277043 277053 278039 278054) (-234 "DIOPS.spad" 276001 276013 276999 277004) (-233 "DIFRING.spad" 275293 275301 275981 275996) (-232 "DIFRING.spad" 274593 274603 275283 275288) (-231 "DIFEXT.spad" 273752 273762 274573 274588) (-230 "DIFEXT.spad" 272828 272840 273651 273656) (-229 "DIAGG.spad" 272458 272468 272808 272823) (-228 "DIAGG.spad" 272096 272108 272448 272453) (-227 "DHMATRIX.spad" 270400 270410 271553 271580) (-226 "DFSFUN.spad" 263808 263816 270390 270395) (-225 "DFLOAT.spad" 260529 260537 263698 263803) (-224 "DFINTTLS.spad" 258738 258754 260519 260524) (-223 "DERHAM.spad" 256648 256680 258718 258733) (-222 "DEQUEUE.spad" 255966 255976 256255 256282) (-221 "DEGRED.spad" 255581 255595 255956 255961) (-220 "DEFINTRF.spad" 253151 253161 255571 255576) (-219 "DEFINTEF.spad" 251675 251691 253141 253146) (-218 "DEFAST.spad" 251043 251051 251665 251670) (-217 "DECIMAL.spad" 249149 249157 249510 249603) (-216 "DDFACT.spad" 246948 246965 249139 249144) (-215 "DBLRESP.spad" 246546 246570 246938 246943) (-214 "DBASE.spad" 245200 245210 246536 246541) (-213 "DATAARY.spad" 244662 244675 245190 245195) (-212 "D03FAFA.spad" 244490 244498 244652 244657) (-211 "D03EEFA.spad" 244310 244318 244480 244485) (-210 "D03AGNT.spad" 243390 243398 244300 244305) (-209 "D02EJFA.spad" 242852 242860 243380 243385) (-208 "D02CJFA.spad" 242330 242338 242842 242847) (-207 "D02BHFA.spad" 241820 241828 242320 242325) (-206 "D02BBFA.spad" 241310 241318 241810 241815) (-205 "D02AGNT.spad" 236114 236122 241300 241305) (-204 "D01WGTS.spad" 234433 234441 236104 236109) (-203 "D01TRNS.spad" 234410 234418 234423 234428) (-202 "D01GBFA.spad" 233932 233940 234400 234405) (-201 "D01FCFA.spad" 233454 233462 233922 233927) (-200 "D01ASFA.spad" 232922 232930 233444 233449) (-199 "D01AQFA.spad" 232368 232376 232912 232917) (-198 "D01APFA.spad" 231792 231800 232358 232363) (-197 "D01ANFA.spad" 231286 231294 231782 231787) (-196 "D01AMFA.spad" 230796 230804 231276 231281) (-195 "D01ALFA.spad" 230336 230344 230786 230791) (-194 "D01AKFA.spad" 229862 229870 230326 230331) (-193 "D01AJFA.spad" 229385 229393 229852 229857) (-192 "D01AGNT.spad" 225444 225452 229375 229380) (-191 "CYCLOTOM.spad" 224950 224958 225434 225439) (-190 "CYCLES.spad" 221782 221790 224940 224945) (-189 "CVMP.spad" 221199 221209 221772 221777) (-188 "CTRIGMNP.spad" 219689 219705 221189 221194) (-187 "CTORKIND.spad" 219292 219300 219679 219684) (-186 "CTORCAT.spad" 218541 218549 219282 219287) (-185 "CTORCAT.spad" 217788 217798 218531 218536) (-184 "CTORCALL.spad" 217368 217376 217778 217783) (-183 "CTOR.spad" 217063 217071 217358 217363) (-182 "CSTTOOLS.spad" 216306 216319 217053 217058) (-181 "CRFP.spad" 210010 210023 216296 216301) (-180 "CRCEAST.spad" 209730 209738 210000 210005) (-179 "CRAPACK.spad" 208773 208783 209720 209725) (-178 "CPMATCH.spad" 208273 208288 208698 208703) (-177 "CPIMA.spad" 207978 207997 208263 208268) (-176 "COORDSYS.spad" 202871 202881 207968 207973) (-175 "CONTOUR.spad" 202273 202281 202861 202866) (-174 "CONTFRAC.spad" 197885 197895 202175 202268) (-173 "CONDUIT.spad" 197643 197651 197875 197880) (-172 "COMRING.spad" 197317 197325 197581 197638) (-171 "COMPPROP.spad" 196831 196839 197307 197312) (-170 "COMPLPAT.spad" 196598 196613 196821 196826) (-169 "COMPLEX2.spad" 196311 196323 196588 196593) (-168 "COMPLEX.spad" 190335 190345 190579 190840) (-167 "COMPFACT.spad" 189937 189951 190325 190330) (-166 "COMPCAT.spad" 188005 188015 189671 189932) (-165 "COMPCAT.spad" 185766 185778 187434 187439) (-164 "COMMUPC.spad" 185512 185530 185756 185761) (-163 "COMMONOP.spad" 185045 185053 185502 185507) (-162 "COMMAAST.spad" 184808 184816 185035 185040) (-161 "COMM.spad" 184617 184625 184798 184803) (-160 "COMBOPC.spad" 183522 183530 184607 184612) (-159 "COMBINAT.spad" 182267 182277 183512 183517) (-158 "COMBF.spad" 179635 179651 182257 182262) (-157 "COLOR.spad" 178472 178480 179625 179630) (-156 "COLONAST.spad" 178138 178146 178462 178467) (-155 "CMPLXRT.spad" 177847 177864 178128 178133) (-154 "CLLCTAST.spad" 177509 177517 177837 177842) (-153 "CLIP.spad" 173601 173609 177499 177504) (-152 "CLIF.spad" 172240 172256 173557 173596) (-151 "CLAGG.spad" 168725 168735 172230 172235) (-150 "CLAGG.spad" 165081 165093 168588 168593) (-149 "CINTSLPE.spad" 164406 164419 165071 165076) (-148 "CHVAR.spad" 162484 162506 164396 164401) (-147 "CHARZ.spad" 162399 162407 162464 162479) (-146 "CHARPOL.spad" 161907 161917 162389 162394) (-145 "CHARNZ.spad" 161660 161668 161887 161902) (-144 "CHAR.spad" 159528 159536 161650 161655) (-143 "CFCAT.spad" 158844 158852 159518 159523) (-142 "CDEN.spad" 158002 158016 158834 158839) (-141 "CCLASS.spad" 156151 156159 157413 157452) (-140 "CATEGORY.spad" 155241 155249 156141 156146) (-139 "CATCTOR.spad" 155132 155140 155231 155236) (-138 "CATAST.spad" 154759 154767 155122 155127) (-137 "CASEAST.spad" 154473 154481 154749 154754) (-136 "CARTEN2.spad" 153859 153886 154463 154468) (-135 "CARTEN.spad" 148962 148986 153849 153854) (-134 "CARD.spad" 146251 146259 148936 148957) (-133 "CAPSLAST.spad" 146025 146033 146241 146246) (-132 "CACHSET.spad" 145647 145655 146015 146020) (-131 "CABMON.spad" 145200 145208 145637 145642) (-130 "BYTEORD.spad" 144875 144883 145190 145195) (-129 "BYTEBUF.spad" 142732 142740 144044 144071) (-128 "BYTE.spad" 142157 142165 142722 142727) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP1.spad" 126718 126728 129288 129293) (-113 "BOP.spad" 122182 122190 126708 126713) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP80.spad" 98053 98066 98721 98726) (-87 "ASP8.spad" 97096 97109 98043 98048) (-86 "ASP78.spad" 96547 96560 97086 97091) (-85 "ASP77.spad" 95916 95929 96537 96542) (-84 "ASP74.spad" 95008 95021 95906 95911) (-83 "ASP73.spad" 94279 94292 94998 95003) (-82 "ASP7.spad" 93439 93452 94269 94274) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP49.spad" 87631 87644 88622 88627) (-77 "ASP42.spad" 86038 86077 87621 87626) (-76 "ASP41.spad" 84617 84656 86028 86033) (-75 "ASP4.spad" 83912 83925 84607 84612) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP19.spad" 62666 62679 67970 67975) (-63 "ASP12.spad" 62080 62093 62656 62661) (-62 "ASP10.spad" 61351 61364 62070 62075) (-61 "ASP1.spad" 60732 60745 61341 61346) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY12.spad" 58761 58772 60082 60087) (-58 "ARRAY1.spad" 57596 57605 57944 57971) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY1.spad" 46438 46447 47357 47362) (-51 "ANY.spad" 44780 44787 46428 46433) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2282876 2282881 2282886 2282891) (-2 NIL 2282856 2282861 2282866 2282871) (-1 NIL 2282836 2282841 2282846 2282851) (0 NIL 2282816 2282821 2282826 2282831) (-1285 "ZMOD.spad" 2282625 2282638 2282754 2282811) (-1284 "ZLINDEP.spad" 2281669 2281680 2282615 2282620) (-1283 "ZDSOLVE.spad" 2271518 2271540 2281659 2281664) (-1282 "YSTREAM.spad" 2271011 2271022 2271508 2271513) (-1281 "XRPOLY.spad" 2270231 2270251 2270867 2270936) (-1280 "XPR.spad" 2268022 2268035 2269949 2270048) (-1279 "XPOLY.spad" 2267577 2267588 2267878 2267947) (-1278 "XPOLYC.spad" 2266894 2266910 2267503 2267572) (-1277 "XPBWPOLY.spad" 2265331 2265351 2266674 2266743) (-1276 "XF.spad" 2263792 2263807 2265233 2265326) (-1275 "XF.spad" 2262233 2262250 2263676 2263681) (-1274 "XFALG.spad" 2259257 2259273 2262159 2262228) (-1273 "XEXPPKG.spad" 2258508 2258534 2259247 2259252) (-1272 "XDPOLY.spad" 2258122 2258138 2258364 2258433) (-1271 "XALG.spad" 2257782 2257793 2258078 2258117) (-1270 "WUTSET.spad" 2253621 2253638 2257428 2257455) (-1269 "WP.spad" 2252820 2252864 2253479 2253546) (-1268 "WHILEAST.spad" 2252618 2252627 2252810 2252815) (-1267 "WHEREAST.spad" 2252289 2252298 2252608 2252613) (-1266 "WFFINTBS.spad" 2249852 2249874 2252279 2252284) (-1265 "WEIER.spad" 2248066 2248077 2249842 2249847) (-1264 "VSPACE.spad" 2247739 2247750 2248034 2248061) (-1263 "VSPACE.spad" 2247432 2247445 2247729 2247734) (-1262 "VOID.spad" 2247109 2247118 2247422 2247427) (-1261 "VIEW.spad" 2244731 2244740 2247099 2247104) (-1260 "VIEWDEF.spad" 2239928 2239937 2244721 2244726) (-1259 "VIEW3D.spad" 2223763 2223772 2239918 2239923) (-1258 "VIEW2D.spad" 2211500 2211509 2223753 2223758) (-1257 "VECTOR.spad" 2210175 2210186 2210426 2210453) (-1256 "VECTOR2.spad" 2208802 2208815 2210165 2210170) (-1255 "VECTCAT.spad" 2206702 2206713 2208770 2208797) (-1254 "VECTCAT.spad" 2204410 2204423 2206480 2206485) (-1253 "VARIABLE.spad" 2204190 2204205 2204400 2204405) (-1252 "UTYPE.spad" 2203834 2203843 2204180 2204185) (-1251 "UTSODETL.spad" 2203127 2203151 2203790 2203795) (-1250 "UTSODE.spad" 2201315 2201335 2203117 2203122) (-1249 "UTS.spad" 2196104 2196132 2199782 2199879) (-1248 "UTSCAT.spad" 2193555 2193571 2196002 2196099) (-1247 "UTSCAT.spad" 2190650 2190668 2193099 2193104) (-1246 "UTS2.spad" 2190243 2190278 2190640 2190645) (-1245 "URAGG.spad" 2184875 2184886 2190233 2190238) (-1244 "URAGG.spad" 2179471 2179484 2184831 2184836) (-1243 "UPXSSING.spad" 2177114 2177140 2178552 2178685) (-1242 "UPXS.spad" 2174262 2174290 2175246 2175395) (-1241 "UPXSCONS.spad" 2172019 2172039 2172394 2172543) (-1240 "UPXSCCA.spad" 2170584 2170604 2171865 2172014) (-1239 "UPXSCCA.spad" 2169291 2169313 2170574 2170579) (-1238 "UPXSCAT.spad" 2167872 2167888 2169137 2169286) (-1237 "UPXS2.spad" 2167413 2167466 2167862 2167867) (-1236 "UPSQFREE.spad" 2165825 2165839 2167403 2167408) (-1235 "UPSCAT.spad" 2163418 2163442 2165723 2165820) (-1234 "UPSCAT.spad" 2160717 2160743 2163024 2163029) (-1233 "UPOLYC.spad" 2155695 2155706 2160559 2160712) (-1232 "UPOLYC.spad" 2150565 2150578 2155431 2155436) (-1231 "UPOLYC2.spad" 2150034 2150053 2150555 2150560) (-1230 "UP.spad" 2147191 2147206 2147584 2147737) (-1229 "UPMP.spad" 2146081 2146094 2147181 2147186) (-1228 "UPDIVP.spad" 2145644 2145658 2146071 2146076) (-1227 "UPDECOMP.spad" 2143881 2143895 2145634 2145639) (-1226 "UPCDEN.spad" 2143088 2143104 2143871 2143876) (-1225 "UP2.spad" 2142450 2142471 2143078 2143083) (-1224 "UNISEG.spad" 2141803 2141814 2142369 2142374) (-1223 "UNISEG2.spad" 2141296 2141309 2141759 2141764) (-1222 "UNIFACT.spad" 2140397 2140409 2141286 2141291) (-1221 "ULS.spad" 2130949 2130977 2132042 2132471) (-1220 "ULSCONS.spad" 2123343 2123363 2123715 2123864) (-1219 "ULSCCAT.spad" 2121072 2121092 2123189 2123338) (-1218 "ULSCCAT.spad" 2118909 2118931 2121028 2121033) (-1217 "ULSCAT.spad" 2117125 2117141 2118755 2118904) (-1216 "ULS2.spad" 2116637 2116690 2117115 2117120) (-1215 "UINT8.spad" 2116514 2116523 2116627 2116632) (-1214 "UINT32.spad" 2116390 2116399 2116504 2116509) (-1213 "UINT16.spad" 2116266 2116275 2116380 2116385) (-1212 "UFD.spad" 2115331 2115340 2116192 2116261) (-1211 "UFD.spad" 2114458 2114469 2115321 2115326) (-1210 "UDVO.spad" 2113305 2113314 2114448 2114453) (-1209 "UDPO.spad" 2110732 2110743 2113261 2113266) (-1208 "TYPE.spad" 2110664 2110673 2110722 2110727) (-1207 "TYPEAST.spad" 2110583 2110592 2110654 2110659) (-1206 "TWOFACT.spad" 2109233 2109248 2110573 2110578) (-1205 "TUPLE.spad" 2108717 2108728 2109132 2109137) (-1204 "TUBETOOL.spad" 2105554 2105563 2108707 2108712) (-1203 "TUBE.spad" 2104195 2104212 2105544 2105549) (-1202 "TS.spad" 2102784 2102800 2103760 2103857) (-1201 "TSETCAT.spad" 2089911 2089928 2102752 2102779) (-1200 "TSETCAT.spad" 2077024 2077043 2089867 2089872) (-1199 "TRMANIP.spad" 2071390 2071407 2076730 2076735) (-1198 "TRIMAT.spad" 2070349 2070374 2071380 2071385) (-1197 "TRIGMNIP.spad" 2068866 2068883 2070339 2070344) (-1196 "TRIGCAT.spad" 2068378 2068387 2068856 2068861) (-1195 "TRIGCAT.spad" 2067888 2067899 2068368 2068373) (-1194 "TREE.spad" 2066459 2066470 2067495 2067522) (-1193 "TRANFUN.spad" 2066290 2066299 2066449 2066454) (-1192 "TRANFUN.spad" 2066119 2066130 2066280 2066285) (-1191 "TOPSP.spad" 2065793 2065802 2066109 2066114) (-1190 "TOOLSIGN.spad" 2065456 2065467 2065783 2065788) (-1189 "TEXTFILE.spad" 2064013 2064022 2065446 2065451) (-1188 "TEX.spad" 2061145 2061154 2064003 2064008) (-1187 "TEX1.spad" 2060701 2060712 2061135 2061140) (-1186 "TEMUTL.spad" 2060256 2060265 2060691 2060696) (-1185 "TBCMPPK.spad" 2058349 2058372 2060246 2060251) (-1184 "TBAGG.spad" 2057385 2057408 2058329 2058344) (-1183 "TBAGG.spad" 2056429 2056454 2057375 2057380) (-1182 "TANEXP.spad" 2055805 2055816 2056419 2056424) (-1181 "TABLE.spad" 2054216 2054239 2054486 2054513) (-1180 "TABLEAU.spad" 2053697 2053708 2054206 2054211) (-1179 "TABLBUMP.spad" 2050480 2050491 2053687 2053692) (-1178 "SYSTEM.spad" 2049708 2049717 2050470 2050475) (-1177 "SYSSOLP.spad" 2047181 2047192 2049698 2049703) (-1176 "SYSNNI.spad" 2046361 2046372 2047171 2047176) (-1175 "SYSINT.spad" 2045765 2045776 2046351 2046356) (-1174 "SYNTAX.spad" 2042035 2042044 2045755 2045760) (-1173 "SYMTAB.spad" 2040091 2040100 2042025 2042030) (-1172 "SYMS.spad" 2036076 2036085 2040081 2040086) (-1171 "SYMPOLY.spad" 2035083 2035094 2035165 2035292) (-1170 "SYMFUNC.spad" 2034558 2034569 2035073 2035078) (-1169 "SYMBOL.spad" 2031985 2031994 2034548 2034553) (-1168 "SWITCH.spad" 2028742 2028751 2031975 2031980) (-1167 "SUTS.spad" 2025641 2025669 2027209 2027306) (-1166 "SUPXS.spad" 2022776 2022804 2023773 2023922) (-1165 "SUP.spad" 2019545 2019556 2020326 2020479) (-1164 "SUPFRACF.spad" 2018650 2018668 2019535 2019540) (-1163 "SUP2.spad" 2018040 2018053 2018640 2018645) (-1162 "SUMRF.spad" 2017006 2017017 2018030 2018035) (-1161 "SUMFS.spad" 2016639 2016656 2016996 2017001) (-1160 "SULS.spad" 2007178 2007206 2008284 2008713) (-1159 "SUCHTAST.spad" 2006947 2006956 2007168 2007173) (-1158 "SUCH.spad" 2006627 2006642 2006937 2006942) (-1157 "SUBSPACE.spad" 1998634 1998649 2006617 2006622) (-1156 "SUBRESP.spad" 1997794 1997808 1998590 1998595) (-1155 "STTF.spad" 1993893 1993909 1997784 1997789) (-1154 "STTFNC.spad" 1990361 1990377 1993883 1993888) (-1153 "STTAYLOR.spad" 1982759 1982770 1990242 1990247) (-1152 "STRTBL.spad" 1981264 1981281 1981413 1981440) (-1151 "STRING.spad" 1980673 1980682 1980687 1980714) (-1150 "STRICAT.spad" 1980461 1980470 1980641 1980668) (-1149 "STREAM.spad" 1977319 1977330 1979986 1980001) (-1148 "STREAM3.spad" 1976864 1976879 1977309 1977314) (-1147 "STREAM2.spad" 1975932 1975945 1976854 1976859) (-1146 "STREAM1.spad" 1975636 1975647 1975922 1975927) (-1145 "STINPROD.spad" 1974542 1974558 1975626 1975631) (-1144 "STEP.spad" 1973743 1973752 1974532 1974537) (-1143 "STBL.spad" 1972269 1972297 1972436 1972451) (-1142 "STAGG.spad" 1971344 1971355 1972259 1972264) (-1141 "STAGG.spad" 1970417 1970430 1971334 1971339) (-1140 "STACK.spad" 1969768 1969779 1970024 1970051) (-1139 "SREGSET.spad" 1967472 1967489 1969414 1969441) (-1138 "SRDCMPK.spad" 1966017 1966037 1967462 1967467) (-1137 "SRAGG.spad" 1961114 1961123 1965985 1966012) (-1136 "SRAGG.spad" 1956231 1956242 1961104 1961109) (-1135 "SQMATRIX.spad" 1953847 1953865 1954763 1954850) (-1134 "SPLTREE.spad" 1948399 1948412 1953283 1953310) (-1133 "SPLNODE.spad" 1944987 1945000 1948389 1948394) (-1132 "SPFCAT.spad" 1943764 1943773 1944977 1944982) (-1131 "SPECOUT.spad" 1942314 1942323 1943754 1943759) (-1130 "SPADXPT.spad" 1934453 1934462 1942304 1942309) (-1129 "spad-parser.spad" 1933918 1933927 1934443 1934448) (-1128 "SPADAST.spad" 1933619 1933628 1933908 1933913) (-1127 "SPACEC.spad" 1917632 1917643 1933609 1933614) (-1126 "SPACE3.spad" 1917408 1917419 1917622 1917627) (-1125 "SORTPAK.spad" 1916953 1916966 1917364 1917369) (-1124 "SOLVETRA.spad" 1914710 1914721 1916943 1916948) (-1123 "SOLVESER.spad" 1913230 1913241 1914700 1914705) (-1122 "SOLVERAD.spad" 1909240 1909251 1913220 1913225) (-1121 "SOLVEFOR.spad" 1907660 1907678 1909230 1909235) (-1120 "SNTSCAT.spad" 1907260 1907277 1907628 1907655) (-1119 "SMTS.spad" 1905520 1905546 1906825 1906922) (-1118 "SMP.spad" 1902959 1902979 1903349 1903476) (-1117 "SMITH.spad" 1901802 1901827 1902949 1902954) (-1116 "SMATCAT.spad" 1899912 1899942 1901746 1901797) (-1115 "SMATCAT.spad" 1897954 1897986 1899790 1899795) (-1114 "SKAGG.spad" 1896915 1896926 1897922 1897949) (-1113 "SINT.spad" 1895741 1895750 1896781 1896910) (-1112 "SIMPAN.spad" 1895469 1895478 1895731 1895736) (-1111 "SIG.spad" 1894797 1894806 1895459 1895464) (-1110 "SIGNRF.spad" 1893905 1893916 1894787 1894792) (-1109 "SIGNEF.spad" 1893174 1893191 1893895 1893900) (-1108 "SIGAST.spad" 1892555 1892564 1893164 1893169) (-1107 "SHP.spad" 1890473 1890488 1892511 1892516) (-1106 "SHDP.spad" 1880184 1880211 1880693 1880824) (-1105 "SGROUP.spad" 1879792 1879801 1880174 1880179) (-1104 "SGROUP.spad" 1879398 1879409 1879782 1879787) (-1103 "SGCF.spad" 1872279 1872288 1879388 1879393) (-1102 "SFRTCAT.spad" 1871207 1871224 1872247 1872274) (-1101 "SFRGCD.spad" 1870270 1870290 1871197 1871202) (-1100 "SFQCMPK.spad" 1864907 1864927 1870260 1870265) (-1099 "SFORT.spad" 1864342 1864356 1864897 1864902) (-1098 "SEXOF.spad" 1864185 1864225 1864332 1864337) (-1097 "SEX.spad" 1864077 1864086 1864175 1864180) (-1096 "SEXCAT.spad" 1861628 1861668 1864067 1864072) (-1095 "SET.spad" 1859928 1859939 1861049 1861088) (-1094 "SETMN.spad" 1858362 1858379 1859918 1859923) (-1093 "SETCAT.spad" 1857847 1857856 1858352 1858357) (-1092 "SETCAT.spad" 1857330 1857341 1857837 1857842) (-1091 "SETAGG.spad" 1853851 1853862 1857310 1857325) (-1090 "SETAGG.spad" 1850380 1850393 1853841 1853846) (-1089 "SEQAST.spad" 1850083 1850092 1850370 1850375) (-1088 "SEGXCAT.spad" 1849205 1849218 1850073 1850078) (-1087 "SEG.spad" 1849018 1849029 1849124 1849129) (-1086 "SEGCAT.spad" 1847925 1847936 1849008 1849013) (-1085 "SEGBIND.spad" 1846997 1847008 1847880 1847885) (-1084 "SEGBIND2.spad" 1846693 1846706 1846987 1846992) (-1083 "SEGAST.spad" 1846407 1846416 1846683 1846688) (-1082 "SEG2.spad" 1845832 1845845 1846363 1846368) (-1081 "SDVAR.spad" 1845108 1845119 1845822 1845827) (-1080 "SDPOL.spad" 1842498 1842509 1842789 1842916) (-1079 "SCPKG.spad" 1840577 1840588 1842488 1842493) (-1078 "SCOPE.spad" 1839722 1839731 1840567 1840572) (-1077 "SCACHE.spad" 1838404 1838415 1839712 1839717) (-1076 "SASTCAT.spad" 1838313 1838322 1838394 1838399) (-1075 "SAOS.spad" 1838185 1838194 1838303 1838308) (-1074 "SAERFFC.spad" 1837898 1837918 1838175 1838180) (-1073 "SAE.spad" 1836073 1836089 1836684 1836819) (-1072 "SAEFACT.spad" 1835774 1835794 1836063 1836068) (-1071 "RURPK.spad" 1833415 1833431 1835764 1835769) (-1070 "RULESET.spad" 1832856 1832880 1833405 1833410) (-1069 "RULE.spad" 1831060 1831084 1832846 1832851) (-1068 "RULECOLD.spad" 1830912 1830925 1831050 1831055) (-1067 "RSTRCAST.spad" 1830629 1830638 1830902 1830907) (-1066 "RSETGCD.spad" 1827007 1827027 1830619 1830624) (-1065 "RSETCAT.spad" 1816791 1816808 1826975 1827002) (-1064 "RSETCAT.spad" 1806595 1806614 1816781 1816786) (-1063 "RSDCMPK.spad" 1805047 1805067 1806585 1806590) (-1062 "RRCC.spad" 1803431 1803461 1805037 1805042) (-1061 "RRCC.spad" 1801813 1801845 1803421 1803426) (-1060 "RPTAST.spad" 1801515 1801524 1801803 1801808) (-1059 "RPOLCAT.spad" 1780875 1780890 1801383 1801510) (-1058 "RPOLCAT.spad" 1759949 1759966 1780459 1780464) (-1057 "ROUTINE.spad" 1755812 1755821 1758596 1758623) (-1056 "ROMAN.spad" 1755140 1755149 1755678 1755807) (-1055 "ROIRC.spad" 1754220 1754252 1755130 1755135) (-1054 "RNS.spad" 1753123 1753132 1754122 1754215) (-1053 "RNS.spad" 1752112 1752123 1753113 1753118) (-1052 "RNG.spad" 1751847 1751856 1752102 1752107) (-1051 "RMODULE.spad" 1751485 1751496 1751837 1751842) (-1050 "RMCAT2.spad" 1750893 1750950 1751475 1751480) (-1049 "RMATRIX.spad" 1749717 1749736 1750060 1750099) (-1048 "RMATCAT.spad" 1745250 1745281 1749673 1749712) (-1047 "RMATCAT.spad" 1740673 1740706 1745098 1745103) (-1046 "RINTERP.spad" 1740561 1740581 1740663 1740668) (-1045 "RING.spad" 1740031 1740040 1740541 1740556) (-1044 "RING.spad" 1739509 1739520 1740021 1740026) (-1043 "RIDIST.spad" 1738893 1738902 1739499 1739504) (-1042 "RGCHAIN.spad" 1737472 1737488 1738378 1738405) (-1041 "RGBCSPC.spad" 1737253 1737265 1737462 1737467) (-1040 "RGBCMDL.spad" 1736783 1736795 1737243 1737248) (-1039 "RF.spad" 1734397 1734408 1736773 1736778) (-1038 "RFFACTOR.spad" 1733859 1733870 1734387 1734392) (-1037 "RFFACT.spad" 1733594 1733606 1733849 1733854) (-1036 "RFDIST.spad" 1732582 1732591 1733584 1733589) (-1035 "RETSOL.spad" 1731999 1732012 1732572 1732577) (-1034 "RETRACT.spad" 1731427 1731438 1731989 1731994) (-1033 "RETRACT.spad" 1730853 1730866 1731417 1731422) (-1032 "RETAST.spad" 1730665 1730674 1730843 1730848) (-1031 "RESULT.spad" 1728725 1728734 1729312 1729339) (-1030 "RESRING.spad" 1728072 1728119 1728663 1728720) (-1029 "RESLATC.spad" 1727396 1727407 1728062 1728067) (-1028 "REPSQ.spad" 1727125 1727136 1727386 1727391) (-1027 "REP.spad" 1724677 1724686 1727115 1727120) (-1026 "REPDB.spad" 1724382 1724393 1724667 1724672) (-1025 "REP2.spad" 1713954 1713965 1724224 1724229) (-1024 "REP1.spad" 1707944 1707955 1713904 1713909) (-1023 "REGSET.spad" 1705741 1705758 1707590 1707617) (-1022 "REF.spad" 1705070 1705081 1705696 1705701) (-1021 "REDORDER.spad" 1704246 1704263 1705060 1705065) (-1020 "RECLOS.spad" 1703029 1703049 1703733 1703826) (-1019 "REALSOLV.spad" 1702161 1702170 1703019 1703024) (-1018 "REAL.spad" 1702033 1702042 1702151 1702156) (-1017 "REAL0Q.spad" 1699315 1699330 1702023 1702028) (-1016 "REAL0.spad" 1696143 1696158 1699305 1699310) (-1015 "RDUCEAST.spad" 1695864 1695873 1696133 1696138) (-1014 "RDIV.spad" 1695515 1695540 1695854 1695859) (-1013 "RDIST.spad" 1695078 1695089 1695505 1695510) (-1012 "RDETRS.spad" 1693874 1693892 1695068 1695073) (-1011 "RDETR.spad" 1691981 1691999 1693864 1693869) (-1010 "RDEEFS.spad" 1691054 1691071 1691971 1691976) (-1009 "RDEEF.spad" 1690050 1690067 1691044 1691049) (-1008 "RCFIELD.spad" 1687236 1687245 1689952 1690045) (-1007 "RCFIELD.spad" 1684508 1684519 1687226 1687231) (-1006 "RCAGG.spad" 1682420 1682431 1684498 1684503) (-1005 "RCAGG.spad" 1680259 1680272 1682339 1682344) (-1004 "RATRET.spad" 1679619 1679630 1680249 1680254) (-1003 "RATFACT.spad" 1679311 1679323 1679609 1679614) (-1002 "RANDSRC.spad" 1678630 1678639 1679301 1679306) (-1001 "RADUTIL.spad" 1678384 1678393 1678620 1678625) (-1000 "RADIX.spad" 1675285 1675299 1676851 1676944) (-999 "RADFF.spad" 1673699 1673735 1673817 1673973) (-998 "RADCAT.spad" 1673293 1673301 1673689 1673694) (-997 "RADCAT.spad" 1672885 1672895 1673283 1673288) (-996 "QUEUE.spad" 1672228 1672238 1672492 1672519) (-995 "QUAT.spad" 1670810 1670820 1671152 1671217) (-994 "QUATCT2.spad" 1670429 1670447 1670800 1670805) (-993 "QUATCAT.spad" 1668594 1668604 1670359 1670424) (-992 "QUATCAT.spad" 1666510 1666522 1668277 1668282) (-991 "QUAGG.spad" 1665336 1665346 1666478 1666505) (-990 "QQUTAST.spad" 1665105 1665113 1665326 1665331) (-989 "QFORM.spad" 1664568 1664582 1665095 1665100) (-988 "QFCAT.spad" 1663271 1663281 1664470 1664563) (-987 "QFCAT.spad" 1661565 1661577 1662766 1662771) (-986 "QFCAT2.spad" 1661256 1661272 1661555 1661560) (-985 "QEQUAT.spad" 1660813 1660821 1661246 1661251) (-984 "QCMPACK.spad" 1655560 1655579 1660803 1660808) (-983 "QALGSET.spad" 1651635 1651667 1655474 1655479) (-982 "QALGSET2.spad" 1649631 1649649 1651625 1651630) (-981 "PWFFINTB.spad" 1646941 1646962 1649621 1649626) (-980 "PUSHVAR.spad" 1646270 1646289 1646931 1646936) (-979 "PTRANFN.spad" 1642396 1642406 1646260 1646265) (-978 "PTPACK.spad" 1639484 1639494 1642386 1642391) (-977 "PTFUNC2.spad" 1639305 1639319 1639474 1639479) (-976 "PTCAT.spad" 1638554 1638564 1639273 1639300) (-975 "PSQFR.spad" 1637861 1637885 1638544 1638549) (-974 "PSEUDLIN.spad" 1636719 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"PRIMCAT.spad" 1582718 1582726 1583085 1583090) (-954 "PRIMARR.spad" 1581723 1581733 1581901 1581928) (-953 "PRIMARR2.spad" 1580446 1580458 1581713 1581718) (-952 "PREASSOC.spad" 1579818 1579830 1580436 1580441) (-951 "PPCURVE.spad" 1578955 1578963 1579808 1579813) (-950 "PORTNUM.spad" 1578730 1578738 1578945 1578950) (-949 "POLYROOT.spad" 1577559 1577581 1578686 1578691) (-948 "POLY.spad" 1574856 1574866 1575373 1575500) (-947 "POLYLIFT.spad" 1574117 1574140 1574846 1574851) (-946 "POLYCATQ.spad" 1572219 1572241 1574107 1574112) (-945 "POLYCAT.spad" 1565625 1565646 1572087 1572214) (-944 "POLYCAT.spad" 1558333 1558356 1564797 1564802) (-943 "POLY2UP.spad" 1557781 1557795 1558323 1558328) (-942 "POLY2.spad" 1557376 1557388 1557771 1557776) (-941 "POLUTIL.spad" 1556317 1556346 1557332 1557337) (-940 "POLTOPOL.spad" 1555065 1555080 1556307 1556312) (-939 "POINT.spad" 1553904 1553914 1553991 1554018) (-938 "PNTHEORY.spad" 1550570 1550578 1553894 1553899) (-937 "PMTOOLS.spad" 1549327 1549341 1550560 1550565) (-936 "PMSYM.spad" 1548872 1548882 1549317 1549322) (-935 "PMQFCAT.spad" 1548459 1548473 1548862 1548867) (-934 "PMPRED.spad" 1547928 1547942 1548449 1548454) (-933 "PMPREDFS.spad" 1547372 1547394 1547918 1547923) (-932 "PMPLCAT.spad" 1546442 1546460 1547304 1547309) (-931 "PMLSAGG.spad" 1546023 1546037 1546432 1546437) (-930 "PMKERNEL.spad" 1545590 1545602 1546013 1546018) (-929 "PMINS.spad" 1545166 1545176 1545580 1545585) (-928 "PMFS.spad" 1544739 1544757 1545156 1545161) (-927 "PMDOWN.spad" 1544025 1544039 1544729 1544734) (-926 "PMASS.spad" 1543037 1543045 1544015 1544020) (-925 "PMASSFS.spad" 1542006 1542022 1543027 1543032) (-924 "PLOTTOOL.spad" 1541786 1541794 1541996 1542001) (-923 "PLOT.spad" 1536617 1536625 1541776 1541781) (-922 "PLOT3D.spad" 1533037 1533045 1536607 1536612) (-921 "PLOT1.spad" 1532178 1532188 1533027 1533032) (-920 "PLEQN.spad" 1519394 1519421 1532168 1532173) (-919 "PINTERP.spad" 1519010 1519029 1519384 1519389) (-918 "PINTERPA.spad" 1518792 1518808 1519000 1519005) (-917 "PI.spad" 1518399 1518407 1518766 1518787) (-916 "PID.spad" 1517355 1517363 1518325 1518394) (-915 "PICOERCE.spad" 1517012 1517022 1517345 1517350) (-914 "PGROEB.spad" 1515609 1515623 1517002 1517007) (-913 "PGE.spad" 1506862 1506870 1515599 1515604) (-912 "PGCD.spad" 1505744 1505761 1506852 1506857) (-911 "PFRPAC.spad" 1504887 1504897 1505734 1505739) (-910 "PFR.spad" 1501544 1501554 1504789 1504882) (-909 "PFOTOOLS.spad" 1500802 1500818 1501534 1501539) (-908 "PFOQ.spad" 1500172 1500190 1500792 1500797) (-907 "PFO.spad" 1499591 1499618 1500162 1500167) (-906 "PF.spad" 1499165 1499177 1499396 1499489) (-905 "PFECAT.spad" 1496831 1496839 1499091 1499160) (-904 "PFECAT.spad" 1494525 1494535 1496787 1496792) (-903 "PFBRU.spad" 1492395 1492407 1494515 1494520) (-902 "PFBR.spad" 1489933 1489956 1492385 1492390) (-901 "PERM.spad" 1485614 1485624 1489763 1489778) (-900 "PERMGRP.spad" 1480350 1480360 1485604 1485609) (-899 "PERMCAT.spad" 1478902 1478912 1480330 1480345) (-898 "PERMAN.spad" 1477434 1477448 1478892 1478897) (-897 "PENDTREE.spad" 1476773 1476783 1477063 1477068) (-896 "PDRING.spad" 1475264 1475274 1476753 1476768) (-895 "PDRING.spad" 1473763 1473775 1475254 1475259) (-894 "PDEPROB.spad" 1472778 1472786 1473753 1473758) (-893 "PDEPACK.spad" 1466780 1466788 1472768 1472773) (-892 "PDECOMP.spad" 1466242 1466259 1466770 1466775) (-891 "PDECAT.spad" 1464596 1464604 1466232 1466237) (-890 "PCOMP.spad" 1464447 1464460 1464586 1464591) (-889 "PBWLB.spad" 1463029 1463046 1464437 1464442) (-888 "PATTERN.spad" 1457460 1457470 1463019 1463024) (-887 "PATTERN2.spad" 1457196 1457208 1457450 1457455) (-886 "PATTERN1.spad" 1455498 1455514 1457186 1457191) (-885 "PATRES.spad" 1453045 1453057 1455488 1455493) (-884 "PATRES2.spad" 1452707 1452721 1453035 1453040) (-883 "PATMATCH.spad" 1450864 1450895 1452415 1452420) (-882 "PATMAB.spad" 1450289 1450299 1450854 1450859) (-881 "PATLRES.spad" 1449373 1449387 1450279 1450284) (-880 "PATAB.spad" 1449137 1449147 1449363 1449368) (-879 "PARTPERM.spad" 1446499 1446507 1449127 1449132) (-878 "PARSURF.spad" 1445927 1445955 1446489 1446494) (-877 "PARSU2.spad" 1445722 1445738 1445917 1445922) (-876 "script-parser.spad" 1445242 1445250 1445712 1445717) (-875 "PARSCURV.spad" 1444670 1444698 1445232 1445237) (-874 "PARSC2.spad" 1444459 1444475 1444660 1444665) (-873 "PARPCURV.spad" 1443917 1443945 1444449 1444454) (-872 "PARPC2.spad" 1443706 1443722 1443907 1443912) (-871 "PAN2EXPR.spad" 1443118 1443126 1443696 1443701) (-870 "PALETTE.spad" 1442088 1442096 1443108 1443113) (-869 "PAIR.spad" 1441071 1441084 1441676 1441681) (-868 "PADICRC.spad" 1438401 1438419 1439576 1439669) (-867 "PADICRAT.spad" 1436416 1436428 1436637 1436730) (-866 "PADIC.spad" 1436111 1436123 1436342 1436411) (-865 "PADICCT.spad" 1434652 1434664 1436037 1436106) (-864 "PADEPAC.spad" 1433331 1433350 1434642 1434647) (-863 "PADE.spad" 1432071 1432087 1433321 1433326) (-862 "OWP.spad" 1431311 1431341 1431929 1431996) (-861 "OVERSET.spad" 1430884 1430892 1431301 1431306) (-860 "OVAR.spad" 1430665 1430688 1430874 1430879) (-859 "OUT.spad" 1429749 1429757 1430655 1430660) (-858 "OUTFORM.spad" 1419045 1419053 1429739 1429744) (-857 "OUTBFILE.spad" 1418463 1418471 1419035 1419040) (-856 "OUTBCON.spad" 1417461 1417469 1418453 1418458) (-855 "OUTBCON.spad" 1416457 1416467 1417451 1417456) (-854 "OSI.spad" 1415932 1415940 1416447 1416452) (-853 "OSGROUP.spad" 1415850 1415858 1415922 1415927) (-852 "ORTHPOL.spad" 1414311 1414321 1415767 1415772) (-851 "OREUP.spad" 1413764 1413792 1413991 1414030) (-850 "ORESUP.spad" 1413063 1413087 1413444 1413483) (-849 "OREPCTO.spad" 1410882 1410894 1412983 1412988) (-848 "OREPCAT.spad" 1404939 1404949 1410838 1410877) (-847 "OREPCAT.spad" 1398886 1398898 1404787 1404792) (-846 "ORDSET.spad" 1398052 1398060 1398876 1398881) (-845 "ORDSET.spad" 1397216 1397226 1398042 1398047) (-844 "ORDRING.spad" 1396606 1396614 1397196 1397211) (-843 "ORDRING.spad" 1396004 1396014 1396596 1396601) (-842 "ORDMON.spad" 1395859 1395867 1395994 1395999) (-841 "ORDFUNS.spad" 1394985 1395001 1395849 1395854) (-840 "ORDFIN.spad" 1394805 1394813 1394975 1394980) (-839 "ORDCOMP.spad" 1393270 1393280 1394352 1394381) (-838 "ORDCOMP2.spad" 1392555 1392567 1393260 1393265) (-837 "OPTPROB.spad" 1391193 1391201 1392545 1392550) (-836 "OPTPACK.spad" 1383578 1383586 1391183 1391188) (-835 "OPTCAT.spad" 1381253 1381261 1383568 1383573) (-834 "OPSIG.spad" 1380905 1380913 1381243 1381248) (-833 "OPQUERY.spad" 1380454 1380462 1380895 1380900) (-832 "OP.spad" 1380196 1380206 1380276 1380343) (-831 "OPERCAT.spad" 1379784 1379794 1380186 1380191) (-830 "OPERCAT.spad" 1379370 1379382 1379774 1379779) (-829 "ONECOMP.spad" 1378115 1378125 1378917 1378946) (-828 "ONECOMP2.spad" 1377533 1377545 1378105 1378110) (-827 "OMSERVER.spad" 1376535 1376543 1377523 1377528) (-826 "OMSAGG.spad" 1376323 1376333 1376491 1376530) (-825 "OMPKG.spad" 1374935 1374943 1376313 1376318) (-824 "OM.spad" 1373900 1373908 1374925 1374930) (-823 "OMLO.spad" 1373325 1373337 1373786 1373825) (-822 "OMEXPR.spad" 1373159 1373169 1373315 1373320) (-821 "OMERR.spad" 1372702 1372710 1373149 1373154) (-820 "OMERRK.spad" 1371736 1371744 1372692 1372697) (-819 "OMENC.spad" 1371080 1371088 1371726 1371731) (-818 "OMDEV.spad" 1365369 1365377 1371070 1371075) (-817 "OMCONN.spad" 1364778 1364786 1365359 1365364) (-816 "OINTDOM.spad" 1364541 1364549 1364704 1364773) (-815 "OFMONOID.spad" 1360728 1360738 1364531 1364536) (-814 "ODVAR.spad" 1359989 1359999 1360718 1360723) (-813 "ODR.spad" 1359633 1359659 1359801 1359950) (-812 "ODPOL.spad" 1356979 1356989 1357319 1357446) (-811 "ODP.spad" 1346826 1346846 1347199 1347330) (-810 "ODETOOLS.spad" 1345409 1345428 1346816 1346821) (-809 "ODESYS.spad" 1343059 1343076 1345399 1345404) (-808 "ODERTRIC.spad" 1339000 1339017 1343016 1343021) (-807 "ODERED.spad" 1338387 1338411 1338990 1338995) (-806 "ODERAT.spad" 1335938 1335955 1338377 1338382) (-805 "ODEPRRIC.spad" 1332829 1332851 1335928 1335933) (-804 "ODEPROB.spad" 1332086 1332094 1332819 1332824) (-803 "ODEPRIM.spad" 1329360 1329382 1332076 1332081) (-802 "ODEPAL.spad" 1328736 1328760 1329350 1329355) (-801 "ODEPACK.spad" 1315338 1315346 1328726 1328731) (-800 "ODEINT.spad" 1314769 1314785 1315328 1315333) (-799 "ODEIFTBL.spad" 1312164 1312172 1314759 1314764) (-798 "ODEEF.spad" 1307531 1307547 1312154 1312159) (-797 "ODECONST.spad" 1307050 1307068 1307521 1307526) (-796 "ODECAT.spad" 1305646 1305654 1307040 1307045) (-795 "OCT.spad" 1303784 1303794 1304500 1304539) (-794 "OCTCT2.spad" 1303428 1303449 1303774 1303779) (-793 "OC.spad" 1301202 1301212 1303384 1303423) (-792 "OC.spad" 1298701 1298713 1300885 1300890) (-791 "OCAMON.spad" 1298549 1298557 1298691 1298696) (-790 "OASGP.spad" 1298364 1298372 1298539 1298544) (-789 "OAMONS.spad" 1297884 1297892 1298354 1298359) (-788 "OAMON.spad" 1297745 1297753 1297874 1297879) (-787 "OAGROUP.spad" 1297607 1297615 1297735 1297740) (-786 "NUMTUBE.spad" 1297194 1297210 1297597 1297602) (-785 "NUMQUAD.spad" 1285056 1285064 1297184 1297189) (-784 "NUMODE.spad" 1276192 1276200 1285046 1285051) (-783 "NUMINT.spad" 1273750 1273758 1276182 1276187) (-782 "NUMFMT.spad" 1272590 1272598 1273740 1273745) (-781 "NUMERIC.spad" 1264662 1264672 1272395 1272400) (-780 "NTSCAT.spad" 1263164 1263180 1264630 1264657) (-779 "NTPOLFN.spad" 1262709 1262719 1263081 1263086) (-778 "NSUP.spad" 1255719 1255729 1260259 1260412) (-777 "NSUP2.spad" 1255111 1255123 1255709 1255714) (-776 "NSMP.spad" 1251306 1251325 1251614 1251741) (-775 "NREP.spad" 1249678 1249692 1251296 1251301) (-774 "NPCOEF.spad" 1248924 1248944 1249668 1249673) (-773 "NORMRETR.spad" 1248522 1248561 1248914 1248919) (-772 "NORMPK.spad" 1246424 1246443 1248512 1248517) (-771 "NORMMA.spad" 1246112 1246138 1246414 1246419) (-770 "NONE.spad" 1245853 1245861 1246102 1246107) (-769 "NONE1.spad" 1245529 1245539 1245843 1245848) (-768 "NODE1.spad" 1244998 1245014 1245519 1245524) (-767 "NNI.spad" 1243885 1243893 1244972 1244993) (-766 "NLINSOL.spad" 1242507 1242517 1243875 1243880) (-765 "NIPROB.spad" 1241048 1241056 1242497 1242502) (-764 "NFINTBAS.spad" 1238508 1238525 1241038 1241043) (-763 "NETCLT.spad" 1238482 1238493 1238498 1238503) (-762 "NCODIV.spad" 1236680 1236696 1238472 1238477) (-761 "NCNTFRAC.spad" 1236322 1236336 1236670 1236675) (-760 "NCEP.spad" 1234482 1234496 1236312 1236317) (-759 "NASRING.spad" 1234078 1234086 1234472 1234477) (-758 "NASRING.spad" 1233672 1233682 1234068 1234073) (-757 "NARNG.spad" 1233016 1233024 1233662 1233667) (-756 "NARNG.spad" 1232358 1232368 1233006 1233011) (-755 "NAGSP.spad" 1231431 1231439 1232348 1232353) (-754 "NAGS.spad" 1220956 1220964 1231421 1231426) (-753 "NAGF07.spad" 1219349 1219357 1220946 1220951) (-752 "NAGF04.spad" 1213581 1213589 1219339 1219344) (-751 "NAGF02.spad" 1207390 1207398 1213571 1213576) (-750 "NAGF01.spad" 1202993 1203001 1207380 1207385) (-749 "NAGE04.spad" 1196453 1196461 1202983 1202988) (-748 "NAGE02.spad" 1186795 1186803 1196443 1196448) (-747 "NAGE01.spad" 1182679 1182687 1186785 1186790) (-746 "NAGD03.spad" 1180599 1180607 1182669 1182674) (-745 "NAGD02.spad" 1173130 1173138 1180589 1180594) (-744 "NAGD01.spad" 1167243 1167251 1173120 1173125) (-743 "NAGC06.spad" 1163030 1163038 1167233 1167238) (-742 "NAGC05.spad" 1161499 1161507 1163020 1163025) (-741 "NAGC02.spad" 1160754 1160762 1161489 1161494) (-740 "NAALG.spad" 1160289 1160299 1160722 1160749) (-739 "NAALG.spad" 1159844 1159856 1160279 1160284) (-738 "MULTSQFR.spad" 1156802 1156819 1159834 1159839) (-737 "MULTFACT.spad" 1156185 1156202 1156792 1156797) (-736 "MTSCAT.spad" 1154219 1154240 1156083 1156180) (-735 "MTHING.spad" 1153876 1153886 1154209 1154214) (-734 "MSYSCMD.spad" 1153310 1153318 1153866 1153871) (-733 "MSET.spad" 1151252 1151262 1153016 1153055) (-732 "MSETAGG.spad" 1151097 1151107 1151220 1151247) (-731 "MRING.spad" 1148068 1148080 1150805 1150872) (-730 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1045280 1045660 1045665) (-654 "LODOOPS.spad" 1044188 1044200 1045260 1045265) (-653 "LODO.spad" 1043572 1043588 1043868 1043907) (-652 "LODOF.spad" 1042616 1042633 1043529 1043534) (-651 "LODOCAT.spad" 1041274 1041284 1042572 1042611) (-650 "LODOCAT.spad" 1039930 1039942 1041230 1041235) (-649 "LODO2.spad" 1039203 1039215 1039610 1039649) (-648 "LODO1.spad" 1038603 1038613 1038883 1038922) (-647 "LODEEF.spad" 1037375 1037393 1038593 1038598) (-646 "LNAGG.spad" 1033177 1033187 1037365 1037370) (-645 "LNAGG.spad" 1028943 1028955 1033133 1033138) (-644 "LMOPS.spad" 1025679 1025696 1028933 1028938) (-643 "LMODULE.spad" 1025321 1025331 1025669 1025674) (-642 "LMDICT.spad" 1024604 1024614 1024872 1024899) (-641 "LITERAL.spad" 1024510 1024521 1024594 1024599) (-640 "LIST.spad" 1022228 1022238 1023657 1023684) (-639 "LIST3.spad" 1021519 1021533 1022218 1022223) (-638 "LIST2.spad" 1020159 1020171 1021509 1021514) (-637 "LIST2MAP.spad" 1017036 1017048 1020149 1020154) (-636 "LINEXP.spad" 1016468 1016478 1017016 1017031) (-635 "LINDEP.spad" 1015245 1015257 1016380 1016385) (-634 "LIMITRF.spad" 1013159 1013169 1015235 1015240) (-633 "LIMITPS.spad" 1012042 1012055 1013149 1013154) (-632 "LIE.spad" 1010056 1010068 1011332 1011477) (-631 "LIECAT.spad" 1009532 1009542 1009982 1010051) (-630 "LIECAT.spad" 1009036 1009048 1009488 1009493) (-629 "LIB.spad" 1007084 1007092 1007695 1007710) (-628 "LGROBP.spad" 1004437 1004456 1007074 1007079) (-627 "LF.spad" 1003356 1003372 1004427 1004432) (-626 "LFCAT.spad" 1002375 1002383 1003346 1003351) (-625 "LEXTRIPK.spad" 997878 997893 1002365 1002370) (-624 "LEXP.spad" 995881 995908 997858 997873) (-623 "LETAST.spad" 995580 995588 995871 995876) (-622 "LEADCDET.spad" 993964 993981 995570 995575) (-621 "LAZM3PK.spad" 992668 992690 993954 993959) (-620 "LAUPOL.spad" 991357 991370 992261 992330) (-619 "LAPLACE.spad" 990930 990946 991347 991352) (-618 "LA.spad" 990370 990384 990852 990891) (-617 "LALG.spad" 990146 990156 990350 990365) (-616 "LALG.spad" 989930 989942 990136 990141) (-615 "KVTFROM.spad" 989665 989675 989920 989925) (-614 "KTVLOGIC.spad" 989088 989096 989655 989660) (-613 "KRCFROM.spad" 988826 988836 989078 989083) (-612 "KOVACIC.spad" 987539 987556 988816 988821) (-611 "KONVERT.spad" 987261 987271 987529 987534) (-610 "KOERCE.spad" 986998 987008 987251 987256) (-609 "KERNEL.spad" 985533 985543 986782 986787) (-608 "KERNEL2.spad" 985236 985248 985523 985528) (-607 "KDAGG.spad" 984339 984361 985216 985231) (-606 "KDAGG.spad" 983450 983474 984329 984334) (-605 "KAFILE.spad" 982413 982429 982648 982675) (-604 "JORDAN.spad" 980240 980252 981703 981848) (-603 "JOINAST.spad" 979934 979942 980230 980235) (-602 "JAVACODE.spad" 979800 979808 979924 979929) (-601 "IXAGG.spad" 977923 977947 979790 979795) (-600 "IXAGG.spad" 975901 975927 977770 977775) (-599 "IVECTOR.spad" 974672 974687 974827 974854) (-598 "ITUPLE.spad" 973817 973827 974662 974667) (-597 "ITRIGMNP.spad" 972628 972647 973807 973812) (-596 "ITFUN3.spad" 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(-575 "IOBCON.spad" 946853 946861 946978 946983) (-574 "INVLAPLA.spad" 946498 946514 946843 946848) (-573 "INTTR.spad" 939744 939761 946488 946493) (-572 "INTTOOLS.spad" 937455 937471 939318 939323) (-571 "INTSLPE.spad" 936761 936769 937445 937450) (-570 "INTRVL.spad" 936327 936337 936675 936756) (-569 "INTRF.spad" 934691 934705 936317 936322) (-568 "INTRET.spad" 934123 934133 934681 934686) (-567 "INTRAT.spad" 932798 932815 934113 934118) (-566 "INTPM.spad" 931161 931177 932441 932446) (-565 "INTPAF.spad" 928929 928947 931093 931098) (-564 "INTPACK.spad" 919239 919247 928919 928924) (-563 "INT.spad" 918600 918608 919093 919234) (-562 "INTHERTR.spad" 917866 917883 918590 918595) (-561 "INTHERAL.spad" 917532 917556 917856 917861) (-560 "INTHEORY.spad" 913945 913953 917522 917527) (-559 "INTG0.spad" 907408 907426 913877 913882) (-558 "INTFTBL.spad" 901437 901445 907398 907403) (-557 "INTFACT.spad" 900496 900506 901427 901432) (-556 "INTEF.spad" 898811 898827 900486 900491) (-555 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"FORDER.spad" 644362 644386 644661 644666) (-391 "FOP.spad" 643563 643571 644352 644357) (-390 "FNLA.spad" 642987 643009 643531 643558) (-389 "FNCAT.spad" 641574 641582 642977 642982) (-388 "FNAME.spad" 641466 641474 641564 641569) (-387 "FMTC.spad" 641264 641272 641392 641461) (-386 "FMONOID.spad" 638319 638329 641220 641225) (-385 "FM.spad" 638014 638026 638253 638280) (-384 "FMFUN.spad" 635044 635052 638004 638009) (-383 "FMC.spad" 634096 634104 635034 635039) (-382 "FMCAT.spad" 631750 631768 634064 634091) (-381 "FM1.spad" 631107 631119 631684 631711) (-380 "FLOATRP.spad" 628828 628842 631097 631102) (-379 "FLOAT.spad" 622116 622124 628694 628823) (-378 "FLOATCP.spad" 619533 619547 622106 622111) (-377 "FLINEXP.spad" 619245 619255 619513 619528) (-376 "FLINEXP.spad" 618911 618923 619181 619186) (-375 "FLASORT.spad" 618231 618243 618901 618906) (-374 "FLALG.spad" 615877 615896 618157 618226) (-373 "FLAGG.spad" 612895 612905 615857 615872) (-372 "FLAGG.spad" 609814 609826 612778 612783) (-371 "FLAGG2.spad" 608495 608511 609804 609809) (-370 "FINRALG.spad" 606524 606537 608451 608490) (-369 "FINRALG.spad" 604479 604494 606408 606413) (-368 "FINITE.spad" 603631 603639 604469 604474) (-367 "FINAALG.spad" 592612 592622 603573 603626) (-366 "FINAALG.spad" 581605 581617 592568 592573) (-365 "FILE.spad" 581188 581198 581595 581600) (-364 "FILECAT.spad" 579706 579723 581178 581183) (-363 "FIELD.spad" 579112 579120 579608 579701) (-362 "FIELD.spad" 578604 578614 579102 579107) (-361 "FGROUP.spad" 577213 577223 578584 578599) (-360 "FGLMICPK.spad" 576000 576015 577203 577208) (-359 "FFX.spad" 575375 575390 575716 575809) (-358 "FFSLPE.spad" 574864 574885 575365 575370) (-357 "FFPOLY.spad" 566116 566127 574854 574859) (-356 "FFPOLY2.spad" 565176 565193 566106 566111) (-355 "FFP.spad" 564573 564593 564892 564985) (-354 "FF.spad" 564021 564037 564254 564347) (-353 "FFNBX.spad" 562533 562553 563737 563830) (-352 "FFNBP.spad" 561046 561063 562249 562342) (-351 "FFNB.spad" 559511 559532 560727 560820) (-350 "FFINTBAS.spad" 556925 556944 559501 559506) (-349 "FFIELDC.spad" 554500 554508 556827 556920) (-348 "FFIELDC.spad" 552161 552171 554490 554495) (-347 "FFHOM.spad" 550909 550926 552151 552156) (-346 "FFF.spad" 548344 548355 550899 550904) (-345 "FFCGX.spad" 547191 547211 548060 548153) (-344 "FFCGP.spad" 546080 546100 546907 547000) (-343 "FFCG.spad" 544872 544893 545761 545854) (-342 "FFCAT.spad" 537899 537921 544711 544867) (-341 "FFCAT.spad" 531005 531029 537819 537824) (-340 "FFCAT2.spad" 530750 530790 530995 531000) (-339 "FEXPR.spad" 522459 522505 530506 530545) (-338 "FEVALAB.spad" 522165 522175 522449 522454) (-337 "FEVALAB.spad" 521656 521668 521942 521947) (-336 "FDIV.spad" 521098 521122 521646 521651) (-335 "FDIVCAT.spad" 519140 519164 521088 521093) (-334 "FDIVCAT.spad" 517180 517206 519130 519135) (-333 "FDIV2.spad" 516834 516874 517170 517175) (-332 "FCPAK1.spad" 515387 515395 516824 516829) (-331 "FCOMP.spad" 514766 514776 515377 515382) (-330 "FC.spad" 504681 504689 514756 514761) (-329 "FAXF.spad" 497616 497630 504583 504676) (-328 "FAXF.spad" 490603 490619 497572 497577) (-327 "FARRAY.spad" 488749 488759 489786 489813) (-326 "FAMR.spad" 486869 486881 488647 488744) (-325 "FAMR.spad" 484973 484987 486753 486758) (-324 "FAMONOID.spad" 484623 484633 484927 484932) (-323 "FAMONC.spad" 482845 482857 484613 484618) (-322 "FAGROUP.spad" 482451 482461 482741 482768) (-321 "FACUTIL.spad" 480647 480664 482441 482446) (-320 "FACTFUNC.spad" 479823 479833 480637 480642) (-319 "EXPUPXS.spad" 476656 476679 477955 478104) (-318 "EXPRTUBE.spad" 473884 473892 476646 476651) (-317 "EXPRODE.spad" 470756 470772 473874 473879) (-316 "EXPR.spad" 466031 466041 466745 467152) (-315 "EXPR2UPS.spad" 462123 462136 466021 466026) (-314 "EXPR2.spad" 461826 461838 462113 462118) (-313 "EXPEXPAN.spad" 458764 458789 459398 459491) (-312 "EXIT.spad" 458435 458443 458754 458759) (-311 "EXITAST.spad" 458171 458179 458425 458430) (-310 "EVALCYC.spad" 457629 457643 458161 458166) (-309 "EVALAB.spad" 457193 457203 457619 457624) (-308 "EVALAB.spad" 456755 456767 457183 457188) (-307 "EUCDOM.spad" 454297 454305 456681 456750) (-306 "EUCDOM.spad" 451901 451911 454287 454292) (-305 "ESTOOLS.spad" 443741 443749 451891 451896) (-304 "ESTOOLS2.spad" 443342 443356 443731 443736) (-303 "ESTOOLS1.spad" 443027 443038 443332 443337) (-302 "ES.spad" 435574 435582 443017 443022) (-301 "ES.spad" 428027 428037 435472 435477) (-300 "ESCONT.spad" 424800 424808 428017 428022) (-299 "ESCONT1.spad" 424549 424561 424790 424795) (-298 "ES2.spad" 424044 424060 424539 424544) (-297 "ES1.spad" 423610 423626 424034 424039) (-296 "ERROR.spad" 420931 420939 423600 423605) (-295 "EQTBL.spad" 419403 419425 419612 419639) (-294 "EQ.spad" 414277 414287 417076 417188) (-293 "EQ2.spad" 413993 414005 414267 414272) (-292 "EP.spad" 410307 410317 413983 413988) (-291 "ENV.spad" 409009 409017 410297 410302) (-290 "ENTIRER.spad" 408677 408685 408953 409004) (-289 "EMR.spad" 407878 407919 408603 408672) (-288 "ELTAGG.spad" 406118 406137 407868 407873) (-287 "ELTAGG.spad" 404322 404343 406074 406079) (-286 "ELTAB.spad" 403769 403787 404312 404317) (-285 "ELFUTS.spad" 403148 403167 403759 403764) (-284 "ELEMFUN.spad" 402837 402845 403138 403143) (-283 "ELEMFUN.spad" 402524 402534 402827 402832) (-282 "ELAGG.spad" 400467 400477 402504 402519) (-281 "ELAGG.spad" 398347 398359 400386 400391) (-280 "ELABEXPR.spad" 397278 397286 398337 398342) (-279 "EFUPXS.spad" 394054 394084 397234 397239) (-278 "EFULS.spad" 390890 390913 394010 394015) (-277 "EFSTRUC.spad" 388845 388861 390880 390885) (-276 "EF.spad" 383611 383627 388835 388840) (-275 "EAB.spad" 381887 381895 383601 383606) (-274 "E04UCFA.spad" 381423 381431 381877 381882) (-273 "E04NAFA.spad" 381000 381008 381413 381418) (-272 "E04MBFA.spad" 380580 380588 380990 380995) (-271 "E04JAFA.spad" 380116 380124 380570 380575) (-270 "E04GCFA.spad" 379652 379660 380106 380111) (-269 "E04FDFA.spad" 379188 379196 379642 379647) (-268 "E04DGFA.spad" 378724 378732 379178 379183) (-267 "E04AGNT.spad" 374566 374574 378714 378719) (-266 "DVARCAT.spad" 371251 371261 374556 374561) (-265 "DVARCAT.spad" 367934 367946 371241 371246) (-264 "DSMP.spad" 365365 365379 365670 365797) (-263 "DROPT.spad" 359310 359318 365355 365360) (-262 "DROPT1.spad" 358973 358983 359300 359305) (-261 "DROPT0.spad" 353800 353808 358963 358968) (-260 "DRAWPT.spad" 351955 351963 353790 353795) (-259 "DRAW.spad" 344555 344568 351945 351950) (-258 "DRAWHACK.spad" 343863 343873 344545 344550) (-257 "DRAWCX.spad" 341305 341313 343853 343858) (-256 "DRAWCURV.spad" 340842 340857 341295 341300) (-255 "DRAWCFUN.spad" 330014 330022 340832 340837) (-254 "DQAGG.spad" 328182 328192 329982 330009) (-253 "DPOLCAT.spad" 323523 323539 328050 328177) (-252 "DPOLCAT.spad" 318950 318968 323479 323484) (-251 "DPMO.spad" 311176 311192 311314 311615) (-250 "DPMM.spad" 303415 303433 303540 303841) (-249 "DOMCTOR.spad" 303307 303315 303405 303410) (-248 "DOMAIN.spad" 302438 302446 303297 303302) (-247 "DMP.spad" 299660 299675 300232 300359) (-246 "DLP.spad" 299008 299018 299650 299655) (-245 "DLIST.spad" 297587 297597 298191 298218) (-244 "DLAGG.spad" 295998 296008 297577 297582) (-243 "DIVRING.spad" 295540 295548 295942 295993) (-242 "DIVRING.spad" 295126 295136 295530 295535) (-241 "DISPLAY.spad" 293306 293314 295116 295121) (-240 "DIRPROD.spad" 282886 282902 283526 283657) (-239 "DIRPROD2.spad" 281694 281712 282876 282881) (-238 "DIRPCAT.spad" 280636 280652 281558 281689) (-237 "DIRPCAT.spad" 279307 279325 280231 280236) (-236 "DIOSP.spad" 278132 278140 279297 279302) (-235 "DIOPS.spad" 277116 277126 278112 278127) (-234 "DIOPS.spad" 276074 276086 277072 277077) (-233 "DIFRING.spad" 275366 275374 276054 276069) (-232 "DIFRING.spad" 274666 274676 275356 275361) (-231 "DIFEXT.spad" 273825 273835 274646 274661) (-230 "DIFEXT.spad" 272901 272913 273724 273729) (-229 "DIAGG.spad" 272531 272541 272881 272896) (-228 "DIAGG.spad" 272169 272181 272521 272526) (-227 "DHMATRIX.spad" 270473 270483 271626 271653) (-226 "DFSFUN.spad" 263881 263889 270463 270468) (-225 "DFLOAT.spad" 260602 260610 263771 263876) (-224 "DFINTTLS.spad" 258811 258827 260592 260597) (-223 "DERHAM.spad" 256721 256753 258791 258806) (-222 "DEQUEUE.spad" 256039 256049 256328 256355) (-221 "DEGRED.spad" 255654 255668 256029 256034) (-220 "DEFINTRF.spad" 253179 253189 255644 255649) (-219 "DEFINTEF.spad" 251675 251691 253169 253174) (-218 "DEFAST.spad" 251043 251051 251665 251670) (-217 "DECIMAL.spad" 249149 249157 249510 249603) (-216 "DDFACT.spad" 246948 246965 249139 249144) (-215 "DBLRESP.spad" 246546 246570 246938 246943) (-214 "DBASE.spad" 245200 245210 246536 246541) (-213 "DATAARY.spad" 244662 244675 245190 245195) (-212 "D03FAFA.spad" 244490 244498 244652 244657) (-211 "D03EEFA.spad" 244310 244318 244480 244485) (-210 "D03AGNT.spad" 243390 243398 244300 244305) (-209 "D02EJFA.spad" 242852 242860 243380 243385) (-208 "D02CJFA.spad" 242330 242338 242842 242847) (-207 "D02BHFA.spad" 241820 241828 242320 242325) (-206 "D02BBFA.spad" 241310 241318 241810 241815) (-205 "D02AGNT.spad" 236114 236122 241300 241305) (-204 "D01WGTS.spad" 234433 234441 236104 236109) (-203 "D01TRNS.spad" 234410 234418 234423 234428) (-202 "D01GBFA.spad" 233932 233940 234400 234405) (-201 "D01FCFA.spad" 233454 233462 233922 233927) (-200 "D01ASFA.spad" 232922 232930 233444 233449) (-199 "D01AQFA.spad" 232368 232376 232912 232917) (-198 "D01APFA.spad" 231792 231800 232358 232363) (-197 "D01ANFA.spad" 231286 231294 231782 231787) (-196 "D01AMFA.spad" 230796 230804 231276 231281) (-195 "D01ALFA.spad" 230336 230344 230786 230791) (-194 "D01AKFA.spad" 229862 229870 230326 230331) (-193 "D01AJFA.spad" 229385 229393 229852 229857) (-192 "D01AGNT.spad" 225444 225452 229375 229380) (-191 "CYCLOTOM.spad" 224950 224958 225434 225439) (-190 "CYCLES.spad" 221782 221790 224940 224945) (-189 "CVMP.spad" 221199 221209 221772 221777) (-188 "CTRIGMNP.spad" 219689 219705 221189 221194) (-187 "CTOR.spad" 219384 219392 219679 219684) (-186 "CTORKIND.spad" 218987 218995 219374 219379) (-185 "CTORCAT.spad" 218236 218244 218977 218982) (-184 "CTORCAT.spad" 217483 217493 218226 218231) (-183 "CTORCALL.spad" 217063 217071 217473 217478) (-182 "CSTTOOLS.spad" 216306 216319 217053 217058) (-181 "CRFP.spad" 210010 210023 216296 216301) (-180 "CRCEAST.spad" 209730 209738 210000 210005) (-179 "CRAPACK.spad" 208773 208783 209720 209725) (-178 "CPMATCH.spad" 208273 208288 208698 208703) (-177 "CPIMA.spad" 207978 207997 208263 208268) (-176 "COORDSYS.spad" 202871 202881 207968 207973) (-175 "CONTOUR.spad" 202273 202281 202861 202866) (-174 "CONTFRAC.spad" 197885 197895 202175 202268) (-173 "CONDUIT.spad" 197643 197651 197875 197880) (-172 "COMRING.spad" 197317 197325 197581 197638) (-171 "COMPPROP.spad" 196831 196839 197307 197312) (-170 "COMPLPAT.spad" 196598 196613 196821 196826) (-169 "COMPLEX.spad" 190622 190632 190866 191127) (-168 "COMPLEX2.spad" 190335 190347 190612 190617) (-167 "COMPFACT.spad" 189937 189951 190325 190330) (-166 "COMPCAT.spad" 188005 188015 189671 189932) (-165 "COMPCAT.spad" 185766 185778 187434 187439) (-164 "COMMUPC.spad" 185512 185530 185756 185761) (-163 "COMMONOP.spad" 185045 185053 185502 185507) (-162 "COMM.spad" 184854 184862 185035 185040) (-161 "COMMAAST.spad" 184617 184625 184844 184849) (-160 "COMBOPC.spad" 183522 183530 184607 184612) (-159 "COMBINAT.spad" 182267 182277 183512 183517) (-158 "COMBF.spad" 179635 179651 182257 182262) (-157 "COLOR.spad" 178472 178480 179625 179630) (-156 "COLONAST.spad" 178138 178146 178462 178467) (-155 "CMPLXRT.spad" 177847 177864 178128 178133) (-154 "CLLCTAST.spad" 177509 177517 177837 177842) (-153 "CLIP.spad" 173601 173609 177499 177504) (-152 "CLIF.spad" 172240 172256 173557 173596) (-151 "CLAGG.spad" 168725 168735 172230 172235) (-150 "CLAGG.spad" 165081 165093 168588 168593) (-149 "CINTSLPE.spad" 164406 164419 165071 165076) (-148 "CHVAR.spad" 162484 162506 164396 164401) (-147 "CHARZ.spad" 162399 162407 162464 162479) (-146 "CHARPOL.spad" 161907 161917 162389 162394) (-145 "CHARNZ.spad" 161660 161668 161887 161902) (-144 "CHAR.spad" 159528 159536 161650 161655) (-143 "CFCAT.spad" 158844 158852 159518 159523) (-142 "CDEN.spad" 158002 158016 158834 158839) (-141 "CCLASS.spad" 156151 156159 157413 157452) (-140 "CATEGORY.spad" 155241 155249 156141 156146) (-139 "CATCTOR.spad" 155132 155140 155231 155236) (-138 "CATAST.spad" 154759 154767 155122 155127) (-137 "CASEAST.spad" 154473 154481 154749 154754) (-136 "CARTEN.spad" 149576 149600 154463 154468) (-135 "CARTEN2.spad" 148962 148989 149566 149571) (-134 "CARD.spad" 146251 146259 148936 148957) (-133 "CAPSLAST.spad" 146025 146033 146241 146246) (-132 "CACHSET.spad" 145647 145655 146015 146020) (-131 "CABMON.spad" 145200 145208 145637 145642) (-130 "BYTEORD.spad" 144875 144883 145190 145195) (-129 "BYTE.spad" 144300 144308 144865 144870) (-128 "BYTEBUF.spad" 142157 142165 143469 143496) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 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-493) 150830) ((-1221 . -284) 150796) ((-1221 . -95) 150762) ((-1221 . -35) 150728) ((-1221 . -1235) 150705) ((-1221 . -47) 150682) ((-1221 . -613) 150430) ((-1221 . -713) 150244) ((-1221 . -643) 150114) ((-1221 . -1051) 149922) ((-1221 . -111) 149711) ((-1221 . -38) 149525) ((-1221 . -969) 149494) ((-1221 . -286) 149414) ((-1221 . -1218) 149398) ((-1221 . -722) T) ((-1221 . -1105) T) ((-1221 . -1052) T) ((-1221 . -1045) T) ((-1221 . -21) T) ((-1221 . -23) T) ((-1221 . -1094) T) ((-1221 . -610) 149380) ((-1221 . -102) T) ((-1221 . -25) T) ((-1221 . -131) T) ((-1221 . -145) 149305) ((-1221 . -147) 149230) ((-1221 . -611) 148901) ((-1221 . -231) 148871) ((-1221 . -896) 148722) ((-1221 . -233) 148627) ((-1221 . -363) 148606) ((-1221 . -1212) 148585) ((-1221 . -917) 148564) ((-1221 . -556) 148515) ((-1221 . -172) 148446) ((-1221 . -452) 148425) ((-1221 . -307) 148404) ((-1221 . -290) 148355) ((-1221 . -243) 148334) ((-1221 . -338) 148304) ((-1221 . -514) 148164) ((-1221 . -309) 148103) ((-1221 . -377) 148073) ((-1221 . -636) 147981) ((-1221 . -400) 147951) ((-1221 . -1207) 147930) ((-1221 . -882) 147803) ((-1221 . -816) 147756) ((-1221 . -787) 147709) ((-1221 . -788) 147662) ((-1221 . -846) 147561) ((-1221 . -790) 147514) ((-1221 . -793) 147467) ((-1221 . -844) 147420) ((-1221 . -880) 147390) ((-1221 . -906) 147343) ((-1221 . -1016) 147295) ((-1221 . -1034) 147081) ((-1221 . -1144) 147033) ((-1221 . -987) 147003) ((-1216 . -1220) 146964) ((-1216 . -998) 146930) ((-1216 . -1193) 146896) ((-1216 . -1196) 146862) ((-1216 . -493) 146828) ((-1216 . -284) 146794) ((-1216 . -95) 146760) ((-1216 . -35) 146726) ((-1216 . -1235) 146703) ((-1216 . -47) 146680) ((-1216 . -613) 146475) ((-1216 . -713) 146271) ((-1216 . -643) 146123) ((-1216 . -1051) 145913) ((-1216 . -111) 145682) ((-1216 . -38) 145478) ((-1216 . -969) 145447) ((-1216 . -286) 145295) ((-1216 . -1218) 145279) ((-1216 . -722) T) ((-1216 . -1105) T) ((-1216 . -1052) T) ((-1216 . -1045) T) ((-1216 . -21) T) ((-1216 . -23) T) ((-1216 . -1094) T) ((-1216 . -610) 145261) ((-1216 . -102) T) ((-1216 . -25) T) ((-1216 . -131) T) ((-1216 . -145) 145168) ((-1216 . -147) 145075) ((-1216 . -611) NIL) ((-1216 . -231) 145027) ((-1216 . -896) 144860) ((-1216 . -233) 144747) ((-1216 . -363) 144726) ((-1216 . -1212) 144705) ((-1216 . -917) 144684) ((-1216 . -556) 144635) ((-1216 . -172) 144566) ((-1216 . -452) 144545) ((-1216 . -307) 144524) ((-1216 . -290) 144475) ((-1216 . -243) 144454) ((-1216 . -338) 144406) ((-1216 . -514) 144175) ((-1216 . -309) 144060) ((-1216 . -377) 144012) ((-1216 . -636) 143964) ((-1216 . -400) 143916) ((-1216 . -1207) 143895) ((-1216 . -882) NIL) ((-1216 . -816) NIL) ((-1216 . -787) NIL) ((-1216 . -788) NIL) ((-1216 . -846) NIL) ((-1216 . -790) NIL) ((-1216 . -793) NIL) ((-1216 . -844) NIL) ((-1216 . -880) 143847) ((-1216 . -906) NIL) ((-1216 . -1016) NIL) ((-1216 . -1034) 143813) ((-1216 . -1144) NIL) ((-1216 . -987) 143765) ((-1215 . -840) T) ((-1215 . -846) T) ((-1215 . -1094) T) ((-1215 . -610) 143747) ((-1215 . -102) T) ((-1215 . -368) T) ((-1214 . -840) T) ((-1214 . -846) T) ((-1214 . -1094) T) ((-1214 . -610) 143729) ((-1214 . -102) T) ((-1214 . -368) T) ((-1213 . -840) T) ((-1213 . -846) T) ((-1213 . -1094) T) ((-1213 . -610) 143711) ((-1213 . -102) T) ((-1213 . -368) T) ((-1208 . -1076) T) ((-1208 . -490) 143692) ((-1208 . -610) 143658) ((-1208 . -613) 143639) ((-1208 . -1094) T) ((-1208 . -102) T) ((-1208 . -93) T) ((-1205 . -490) 143616) ((-1205 . -610) 143528) ((-1205 . -613) 143505) ((-1205 . -1094) 143483) ((-1205 . -102) 143461) ((-1200 . -736) 143437) ((-1200 . -35) 143403) ((-1200 . -95) 143369) ((-1200 . -284) 143335) ((-1200 . -493) 143301) ((-1200 . -1196) 143267) ((-1200 . -1193) 143233) ((-1200 . -998) 143199) ((-1200 . -47) 143168) ((-1200 . -38) 143065) ((-1200 . -713) 142962) ((-1200 . -613) 142844) ((-1200 . -290) 142823) ((-1200 . -556) 142802) ((-1200 . -111) 142671) ((-1200 . -1051) 142554) ((-1200 . -172) 142505) ((-1200 . -147) 142484) ((-1200 . -145) 142463) ((-1200 . -643) 142388) ((-1200 . -969) 142350) ((-1200 . -1045) T) ((-1200 . -1052) T) ((-1200 . -1105) T) ((-1200 . -722) T) ((-1200 . -21) T) ((-1200 . -23) T) ((-1200 . -1094) T) ((-1200 . -610) 142332) ((-1200 . -102) T) ((-1200 . -25) T) ((-1200 . -131) T) ((-1200 . -896) 142313) ((-1200 . -514) 142280) ((-1200 . -309) 142267) ((-1194 . -1006) 142251) ((-1194 . -34) T) ((-1194 . -1207) T) ((-1194 . -610) 142183) ((-1194 . -309) 142121) ((-1194 . -514) 142054) ((-1194 . -1094) 142032) ((-1194 . -102) 142010) ((-1194 . -489) 141994) ((-1189 . -365) 141968) ((-1189 . -102) T) ((-1189 . -610) 141950) ((-1189 . -1094) T) ((-1187 . -1094) T) ((-1187 . -610) 141932) ((-1187 . -102) T) ((-1187 . -613) 141914) ((-1180 . -1184) 141893) ((-1180 . -229) 141843) ((-1180 . -107) 141793) ((-1180 . -309) 141597) ((-1180 . -514) 141389) ((-1180 . -489) 141326) ((-1180 . -151) 141276) ((-1180 . -611) NIL) ((-1180 . -235) 141226) ((-1180 . -607) 141205) ((-1180 . -288) 141184) ((-1180 . -286) 141163) ((-1180 . -102) T) ((-1180 . -1094) T) ((-1180 . -610) 141145) ((-1180 . -1207) T) ((-1180 . -34) T) ((-1180 . -601) 141124) ((-1178 . -1207) T) ((-1176 . -840) T) ((-1176 . -846) T) ((-1176 . -1094) T) ((-1176 . -610) 141106) ((-1176 . -102) T) ((-1176 . -368) T) ((-1175 . -840) T) ((-1175 . -846) T) ((-1175 . -1094) T) ((-1175 . -610) 141088) ((-1175 . -102) T) ((-1175 . -368) T) ((-1174 . -1252) T) ((-1174 . -1094) T) ((-1174 . -610) 141055) ((-1174 . -102) T) ((-1174 . -1034) 140990) ((-1174 . -613) 140925) ((-1173 . -610) 140907) ((-1172 . -610) 140889) ((-1171 . -326) 140866) ((-1171 . -1034) 140762) ((-1171 . -412) 140746) ((-1171 . -38) 140643) ((-1171 . -613) 140496) ((-1171 . -643) 140421) ((-1171 . -722) T) ((-1171 . -1105) T) ((-1171 . -1052) T) ((-1171 . -1045) T) ((-1171 . -111) 140290) ((-1171 . -1051) 140173) ((-1171 . -21) T) ((-1171 . -23) T) ((-1171 . -1094) T) ((-1171 . -610) 140155) ((-1171 . -102) T) ((-1171 . -25) T) ((-1171 . -131) T) ((-1171 . -713) 140052) ((-1171 . -145) 140031) ((-1171 . -147) 140010) ((-1171 . -172) 139961) ((-1171 . -556) 139940) ((-1171 . -290) 139919) ((-1171 . -47) 139896) ((-1169 . -846) T) ((-1169 . -102) T) ((-1169 . -610) 139878) ((-1169 . -1094) T) ((-1169 . -611) 139800) ((-1169 . -817) T) ((-1169 . -613) 139781) ((-1169 . -882) 139748) ((-1168 . -610) 139730) ((-1167 . -1249) 139714) ((-1167 . -233) 139673) ((-1167 . -613) 139555) ((-1167 . -643) 139480) ((-1167 . -131) T) ((-1167 . -25) T) ((-1167 . -102) T) ((-1167 . -610) 139462) ((-1167 . -1094) T) ((-1167 . -23) T) ((-1167 . -21) T) ((-1167 . -722) T) ((-1167 . -1105) T) ((-1167 . -1052) T) ((-1167 . -1045) T) ((-1167 . -286) 139447) ((-1167 . -896) 139360) ((-1167 . -969) 139329) ((-1167 . -38) 139226) ((-1167 . -111) 139095) ((-1167 . -1051) 138978) ((-1167 . -713) 138875) ((-1167 . -145) 138854) ((-1167 . -147) 138833) ((-1167 . -172) 138784) ((-1167 . -556) 138763) ((-1167 . -290) 138742) ((-1167 . -47) 138719) ((-1167 . -1235) 138696) ((-1167 . -35) 138662) ((-1167 . -95) 138628) ((-1167 . -284) 138594) ((-1167 . -493) 138560) ((-1167 . -1196) 138526) ((-1167 . -1193) 138492) ((-1167 . -998) 138458) ((-1166 . -1241) 138419) ((-1166 . -363) 138398) ((-1166 . -1212) 138377) ((-1166 . -917) 138356) ((-1166 . -556) 138307) ((-1166 . -172) 138238) ((-1166 . -613) 137981) ((-1166 . -713) 137822) ((-1166 . -38) 137663) ((-1166 . -452) 137642) ((-1166 . -307) 137621) ((-1166 . -643) 137518) ((-1166 . -722) T) ((-1166 . -1105) T) ((-1166 . -1052) T) ((-1166 . -1045) T) ((-1166 . -111) 137339) ((-1166 . -1051) 137174) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1094) T) ((-1166 . -610) 137156) ((-1166 . -102) T) ((-1166 . -25) T) ((-1166 . -131) T) ((-1166 . -290) 137107) ((-1166 . -243) 137086) ((-1166 . -998) 137052) ((-1166 . -1193) 137018) ((-1166 . -1196) 136984) ((-1166 . -493) 136950) ((-1166 . -284) 136916) ((-1166 . -95) 136882) ((-1166 . -35) 136848) ((-1166 . -1235) 136818) ((-1166 . -47) 136788) ((-1166 . -147) 136767) ((-1166 . -145) 136746) ((-1166 . -969) 136708) ((-1166 . -896) 136614) ((-1166 . -286) 136599) ((-1166 . -233) 136551) ((-1166 . -1239) 136535) ((-1166 . -1034) 136470) ((-1163 . -1232) 136454) ((-1163 . -1144) 136432) ((-1163 . -611) NIL) ((-1163 . -309) 136419) ((-1163 . -514) 136366) ((-1163 . -326) 136343) ((-1163 . -1034) 136223) ((-1163 . -412) 136207) ((-1163 . -38) 136036) ((-1163 . -111) 135845) ((-1163 . -1051) 135668) ((-1163 . -643) 135593) ((-1163 . -713) 135422) ((-1163 . -613) 135191) ((-1163 . -145) 135170) ((-1163 . -147) 135149) ((-1163 . -47) 135126) ((-1163 . -377) 135110) ((-1163 . -636) 135058) ((-1163 . -846) 135037) ((-1163 . -896) 134980) ((-1163 . -882) NIL) ((-1163 . -906) 134959) ((-1163 . -1212) 134938) ((-1163 . -946) 134907) ((-1163 . -917) 134886) ((-1163 . -556) 134797) ((-1163 . -290) 134708) ((-1163 . -172) 134599) ((-1163 . -452) 134530) ((-1163 . -307) 134509) ((-1163 . -286) 134436) ((-1163 . -233) T) ((-1163 . -131) T) ((-1163 . -25) T) ((-1163 . -102) T) ((-1163 . -610) 134418) ((-1163 . -1094) T) ((-1163 . -23) T) ((-1163 . -21) T) ((-1163 . -722) T) ((-1163 . -1105) T) ((-1163 . -1052) T) ((-1163 . -1045) T) ((-1163 . -231) 134402) ((-1160 . -1220) 134363) ((-1160 . -998) 134329) ((-1160 . -1193) 134295) ((-1160 . -1196) 134261) ((-1160 . -493) 134227) ((-1160 . -284) 134193) ((-1160 . -95) 134159) ((-1160 . -35) 134125) ((-1160 . -1235) 134102) ((-1160 . -47) 134079) ((-1160 . -613) 133874) ((-1160 . -713) 133670) ((-1160 . -643) 133522) ((-1160 . -1051) 133312) ((-1160 . -111) 133081) ((-1160 . -38) 132877) ((-1160 . -969) 132846) ((-1160 . -286) 132694) ((-1160 . -1218) 132678) ((-1160 . -722) T) ((-1160 . -1105) T) ((-1160 . -1052) T) ((-1160 . -1045) T) ((-1160 . -21) T) ((-1160 . -23) T) ((-1160 . -1094) T) ((-1160 . -610) 132660) ((-1160 . -102) T) ((-1160 . -25) T) ((-1160 . -131) T) ((-1160 . -145) 132567) ((-1160 . -147) 132474) ((-1160 . -611) NIL) ((-1160 . -231) 132426) ((-1160 . -896) 132259) ((-1160 . -233) 132146) ((-1160 . -363) 132125) ((-1160 . -1212) 132104) ((-1160 . -917) 132083) ((-1160 . -556) 132034) ((-1160 . -172) 131965) ((-1160 . -452) 131944) ((-1160 . -307) 131923) ((-1160 . -290) 131874) ((-1160 . -243) 131853) ((-1160 . -338) 131805) ((-1160 . -514) 131574) ((-1160 . -309) 131459) ((-1160 . -377) 131411) ((-1160 . -636) 131363) ((-1160 . -400) 131315) ((-1160 . -1207) 131294) ((-1160 . -882) NIL) ((-1160 . -816) NIL) ((-1160 . -787) NIL) ((-1160 . -788) NIL) ((-1160 . -846) NIL) ((-1160 . -790) NIL) ((-1160 . -793) NIL) ((-1160 . -844) NIL) ((-1160 . -880) 131246) ((-1160 . -906) NIL) ((-1160 . -1016) NIL) ((-1160 . -1034) 131212) ((-1160 . -1144) NIL) ((-1160 . -987) 131164) ((-1159 . -1076) T) ((-1159 . -490) 131145) ((-1159 . -610) 131111) ((-1159 . -613) 131092) ((-1159 . -1094) T) ((-1159 . -102) T) ((-1159 . -93) T) ((-1158 . -1094) T) ((-1158 . -610) 131074) ((-1158 . -102) T) ((-1157 . -1094) T) ((-1157 . -610) 131056) ((-1157 . -102) T) ((-1152 . -1184) 131032) ((-1152 . -229) 130979) ((-1152 . -107) 130926) ((-1152 . -309) 130721) ((-1152 . -514) 130504) ((-1152 . -489) 130438) ((-1152 . -151) 130385) ((-1152 . -611) NIL) ((-1152 . -235) 130332) ((-1152 . -607) 130308) ((-1152 . -288) 130284) ((-1152 . -286) 130260) ((-1152 . -102) T) ((-1152 . -1094) T) ((-1152 . -610) 130242) ((-1152 . -1207) T) ((-1152 . -34) T) ((-1152 . -601) 130218) ((-1151 . -1150) T) ((-1151 . -19) 130200) ((-1151 . -646) 130182) ((-1151 . -288) 130157) ((-1151 . -286) 130132) ((-1151 . -601) 130107) ((-1151 . -611) NIL) ((-1151 . -489) 130089) ((-1151 . -514) NIL) ((-1151 . -309) NIL) ((-1151 . -1207) T) ((-1151 . -34) T) ((-1151 . -151) 130071) ((-1151 . -846) T) ((-1151 . -372) 130053) ((-1151 . -1137) T) ((-1151 . -102) T) ((-1151 . -610) 130035) ((-1151 . -1094) T) ((-1151 . -817) T) ((-1146 . -669) 130019) ((-1146 . -646) 130003) ((-1146 . -288) 129980) ((-1146 . -286) 129957) ((-1146 . -601) 129934) ((-1146 . -611) 129895) ((-1146 . -489) 129879) ((-1146 . -102) 129857) ((-1146 . -1094) 129835) ((-1146 . -514) 129768) ((-1146 . -309) 129706) ((-1146 . -610) 129638) ((-1146 . -1207) T) ((-1146 . -34) T) ((-1146 . -151) 129622) ((-1146 . -1245) 129606) ((-1146 . -1006) 129590) ((-1146 . -1142) 129574) ((-1146 . -613) 129551) ((-1143 . -1184) 129530) ((-1143 . -229) 129480) ((-1143 . -107) 129430) ((-1143 . -309) 129234) ((-1143 . -514) 129026) ((-1143 . -489) 128963) ((-1143 . -151) 128913) ((-1143 . -611) NIL) ((-1143 . -235) 128863) ((-1143 . -607) 128842) ((-1143 . -288) 128821) ((-1143 . -286) 128800) ((-1143 . -102) T) ((-1143 . -1094) T) ((-1143 . -610) 128782) ((-1143 . -1207) T) ((-1143 . -34) T) ((-1143 . -601) 128761) ((-1140 . -1114) 128745) ((-1140 . -489) 128729) ((-1140 . -102) 128707) ((-1140 . -1094) 128685) ((-1140 . -514) 128618) ((-1140 . -309) 128556) ((-1140 . -610) 128488) ((-1140 . -1207) T) ((-1140 . -34) T) ((-1140 . -107) 128472) ((-1139 . -1102) 128441) ((-1139 . -1202) 128410) ((-1139 . -610) 128372) ((-1139 . -151) 128356) ((-1139 . -34) T) ((-1139 . -1207) T) ((-1139 . -309) 128294) ((-1139 . -514) 128227) ((-1139 . -1094) T) ((-1139 . -102) T) ((-1139 . -489) 128211) ((-1139 . -611) 128172) ((-1139 . -972) 128141) ((-1139 . -1065) 128110) ((-1135 . -1116) 128055) ((-1135 . -489) 128039) ((-1135 . -514) 127972) ((-1135 . -309) 127910) ((-1135 . -1207) T) ((-1135 . -34) T) ((-1135 . -1048) 127850) ((-1135 . -1034) 127746) ((-1135 . -613) 127664) ((-1135 . -412) 127648) ((-1135 . -636) 127596) ((-1135 . -377) 127580) ((-1135 . -233) 127559) ((-1135 . -896) 127518) ((-1135 . -231) 127502) ((-1135 . -713) 127434) ((-1135 . -643) 127408) ((-1135 . -131) T) ((-1135 . -25) T) ((-1135 . -102) T) ((-1135 . -610) 127370) ((-1135 . -1094) T) ((-1135 . -23) T) ((-1135 . -21) T) ((-1135 . -1051) 127354) ((-1135 . -111) 127333) ((-1135 . -1045) T) ((-1135 . -1052) T) ((-1135 . -1105) T) ((-1135 . -722) T) ((-1135 . -38) 127293) ((-1135 . -611) 127254) ((-1134 . -1006) 127225) ((-1134 . -34) T) ((-1134 . -1207) T) ((-1134 . -610) 127207) ((-1134 . -309) 127133) ((-1134 . -514) 127052) ((-1134 . -1094) T) ((-1134 . -102) T) ((-1134 . -489) 127023) ((-1133 . -1094) T) ((-1133 . -610) 127005) ((-1133 . -102) T) ((-1128 . -1130) T) ((-1128 . -1252) T) ((-1128 . -93) T) ((-1128 . -102) T) ((-1128 . -610) 126971) ((-1128 . -1094) T) ((-1128 . -613) 126952) ((-1128 . -490) 126933) ((-1128 . -1076) T) ((-1126 . -1127) 126917) ((-1126 . -102) T) ((-1126 . -610) 126899) ((-1126 . -1094) T) ((-1119 . -736) 126878) ((-1119 . -35) 126844) ((-1119 . -95) 126810) ((-1119 . -284) 126776) ((-1119 . -493) 126742) ((-1119 . -1196) 126708) ((-1119 . -1193) 126674) ((-1119 . -998) 126640) ((-1119 . -47) 126612) ((-1119 . -38) 126509) ((-1119 . -713) 126406) ((-1119 . -613) 126288) ((-1119 . -290) 126267) ((-1119 . -556) 126246) ((-1119 . -111) 126115) ((-1119 . -1051) 125998) ((-1119 . -172) 125949) ((-1119 . -147) 125928) ((-1119 . -145) 125907) ((-1119 . -643) 125832) ((-1119 . -969) 125799) ((-1119 . -1045) T) ((-1119 . -1052) T) ((-1119 . -1105) T) ((-1119 . -722) T) ((-1119 . -21) T) ((-1119 . -23) T) ((-1119 . -1094) T) ((-1119 . -610) 125781) ((-1119 . -102) T) ((-1119 . -25) T) ((-1119 . -131) T) ((-1119 . -896) 125765) ((-1119 . -514) 125735) ((-1119 . -309) 125722) ((-1118 . -946) 125689) ((-1118 . -613) 125481) ((-1118 . -1034) 125364) ((-1118 . -1212) 125343) ((-1118 . -906) 125322) ((-1118 . -882) 125181) ((-1118 . -896) 125165) ((-1118 . -846) 125144) ((-1118 . -514) 125096) ((-1118 . -452) 125047) ((-1118 . -636) 124995) ((-1118 . -377) 124979) ((-1118 . -47) 124951) ((-1118 . -38) 124800) ((-1118 . -713) 124649) ((-1118 . -290) 124580) ((-1118 . -556) 124511) ((-1118 . -111) 124340) ((-1118 . -1051) 124183) ((-1118 . -172) 124094) ((-1118 . -147) 124073) ((-1118 . -145) 124052) ((-1118 . -643) 123977) ((-1118 . -131) T) ((-1118 . -25) T) ((-1118 . -102) T) ((-1118 . -610) 123959) ((-1118 . -1094) T) ((-1118 . -23) T) ((-1118 . -21) T) ((-1118 . -1045) T) ((-1118 . -1052) T) ((-1118 . -1105) T) ((-1118 . -722) T) ((-1118 . -412) 123943) ((-1118 . -326) 123915) ((-1118 . -309) 123902) ((-1118 . -611) 123650) ((-1113 . -545) T) ((-1113 . -1212) T) ((-1113 . -1144) T) ((-1113 . -1034) 123632) ((-1113 . -611) 123547) ((-1113 . -1016) T) ((-1113 . -882) 123529) ((-1113 . -844) T) ((-1113 . -793) T) ((-1113 . -790) T) ((-1113 . -846) T) ((-1113 . -788) T) ((-1113 . -787) T) ((-1113 . -816) T) ((-1113 . -636) 123511) ((-1113 . -917) T) ((-1113 . -556) T) ((-1113 . -290) T) ((-1113 . -172) T) ((-1113 . -613) 123483) ((-1113 . -713) 123470) ((-1113 . -1051) 123457) ((-1113 . -111) 123442) ((-1113 . -38) 123429) ((-1113 . -452) T) ((-1113 . -307) T) ((-1113 . -233) T) ((-1113 . -143) T) ((-1113 . -1045) T) ((-1113 . -1052) T) ((-1113 . -1105) T) ((-1113 . -722) T) ((-1113 . -21) T) ((-1113 . -23) T) ((-1113 . -1094) T) ((-1113 . -610) 123411) ((-1113 . -102) T) ((-1113 . -25) T) ((-1113 . -131) T) ((-1113 . -643) 123398) ((-1113 . -147) T) ((-1113 . -840) T) ((-1113 . -368) T) ((-1113 . -657) T) ((-1113 . -817) T) ((-1109 . -1076) T) ((-1109 . -490) 123379) ((-1109 . -610) 123345) ((-1109 . -613) 123326) ((-1109 . -1094) T) ((-1109 . -102) T) ((-1109 . -93) T) ((-1108 . -1094) T) ((-1108 . -610) 123308) ((-1108 . -102) T) ((-1106 . -238) 123287) ((-1106 . -1264) 123257) ((-1106 . -787) 123236) ((-1106 . -844) 123215) ((-1106 . -793) 123166) ((-1106 . -790) 123117) ((-1106 . -846) 123068) ((-1106 . -788) 123019) ((-1106 . -789) 122998) ((-1106 . -288) 122975) ((-1106 . -286) 122952) ((-1106 . -489) 122936) ((-1106 . -514) 122869) ((-1106 . -309) 122807) ((-1106 . -1207) T) ((-1106 . -34) T) ((-1106 . -601) 122784) ((-1106 . -1034) 122611) ((-1106 . -613) 122341) ((-1106 . -412) 122310) ((-1106 . -636) 122216) ((-1106 . -377) 122185) ((-1106 . -368) 122164) ((-1106 . -233) 122116) ((-1106 . -896) 122048) ((-1106 . -231) 122017) ((-1106 . -111) 121907) ((-1106 . -1051) 121804) ((-1106 . -172) 121783) ((-1106 . -610) 121514) ((-1106 . -713) 121456) ((-1106 . -643) 121304) ((-1106 . -131) 121174) ((-1106 . -23) 121044) ((-1106 . -21) 120954) ((-1106 . -1045) 120884) ((-1106 . -1052) 120814) ((-1106 . -1105) 120724) ((-1106 . -722) 120634) ((-1106 . -38) 120604) ((-1106 . -1094) 120394) ((-1106 . -102) 120184) ((-1106 . -25) 120035) ((-1099 . -396) T) ((-1099 . -1207) T) ((-1099 . -610) 120017) ((-1098 . -1097) 119981) ((-1098 . -102) T) ((-1098 . -610) 119963) ((-1098 . -1094) T) ((-1098 . -615) 119878) ((-1096 . -1097) 119830) ((-1096 . -102) T) ((-1096 . -610) 119812) ((-1096 . -1094) T) ((-1096 . -615) 119715) ((-1095 . -368) T) ((-1095 . -102) T) ((-1095 . -610) 119697) ((-1095 . -1094) T) ((-1090 . -426) 119681) ((-1090 . -1092) 119665) ((-1090 . -368) 119644) ((-1090 . -235) 119628) ((-1090 . -611) 119589) ((-1090 . -151) 119573) ((-1090 . -489) 119557) ((-1090 . -102) T) ((-1090 . -1094) T) ((-1090 . -514) 119490) ((-1090 . -309) 119428) ((-1090 . -610) 119410) ((-1090 . -1207) T) ((-1090 . -34) T) ((-1090 . -107) 119394) ((-1090 . -229) 119378) ((-1089 . -1076) T) ((-1089 . -490) 119359) ((-1089 . -610) 119325) ((-1089 . -613) 119306) ((-1089 . -1094) T) ((-1089 . -102) T) ((-1089 . -93) T) ((-1085 . -1207) T) ((-1085 . -1094) 119284) ((-1085 . -610) 119251) ((-1085 . -102) 119229) ((-1084 . -1076) T) ((-1084 . -490) 119210) ((-1084 . -610) 119176) ((-1084 . -613) 119157) ((-1084 . -1094) T) ((-1084 . -102) T) ((-1084 . -93) T) ((-1082 . -1087) 119141) ((-1082 . -615) 119125) ((-1082 . -1094) 119103) ((-1082 . -610) 119070) ((-1082 . -102) 119048) ((-1082 . -1088) 119006) ((-1081 . -266) 118990) ((-1081 . -613) 118974) ((-1081 . -1034) 118958) ((-1081 . -1094) T) ((-1081 . -610) 118940) ((-1081 . -102) T) ((-1081 . -846) T) ((-1080 . -253) 118877) ((-1080 . -613) 118613) ((-1080 . -1034) 118440) ((-1080 . -611) NIL) ((-1080 . -326) 118401) ((-1080 . -412) 118385) ((-1080 . -38) 118234) ((-1080 . -111) 118063) ((-1080 . -1051) 117906) ((-1080 . -643) 117831) ((-1080 . -713) 117680) ((-1080 . -145) 117659) ((-1080 . -147) 117638) ((-1080 . -172) 117549) ((-1080 . -556) 117480) ((-1080 . -290) 117411) ((-1080 . -47) 117372) ((-1080 . -377) 117356) ((-1080 . -636) 117304) ((-1080 . -452) 117255) ((-1080 . -514) 117122) ((-1080 . -846) 117101) ((-1080 . -896) 117036) ((-1080 . -882) NIL) ((-1080 . -906) 117015) ((-1080 . -1212) 116994) ((-1080 . -946) 116939) ((-1080 . -309) 116926) ((-1080 . -233) 116905) ((-1080 . -131) T) ((-1080 . -25) T) ((-1080 . -102) T) ((-1080 . -610) 116887) ((-1080 . -1094) T) ((-1080 . -23) T) ((-1080 . -21) T) ((-1080 . -722) T) ((-1080 . -1105) T) ((-1080 . -1052) T) ((-1080 . -1045) T) ((-1080 . -231) 116871) ((-1078 . -610) 116853) ((-1075 . -846) T) ((-1075 . -102) T) ((-1075 . -610) 116835) ((-1075 . -1094) T) ((-1075 . -611) 116816) ((-1072 . -720) 116795) ((-1072 . -1034) 116691) ((-1072 . -412) 116675) ((-1072 . -636) 116623) ((-1072 . -377) 116607) ((-1072 . -370) 116586) ((-1072 . -147) 116565) 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114980) ((-1068 . -102) T) ((-1068 . -286) 114959) ((-1068 . -1034) 114936) ((-1068 . -613) 114913) ((-1067 . -1076) T) ((-1067 . -490) 114894) ((-1067 . -610) 114860) ((-1067 . -613) 114841) ((-1067 . -1094) T) ((-1067 . -102) T) ((-1067 . -93) T) ((-1060 . -1076) T) ((-1060 . -490) 114822) ((-1060 . -610) 114788) ((-1060 . -613) 114769) ((-1060 . -1094) T) ((-1060 . -102) T) ((-1060 . -93) T) ((-1057 . -1184) 114744) ((-1057 . -229) 114690) ((-1057 . -107) 114636) ((-1057 . -309) 114487) ((-1057 . -514) 114331) ((-1057 . -489) 114262) ((-1057 . -151) 114208) ((-1057 . -611) NIL) ((-1057 . -235) 114154) ((-1057 . -607) 114129) ((-1057 . -288) 114104) ((-1057 . -286) 114079) ((-1057 . -102) T) ((-1057 . -1094) T) ((-1057 . -610) 114061) ((-1057 . -1207) T) ((-1057 . -34) T) ((-1057 . -601) 114036) ((-1056 . -545) T) ((-1056 . -1212) T) ((-1056 . -1144) T) ((-1056 . -1034) 114018) ((-1056 . -611) 113933) ((-1056 . -1016) T) ((-1056 . -882) 113915) ((-1056 . -844) T) ((-1056 . -793) T) 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((-1049 . -610) 113409) ((-1049 . -1094) T) ((-1049 . -23) T) ((-1049 . -21) T) ((-1049 . -1051) 113393) ((-1049 . -111) 113372) ((-1049 . -1264) 113342) ((-1049 . -611) 113303) ((-1042 . -1065) 113232) ((-1042 . -972) 113161) ((-1042 . -611) 113103) ((-1042 . -489) 113068) ((-1042 . -102) T) ((-1042 . -1094) T) ((-1042 . -514) 112969) ((-1042 . -309) 112877) ((-1042 . -610) 112820) ((-1042 . -1207) T) ((-1042 . -34) T) ((-1042 . -151) 112785) ((-1042 . -1202) 112714) ((-1032 . -1076) T) ((-1032 . -490) 112695) ((-1032 . -610) 112661) ((-1032 . -613) 112642) ((-1032 . -1094) T) ((-1032 . -102) T) ((-1032 . -93) T) ((-1031 . -1184) 112617) ((-1031 . -229) 112563) ((-1031 . -107) 112509) ((-1031 . -309) 112360) ((-1031 . -514) 112204) ((-1031 . -489) 112135) ((-1031 . -151) 112081) ((-1031 . -611) NIL) ((-1031 . -235) 112027) ((-1031 . -607) 112002) ((-1031 . -288) 111977) ((-1031 . -286) 111952) ((-1031 . -102) T) ((-1031 . -1094) T) ((-1031 . -610) 111934) ((-1031 . -1207) T) ((-1031 . -34) T) ((-1031 . -601) 111909) ((-1030 . -172) T) ((-1030 . -613) 111878) ((-1030 . -722) T) ((-1030 . -1105) T) ((-1030 . -1052) T) ((-1030 . -1045) T) ((-1030 . -643) 111852) ((-1030 . -131) T) ((-1030 . -25) T) ((-1030 . -102) T) ((-1030 . -610) 111834) ((-1030 . -1094) T) ((-1030 . -23) T) ((-1030 . -21) T) ((-1030 . -1051) 111808) ((-1030 . -111) 111775) ((-1030 . -38) 111759) ((-1030 . -713) 111743) ((-1023 . -1065) 111712) ((-1023 . -972) 111681) ((-1023 . -611) 111642) ((-1023 . -489) 111626) ((-1023 . -102) T) ((-1023 . -1094) T) ((-1023 . -514) 111559) ((-1023 . -309) 111497) ((-1023 . -610) 111459) ((-1023 . -1207) T) ((-1023 . -34) T) ((-1023 . -151) 111443) ((-1023 . -1202) 111412) ((-1022 . -1207) T) ((-1022 . -1094) 111390) ((-1022 . -610) 111357) ((-1022 . -102) 111335) ((-1020 . -1008) T) ((-1020 . -998) T) ((-1020 . -787) T) ((-1020 . -788) T) ((-1020 . -846) T) ((-1020 . -790) T) ((-1020 . -793) T) ((-1020 . -844) T) ((-1020 . -1034) 111215) ((-1020 . -412) 111177) 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((-1000 . -816) T) ((-1000 . -882) 110474) ((-1000 . -1207) T) ((-1000 . -400) 110456) ((-1000 . -636) 110438) ((-1000 . -377) 110420) ((-1000 . -286) NIL) ((-1000 . -309) NIL) ((-1000 . -514) NIL) ((-1000 . -338) 110402) ((-1000 . -243) T) ((-1000 . -111) 110336) ((-1000 . -1051) 110286) ((-1000 . -290) T) ((-1000 . -713) 110236) ((-1000 . -643) 110186) ((-1000 . -38) 110136) ((-1000 . -307) T) ((-1000 . -452) T) ((-1000 . -172) T) ((-1000 . -556) T) ((-1000 . -917) T) ((-1000 . -1212) T) ((-1000 . -363) T) ((-1000 . -233) T) ((-1000 . -896) NIL) ((-1000 . -231) 110118) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-1000 . -131) T) ((-1000 . -25) T) ((-1000 . -102) T) ((-1000 . -610) 110078) ((-1000 . -1094) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -1045) T) ((-1000 . -1052) T) ((-1000 . -1105) T) ((-1000 . -722) T) ((-999 . -342) 110052) ((-999 . -172) T) ((-999 . -613) 109982) ((-999 . -722) T) ((-999 . -1105) T) ((-999 . -1052) T) ((-999 . -1045) T) ((-999 . -643) 109927) 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-846) 108873) ((-992 . -1034) 108769) ((-992 . -412) 108753) ((-992 . -636) 108701) ((-992 . -377) 108685) ((-992 . -286) 108643) ((-992 . -309) 108608) ((-992 . -514) 108520) ((-992 . -338) 108504) ((-992 . -38) 108452) ((-992 . -111) 108334) ((-992 . -1051) 108230) ((-992 . -643) 108168) ((-992 . -713) 108116) ((-992 . -613) 108006) ((-992 . -290) 107957) ((-992 . -243) 107936) ((-992 . -233) 107915) ((-992 . -896) 107874) ((-992 . -231) 107858) ((-992 . -611) 107819) ((-992 . -147) 107798) ((-992 . -145) 107777) ((-992 . -131) T) ((-992 . -25) T) ((-992 . -102) T) ((-992 . -610) 107759) ((-992 . -1094) T) ((-992 . -23) T) ((-992 . -21) T) ((-992 . -1045) T) ((-992 . -1052) T) ((-992 . -1105) T) ((-992 . -722) T) ((-990 . -1076) T) ((-990 . -490) 107740) ((-990 . -610) 107706) ((-990 . -613) 107687) ((-990 . -1094) T) ((-990 . -102) T) ((-990 . -93) T) ((-989 . -21) T) ((-989 . -23) T) ((-989 . -1094) T) ((-989 . -610) 107669) ((-989 . -102) T) ((-989 . -25) T) ((-989 . -131) T) 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102332) ((-939 . -1207) T) ((-939 . -34) T) ((-939 . -151) 102316) ((-939 . -846) 102295) ((-939 . -372) 102279) ((-939 . -1255) 102263) ((-939 . -615) 102240) ((-923 . -970) T) ((-923 . -610) 102222) ((-921 . -951) T) ((-921 . -610) 102204) ((-915 . -790) T) ((-915 . -846) T) ((-915 . -1094) T) ((-915 . -610) 102186) ((-915 . -102) T) ((-915 . -25) T) ((-915 . -722) T) ((-915 . -1105) T) ((-910 . -363) T) ((-910 . -1212) T) ((-910 . -917) T) ((-910 . -556) T) ((-910 . -172) T) ((-910 . -613) 102123) ((-910 . -713) 102075) ((-910 . -38) 102027) ((-910 . -452) T) ((-910 . -307) T) ((-910 . -643) 101979) ((-910 . -722) T) ((-910 . -1105) T) ((-910 . -1052) T) ((-910 . -1045) T) ((-910 . -111) 101917) ((-910 . -1051) 101869) ((-910 . -21) T) ((-910 . -23) T) ((-910 . -1094) T) ((-910 . -610) 101851) ((-910 . -102) T) ((-910 . -25) T) ((-910 . -131) T) ((-910 . -290) T) ((-910 . -243) T) ((-902 . -350) T) ((-902 . -1144) T) ((-902 . -368) T) ((-902 . -145) T) ((-902 . -363) T) ((-902 . 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99955) ((-868 . -882) 99880) ((-868 . -1207) T) ((-868 . -400) 99864) ((-868 . -636) 99812) ((-868 . -377) 99796) ((-868 . -286) 99754) ((-868 . -309) 99719) ((-868 . -514) 99631) ((-868 . -338) 99615) ((-868 . -243) T) ((-868 . -111) 99553) ((-868 . -1051) 99505) ((-868 . -290) T) ((-868 . -713) 99457) ((-868 . -643) 99409) ((-868 . -38) 99361) ((-868 . -307) T) ((-868 . -452) T) ((-868 . -172) T) ((-868 . -556) T) ((-868 . -917) T) ((-868 . -1212) T) ((-868 . -363) T) ((-868 . -233) 99340) ((-868 . -896) 99299) ((-868 . -231) 99283) ((-868 . -147) 99262) ((-868 . -145) 99241) ((-868 . -131) T) ((-868 . -25) T) ((-868 . -102) T) ((-868 . -610) 99223) ((-868 . -1094) T) ((-868 . -23) T) ((-868 . -21) T) ((-868 . -1045) T) ((-868 . -1052) T) ((-868 . -1105) T) ((-868 . -722) T) ((-867 . -987) 99200) ((-867 . -1144) NIL) ((-867 . -1034) 99177) ((-867 . -613) 99107) ((-867 . -611) NIL) ((-867 . -1016) NIL) ((-867 . -906) NIL) ((-867 . -880) 99084) ((-867 . -844) NIL) ((-867 . -793) NIL) 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96039) ((-828 . -613) 95907) ((-828 . -1034) 95803) ((-828 . -21) 95755) ((-828 . -23) 95707) ((-828 . -25) 95659) ((-828 . -131) 95611) ((-828 . -844) 95590) ((-828 . -643) 95563) ((-828 . -1052) 95542) ((-828 . -1045) 95521) ((-828 . -793) 95500) ((-828 . -790) 95479) ((-828 . -846) 95458) ((-828 . -788) 95437) ((-828 . -787) 95416) ((-828 . -1105) 95395) ((-828 . -722) 95374) ((-824 . -704) 95358) ((-824 . -613) 95313) ((-824 . -713) 95283) ((-824 . -643) 95257) ((-824 . -131) T) ((-824 . -25) T) ((-824 . -102) T) ((-824 . -610) 95239) ((-824 . -1094) T) ((-824 . -23) T) ((-824 . -21) T) ((-824 . -1051) 95223) ((-824 . -111) 95202) ((-824 . -1045) T) ((-824 . -1052) T) ((-824 . -1105) T) ((-824 . -722) T) ((-824 . -38) 95172) ((-824 . -233) 95151) ((-822 . -1094) T) ((-822 . -610) 95133) ((-822 . -102) T) ((-821 . -1094) T) ((-821 . -610) 95115) ((-821 . -102) T) ((-820 . -1094) T) ((-820 . -610) 95097) ((-820 . -102) T) ((-815 . -842) T) ((-815 . -846) T) ((-815 . -853) T) ((-815 . 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93686) ((-812 . -111) 93515) ((-812 . -1051) 93358) ((-812 . -643) 93283) ((-812 . -713) 93132) ((-812 . -145) 93111) ((-812 . -147) 93090) ((-812 . -172) 93001) ((-812 . -556) 92932) ((-812 . -290) 92863) ((-812 . -47) 92825) ((-812 . -377) 92809) ((-812 . -636) 92757) ((-812 . -452) 92708) ((-812 . -514) 92576) ((-812 . -846) 92555) ((-812 . -896) 92491) ((-812 . -882) NIL) ((-812 . -906) 92470) ((-812 . -1212) 92449) ((-812 . -946) 92396) ((-812 . -309) 92383) ((-812 . -233) 92362) ((-812 . -131) T) ((-812 . -25) T) ((-812 . -102) T) ((-812 . -610) 92344) ((-812 . -1094) T) ((-812 . -23) T) ((-812 . -21) T) ((-812 . -722) T) ((-812 . -1105) T) ((-812 . -1052) T) ((-812 . -1045) T) ((-812 . -231) 92328) ((-811 . -238) 92307) ((-811 . -1264) 92277) ((-811 . -787) 92256) ((-811 . -844) 92235) ((-811 . -793) 92186) ((-811 . -790) 92137) ((-811 . -846) 92088) ((-811 . -788) 92039) ((-811 . -789) 92018) ((-811 . -288) 91995) ((-811 . -286) 91972) ((-811 . -489) 91956) ((-811 . -514) 91889) ((-811 . -309) 91827) ((-811 . -1207) T) ((-811 . -34) T) ((-811 . -601) 91804) ((-811 . -1034) 91631) ((-811 . -613) 91361) ((-811 . -412) 91330) ((-811 . -636) 91236) ((-811 . -377) 91205) ((-811 . -368) 91184) ((-811 . -233) 91136) ((-811 . -896) 91068) ((-811 . -231) 91037) ((-811 . -111) 90927) ((-811 . -1051) 90824) ((-811 . -172) 90803) ((-811 . -610) 90534) ((-811 . -713) 90476) ((-811 . -643) 90324) ((-811 . -131) 90194) ((-811 . -23) 90064) ((-811 . -21) 89974) ((-811 . -1045) 89904) ((-811 . -1052) 89834) ((-811 . -1105) 89744) ((-811 . -722) 89654) ((-811 . -38) 89624) ((-811 . -1094) 89414) ((-811 . -102) 89204) ((-811 . -25) 89055) ((-804 . -1094) T) ((-804 . -610) 89037) ((-804 . -102) T) ((-794 . -792) 89021) ((-794 . -846) 89000) ((-794 . -1034) 88783) ((-794 . -613) 88631) ((-794 . -412) 88595) ((-794 . -286) 88553) ((-794 . -309) 88518) ((-794 . -514) 88430) ((-794 . -338) 88414) ((-794 . -368) 88393) ((-794 . -611) 88354) ((-794 . -147) 88333) ((-794 . -145) 88312) ((-794 . -713) 88296) ((-794 . -643) 88270) ((-794 . -131) T) ((-794 . -25) T) ((-794 . -102) T) ((-794 . -610) 88252) ((-794 . -1094) T) ((-794 . -23) T) ((-794 . -21) T) ((-794 . -1051) 88236) ((-794 . -111) 88215) ((-794 . -1045) T) ((-794 . -1052) T) ((-794 . -1105) T) ((-794 . -722) T) ((-794 . -38) 88199) ((-777 . -1232) 88183) ((-777 . -1144) 88161) ((-777 . -611) NIL) ((-777 . -309) 88148) ((-777 . -514) 88095) ((-777 . -326) 88072) ((-777 . -1034) 87931) ((-777 . -412) 87915) ((-777 . -38) 87744) ((-777 . -111) 87553) ((-777 . -1051) 87376) ((-777 . -643) 87301) ((-777 . -713) 87130) ((-777 . -613) 86878) ((-777 . -145) 86857) ((-777 . -147) 86836) ((-777 . -47) 86813) ((-777 . -377) 86797) ((-777 . -636) 86745) ((-777 . -846) 86724) ((-777 . -896) 86667) ((-777 . -882) NIL) ((-777 . -906) 86646) ((-777 . -1212) 86625) ((-777 . -946) 86594) ((-777 . -917) 86573) ((-777 . -556) 86484) ((-777 . -290) 86395) ((-777 . -172) 86286) ((-777 . -452) 86217) ((-777 . -307) 86196) 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. -783) T) ((-203 . -102) T) ((-203 . -610) 13149) ((-203 . -1094) T) ((-202 . -783) T) ((-202 . -102) T) ((-202 . -610) 13131) ((-202 . -1094) T) ((-201 . -783) T) ((-201 . -102) T) ((-201 . -610) 13113) ((-201 . -1094) T) ((-200 . -783) T) ((-200 . -102) T) ((-200 . -610) 13095) ((-200 . -1094) T) ((-199 . -783) T) ((-199 . -102) T) ((-199 . -610) 13077) ((-199 . -1094) T) ((-198 . -783) T) ((-198 . -102) T) ((-198 . -610) 13059) ((-198 . -1094) T) ((-197 . -783) T) ((-197 . -102) T) ((-197 . -610) 13041) ((-197 . -1094) T) ((-196 . -783) T) ((-196 . -102) T) ((-196 . -610) 13023) ((-196 . -1094) T) ((-195 . -783) T) ((-195 . -102) T) ((-195 . -610) 13005) ((-195 . -1094) T) ((-194 . -783) T) ((-194 . -102) T) ((-194 . -610) 12987) ((-194 . -1094) T) ((-193 . -783) T) ((-193 . -102) T) ((-193 . -610) 12969) ((-193 . -1094) T) ((-187 . -1094) T) ((-187 . -610) 12951) ((-187 . -102) T) ((-184 . -1094) T) ((-184 . -610) 12933) ((-184 . -102) T) ((-183 . -186) T) ((-183 . -1094) T) 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137489) ((-954 . -34) T) ((-355 . -233) 137468) ((-355 . -243) T) ((-352 . -233) 137447) ((-352 . -243) T) ((-344 . -233) 137426) ((-344 . -243) T) ((-247 . -326) 137383) ((-264 . -326) 137355) ((-264 . -233) 137334) ((-1149 . -151) 137318) ((-251 . -896) 137250) ((-250 . -896) 137182) ((-1075 . -846) T) ((-414 . -1105) T) ((-1049 . -23) T) ((-906 . -1045) T) ((-322 . -643) 137164) ((-1020 . -844) T) ((-1202 . -998) 137130) ((-1166 . -916) 137109) ((-1160 . -916) 137088) ((-1160 . -816) NIL) ((-906 . -243) T) ((-813 . -363) 137067) ((-385 . -23) T) ((-127 . -1093) 137045) ((-121 . -1093) 137023) ((-906 . -233) T) ((-128 . -34) T) ((-379 . -643) 136988) ((-866 . -713) 136975) ((-1042 . -151) 136940) ((-40 . -172) T) ((-689 . -411) 136922) ((-708 . -309) 136909) ((-832 . -643) 136869) ((-823 . -643) 136843) ((-319 . -25) T) ((-319 . -21) T) ((-653 . -286) 136822) ((-579 . -1093) T) ((-563 . -1093) T) ((-495 . -1093) T) ((-245 . -288) 136799) ((-313 . -231) 136760) ((-1165 . -882) NIL) ((-55 . -1093) T) ((-1118 . -882) 136619) ((-129 . -846) T) ((-1165 . -1034) 136499) ((-1118 . -1034) 136382) ((-183 . -610) 136364) ((-850 . -1034) 136260) ((-778 . -286) 136187) ((-813 . -1105) T) ((-1030 . -722) T) ((-599 . -646) 136171) ((-1042 . -972) 136100) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1144) 136078) ((-689 . -1052) T) ((-599 . -373) 136062) ((-351 . -452) T) ((-343 . -290) T) ((-1258 . -1093) T) ((-248 . -1093) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1093) T) ((-694 . -1093) T) ((-361 . -473) T) ((-1202 . -610) 136044) ((-1165 . -377) 136028) ((-1118 . -377) 136012) ((-1020 . -411) 135974) ((-141 . -229) 135956) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -610) 135938) ((-708 . -38) 135767) ((-1257 . -1255) 135751) ((-351 . -402) T) ((-1257 . -1093) 135701) ((-579 . -713) 135688) ((-563 . -713) 135675) ((-495 . -713) 135640) ((-316 . -626) 135619) ((-832 . -722) T) ((-823 . -722) T) 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. -555) T) ((-478 . -613) 134819) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -555) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -613) 134796) ((-138 . -613) 134777) ((-137 . -613) 134758) ((-133 . -613) 134739) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-579 . -172) T) ((-563 . -172) T) ((-495 . -172) T) ((-653 . -610) 134721) ((-733 . -732) 134705) ((-336 . -610) 134687) ((-68 . -383) T) ((-68 . -395) T) ((-1095 . -107) 134671) ((-1056 . -882) 134653) ((-948 . -882) 134578) ((-648 . -1105) T) ((-620 . -713) 134565) ((-481 . -882) NIL) ((-1139 . -102) T) ((-1087 . -615) 134549) ((-1056 . -1034) 134531) ((-97 . -610) 134513) ((-477 . -147) T) ((-948 . -1034) 134393) ((-117 . -713) 134338) ((-648 . -23) T) ((-481 . -1034) 134214) ((-1080 . -611) NIL) ((-1080 . -610) 134196) ((-778 . -611) NIL) ((-778 . -610) 134157) ((-776 . -611) 133791) ((-776 . -610) 133705) ((-1106 . -636) 133611) ((-461 . -610) 133593) ((-454 . -610) 133575) ((-454 . -611) 133436) ((-1031 . -229) 133382) ((-868 . -905) 133361) ((-126 . -34) T) ((-813 . -131) T) ((-644 . -610) 133343) ((-577 . -102) T) ((-355 . -1276) 133327) ((-352 . -1276) 133311) ((-344 . -1276) 133295) ((-127 . -514) 133228) ((-121 . -514) 133161) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133099) ((-222 . -102) 133077) ((-689 . -1093) T) ((-694 . -172) T) ((-868 . -643) 133029) ((-65 . -384) T) ((-275 . -610) 133011) ((-65 . -395) T) ((-948 . -377) 132995) ((-866 . -290) T) ((-50 . -610) 132977) ((-995 . -38) 132925) ((-580 . -610) 132907) ((-481 . -377) 132891) ((-580 . -611) 132873) ((-518 . -610) 132855) ((-906 . -1276) 132842) ((-867 . -1208) T) ((-696 . -452) T) ((-495 . -514) 132808) ((-487 . -363) T) ((-355 . -368) 132787) ((-352 . -368) 132766) ((-344 . -368) 132745) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1280 . -1271) 132729) ((-867 . -880) 132706) ((-867 . -882) NIL) ((-960 . -846) 132605) ((-811 . -846) 132556) ((-649 . -651) 132540) ((-1194 . -34) T) ((-171 . -610) 132522) ((-1106 . -21) 132432) ((-1106 . -25) 132283) ((-867 . -1034) 132260) ((-948 . -896) 132241) ((-1230 . -47) 132218) ((-906 . -368) T) ((-59 . -646) 132202) ((-516 . -646) 132186) ((-481 . -896) 132163) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -646) 132147) ((-59 . -373) 132131) ((-620 . -172) T) ((-516 . -373) 132115) ((-496 . -373) 132099) ((-823 . -704) 132083) ((-1165 . -307) 132062) ((-1171 . -131) T) ((-117 . -172) T) ((-1139 . -309) 132000) ((-169 . -1208) T) ((-632 . -740) 131984) ((-604 . -740) 131968) ((-1269 . -131) T) ((-1242 . -916) 131947) ((-1221 . -916) 131926) ((-1221 . -816) NIL) ((-689 . -713) 131876) ((-1220 . -905) 131829) ((-1020 . -1093) T) ((-867 . -377) 131806) ((-867 . -338) 131783) ((-901 . -1105) T) ((-169 . -880) 131767) ((-169 . -882) 131692) ((-487 . -1105) T) ((-354 . -1093) T) ((-217 . -1105) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131588) ((-319 . -846) T) ((-1257 . -514) 131521) ((-1241 . -643) 131418) ((-1220 . -643) 131288) ((-868 . -790) 131267) ((-868 . -787) 131246) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -610) 131228) ((-174 . -452) T) ((-222 . -309) 131166) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1281 . -1274) 131145) ((-579 . -290) T) ((-563 . -290) T) ((-672 . -1034) 131129) ((-495 . -290) T) ((-136 . -470) 131084) ((-48 . -1093) T) ((-708 . -231) 131068) ((-867 . -896) NIL) ((-1230 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1093) T) ((-169 . -377) 131052) ((-169 . -338) 131036) ((-1230 . -1034) 130916) ((-851 . -1034) 130812) ((-1135 . -102) T) ((-648 . -131) T) ((-117 . -514) 130720) ((-657 . -788) 130699) ((-657 . -791) 130678) ((-570 . -1034) 130660) ((-294 . -1264) 130630) ((-862 . -102) T) ((-959 . -555) 130609) ((-1202 . -1051) 130492) ((-482 . -636) 130398) ((-900 . -1093) T) ((-1020 . -713) 130335) ((-707 . -1051) 130300) ((-614 . -102) T) ((-599 . -34) T) ((-1140 . -1208) T) ((-1202 . -111) 130169) ((-474 . -643) 130066) ((-354 . -713) 130011) ((-169 . -896) 129970) ((-694 . -290) T) ((-689 . -172) T) ((-707 . -111) 129926) ((-1285 . -1052) T) ((-1230 . -377) 129910) ((-418 . -1212) 129888) ((-1111 . -610) 129870) ((-313 . -844) NIL) ((-418 . -555) T) ((-225 . -307) T) ((-1220 . -787) 129823) ((-1220 . -790) 129776) ((-1241 . -722) T) ((-1220 . -722) T) ((-48 . -713) 129741) ((-225 . -1018) T) ((-351 . -1264) 129718) ((-1243 . -411) 129684) ((-714 . -722) T) ((-1230 . -896) 129627) ((-1202 . -613) 129509) ((-112 . -610) 129491) ((-112 . -611) 129473) ((-714 . -473) T) ((-707 . -613) 129423) ((-482 . -21) 129333) ((-127 . -489) 129317) ((-121 . -489) 129301) ((-482 . -25) 129152) ((-620 . -290) T) ((-584 . -1051) 129127) ((-437 . -1093) T) ((-1056 . -307) T) ((-117 . -290) T) ((-1097 . -102) T) ((-999 . -102) T) ((-584 . -111) 129095) ((-1135 . -309) 129033) ((-1202 . -1045) T) ((-1056 . -1018) T) ((-66 . -1208) T) ((-1049 . -25) T) ((-1049 . -21) T) ((-707 . -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-689 . -514) NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -610) 129015) ((-394 . -610) 128997) ((-474 . -722) T) ((-1113 . -844) T) ((-888 . -1034) 128965) ((-108 . -846) T) ((-653 . -1051) 128949) ((-487 . -131) T) ((-1243 . -1052) T) ((-217 . -131) T) ((-1149 . -102) 128927) ((-99 . -1093) T) ((-245 . -661) 128911) ((-245 . -646) 128895) ((-653 . -111) 128874) ((-584 . -613) 128858) ((-316 . -411) 128842) ((-245 . -373) 128826) ((-1152 . -235) 128773) ((-995 . -231) 128757) ((-74 . -1208) T) ((-48 . -172) T) ((-696 . -387) T) ((-696 . -143) T) ((-1280 . -102) T) ((-1188 . -613) 128739) ((-1080 . -1051) 128582) ((-264 . -905) 128561) ((-247 . -905) 128540) ((-778 . -1051) 128363) ((-776 . -1051) 128206) ((-605 . -1208) T) ((-1157 . -610) 128188) ((-1080 . -111) 128017) ((-1042 . -102) T) ((-475 . -1208) T) ((-461 . -1051) 127988) ((-454 . -1051) 127831) ((-659 . -643) 127815) ((-867 . -307) T) ((-778 . -111) 127624) ((-776 . -111) 127453) ((-355 . -643) 127405) ((-352 . -643) 127357) ((-344 . -643) 127309) ((-264 . -643) 127234) ((-247 . -643) 127159) ((-1151 . -846) T) ((-1081 . -1034) 127143) ((-461 . -111) 127104) ((-454 . -111) 126933) ((-1069 . -1034) 126910) ((-996 . -34) T) ((-962 . -610) 126892) ((-954 . -1208) T) ((-126 . -1006) 126876) ((-959 . -1105) T) ((-867 . -1018) NIL) ((-731 . -1105) T) ((-711 . -1105) T) ((-653 . -613) 126794) ((-1257 . -489) 126778) ((-1135 . -38) 126738) ((-959 . -23) T) ((-861 . -1093) T) ((-839 . -102) T) ((-813 . -21) T) ((-813 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-110 . -656) T) ((-906 . -643) 126703) ((-580 . -1051) 126668) ((-518 . -1051) 126613) ((-227 . -57) 126571) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-689 . -290) T) ((-862 . -38) 126541) ((-580 . -111) 126497) ((-518 . -111) 126426) ((-1080 . -613) 126162) ((-418 . -1105) T) ((-316 . -1052) 126052) ((-313 . -1052) T) ((-128 . -1208) T) ((-778 . -613) 125800) ((-776 . -613) 125566) ((-653 . -1045) T) ((-1285 . -1093) T) ((-454 . -613) 125351) ((-169 . -307) 125282) ((-418 . -23) T) ((-40 . -610) 125264) ((-40 . -611) 125248) ((-108 . -988) 125230) ((-116 . -865) 125214) ((-644 . -613) 125198) ((-48 . -514) 125164) ((-1194 . -1006) 125148) ((-1174 . -610) 125115) ((-1181 . -34) T) ((-950 . -610) 125081) ((-917 . -610) 125063) ((-1106 . -846) 125014) ((-767 . -610) 124996) ((-667 . -610) 124978) ((-1149 . -309) 124916) ((-479 . -34) T) ((-1085 . -1208) T) ((-477 . -452) T) ((-1134 . -34) T) ((-1080 . -1045) T) ((-50 . -613) 124885) ((-778 . -1045) T) ((-776 . -1045) T) ((-642 . -235) 124869) ((-629 . -235) 124815) ((-580 . -613) 124765) ((-518 . -613) 124695) ((-1230 . -307) 124674) ((-1080 . -326) 124635) ((-454 . -1045) T) ((-1171 . -21) T) ((-1080 . -233) 124614) ((-778 . -326) 124591) ((-778 . -233) T) ((-776 . -326) 124563) ((-727 . -1212) 124542) ((-327 . -646) 124526) ((-1171 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124505) ((-327 . -373) 124489) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1144) NIL) ((-727 . -555) 124420) ((-632 . -102) T) ((-604 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124328) ((-897 . -1093) 124306) ((-50 . -1045) T) ((-1269 . -21) T) ((-1269 . -25) T) ((-1167 . -555) 124285) ((-1166 . -1212) 124264) ((-580 . -1045) T) ((-518 . -1045) T) ((-1160 . -1212) 124243) ((-361 . -1034) 124227) ((-322 . -1034) 124211) ((-1020 . -290) T) ((-379 . -882) 124193) ((-1166 . -555) 124144) ((-1160 . -555) 124095) ((-999 . -38) 124040) ((-795 . -1105) T) ((-906 . -722) T) ((-580 . -243) T) ((-580 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1119 . -555) 124019) ((-354 . -290) T) ((-642 . -690) 124003) ((-379 . -1034) 123963) ((-1113 . -1052) T) ((-103 . -125) 123947) ((-795 . -23) T) ((-1279 . -1274) 123923) ((-1257 . -286) 123900) ((-407 . -309) 123865) ((-1277 . -1274) 123844) ((-1243 . -1093) T) ((-866 . -610) 123826) ((-832 . -1034) 123795) ((-203 . -783) T) ((-202 . -783) T) ((-201 . -783) T) ((-200 . -783) T) ((-199 . -783) T) ((-198 . -783) T) ((-197 . -783) T) ((-196 . -783) T) ((-195 . -783) T) ((-194 . -783) T) ((-547 . -610) 123777) ((-495 . -998) T) ((-274 . -835) T) ((-273 . -835) T) ((-272 . -835) T) ((-271 . -835) T) ((-48 . -290) T) ((-270 . -835) T) ((-269 . -835) T) ((-268 . -835) T) ((-193 . -783) T) ((-609 . -846) T) ((-649 . -411) 123761) ((-223 . -613) 123723) ((-110 . -846) T) ((-648 . -21) T) ((-648 . -25) T) ((-1280 . -38) 123693) ((-117 . -286) 123644) ((-1257 . -19) 123628) ((-1257 . -601) 123605) ((-1270 . -1093) T) ((-1070 . -1093) T) ((-983 . -1093) T) ((-959 . -131) T) ((-733 . -1093) T) ((-731 . -131) T) ((-711 . -131) T) ((-511 . -789) T) ((-407 . -1144) 123583) ((-453 . -131) T) ((-511 . -790) T) ((-223 . -1045) T) ((-294 . -102) 123365) ((-141 . -1093) T) ((-694 . -998) T) ((-91 . -1208) T) ((-127 . -610) 123297) ((-121 . -610) 123229) ((-1285 . -172) T) ((-1166 . -363) 123208) ((-1160 . -363) 123187) ((-316 . -1093) T) ((-418 . -131) T) ((-313 . -1093) T) ((-407 . -38) 123139) ((-1126 . -102) T) ((-1243 . -713) 123031) ((-649 . -1052) T) ((-1128 . -1252) T) ((-319 . -145) 123010) ((-319 . -147) 122989) ((-139 . -1093) T) ((-136 . -1093) T) ((-114 . -1093) T) ((-854 . -102) T) ((-579 . -610) 122971) ((-563 . -611) 122870) ((-563 . -610) 122852) ((-495 . -610) 122834) ((-495 . -611) 122779) ((-485 . -23) T) ((-482 . -846) 122730) ((-487 . -636) 122712) ((-961 . -610) 122694) ((-217 . -636) 122676) ((-225 . -404) T) ((-657 . -643) 122660) ((-55 . -610) 122642) ((-1165 . -916) 122621) ((-727 . -1105) T) ((-351 . -102) T) ((-1207 . -1076) T) ((-1113 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122566) ((-1151 . -1150) T) ((-1140 . -107) 122550) ((-1167 . -1105) T) ((-1166 . -1105) T) ((-515 . -1034) 122534) ((-1160 . -1105) T) ((-1119 . -1105) T) ((-343 . -111) 122463) ((-1000 . -1212) T) 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. -643) 116240) ((-245 . -1006) 116224) ((-868 . -307) T) ((-1281 . -1271) 116208) ((-767 . -788) T) ((-767 . -791) T) ((-696 . -38) 116195) ((-563 . -233) T) ((-495 . -243) T) ((-495 . -233) T) ((-1143 . -235) 116145) ((-1080 . -905) 116124) ((-116 . -38) 116111) ((-209 . -796) T) ((-208 . -796) T) ((-207 . -796) T) ((-206 . -796) T) ((-868 . -1018) 116089) ((-1270 . -489) 116073) ((-778 . -905) 116052) ((-776 . -905) 116031) ((-1181 . -1208) T) ((-454 . -905) 116010) ((-733 . -489) 115994) ((-1080 . -643) 115919) ((-694 . -613) 115854) ((-778 . -643) 115779) ((-620 . -1051) 115766) ((-479 . -1208) T) ((-343 . -368) T) ((-141 . -489) 115748) ((-776 . -643) 115673) ((-1134 . -1208) T) ((-548 . -846) T) ((-461 . -643) 115644) ((-264 . -882) 115503) ((-247 . -882) NIL) ((-117 . -1051) 115448) ((-454 . -643) 115373) ((-659 . -1034) 115350) ((-620 . -111) 115335) ((-355 . -1034) 115319) ((-352 . -1034) 115303) ((-344 . -1034) 115287) ((-264 . -1034) 115131) ((-247 . -1034) 115007) ((-117 . 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-791) T) ((-694 . -788) T) ((-999 . -411) 112217) ((-354 . -111) 112146) ((-379 . -916) T) ((-407 . -844) 112125) ((-708 . -290) 112036) ((-223 . -722) T) ((-1249 . -493) 112002) ((-1242 . -493) 111968) ((-1221 . -493) 111934) ((-577 . -1093) T) ((-316 . -998) 111913) ((-222 . -1093) 111891) ((-319 . -969) 111853) ((-105 . -102) T) ((-48 . -1051) 111818) ((-1281 . -102) T) ((-381 . -102) T) ((-48 . -111) 111774) ((-1000 . -636) 111756) ((-1243 . -610) 111738) ((-531 . -102) T) ((-500 . -102) T) ((-1126 . -1127) 111722) ((-152 . -1264) 111706) ((-245 . -1208) T) ((-1207 . -102) T) ((-1020 . -613) 111643) ((-1165 . -1212) 111622) ((-354 . -613) 111552) ((-1118 . -1212) 111531) ((-240 . -21) 111441) ((-240 . -25) 111292) ((-127 . -119) 111276) ((-121 . -119) 111260) ((-44 . -740) 111244) ((-1165 . -555) 111155) ((-1118 . -555) 111086) ((-1031 . -286) 111061) ((-1159 . -1076) T) ((-990 . -1076) T) ((-812 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-355 . -307) T) ((-352 . -307) T) 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109966) ((-139 . -610) 109933) ((-136 . -610) 109915) ((-114 . -610) 109897) ((-477 . -38) 109862) ((-1281 . -1278) 109841) ((-1272 . -131) T) ((-1280 . -1052) T) ((-1075 . -102) T) ((-88 . -1208) T) ((-500 . -309) NIL) ((-996 . -107) 109825) ((-885 . -1093) T) ((-881 . -1093) T) ((-1257 . -646) 109809) ((-1257 . -373) 109793) ((-327 . -1208) T) ((-591 . -846) T) ((-1135 . -1093) T) ((-1135 . -1048) 109733) ((-103 . -514) 109666) ((-923 . -610) 109648) ((-343 . -722) T) ((-30 . -610) 109630) ((-862 . -1093) T) ((-839 . -1052) 109609) ((-40 . -643) 109554) ((-225 . -1212) T) ((-407 . -1052) T) ((-1151 . -151) 109536) ((-995 . -290) 109487) ((-614 . -1093) T) ((-225 . -555) T) ((-319 . -1238) 109471) ((-319 . -1235) 109441) ((-1181 . -1184) 109420) ((-1068 . -610) 109402) ((-642 . -151) 109386) ((-629 . -151) 109332) ((-1181 . -107) 109282) ((-479 . -1184) 109261) ((-487 . -147) T) ((-487 . -145) NIL) ((-1113 . -611) 109176) ((-438 . -610) 109158) ((-217 . -147) T) ((-217 . -145) NIL) 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. -514) 106729) ((-590 . -1076) T) ((-584 . -1034) 106713) ((-1243 . -613) 106587) ((-481 . -23) T) ((-351 . -1052) T) ((-1202 . -896) 106568) ((-665 . -309) 106506) ((-1106 . -1264) 106476) ((-694 . -643) 106441) ((-999 . -172) T) ((-959 . -145) 106420) ((-632 . -1093) T) ((-604 . -1093) T) ((-959 . -147) 106399) ((-1000 . -846) T) ((-731 . -147) 106378) ((-731 . -145) 106357) ((-967 . -846) T) ((-474 . -916) 106336) ((-316 . -1051) 106246) ((-313 . -1051) 106175) ((-995 . -286) 106133) ((-407 . -713) 106085) ((-696 . -844) T) ((-1243 . -1045) T) ((-316 . -111) 105981) ((-313 . -111) 105894) ((-960 . -102) T) ((-811 . -102) 105684) ((-708 . -611) NIL) ((-708 . -610) 105666) ((-653 . -1034) 105562) ((-1243 . -326) 105506) ((-1031 . -288) 105481) ((-579 . -722) T) ((-563 . -790) T) ((-169 . -363) 105432) ((-563 . -787) T) ((-563 . -722) T) ((-495 . -722) T) ((-1139 . -489) 105416) ((-1080 . -882) NIL) ((-867 . -1105) T) ((-117 . -905) NIL) ((-1279 . -1278) 105392) ((-1277 . -1278) 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98413) ((-829 . -1052) 98392) ((-642 . -309) 98330) ((-629 . -309) 98181) ((-1119 . -1193) 98147) ((-708 . -1045) T) ((-1056 . -636) 98129) ((-1073 . -38) 97997) ((-948 . -636) 97945) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1105) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97924) ((-708 . -326) 97901) ((-481 . -636) 97849) ((-40 . -1034) 97737) ((-708 . -233) T) ((-696 . -713) 97724) ((-339 . -1093) T) ((-174 . -1093) T) ((-331 . -846) T) ((-418 . -452) 97674) ((-379 . -23) T) ((-359 . -38) 97639) ((-353 . -38) 97604) ((-345 . -38) 97569) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1105) T) ((-108 . -38) 97519) ((-823 . -1105) T) ((-770 . -1093) T) ((-116 . -713) 97506) ((-667 . -1034) 97490) ((-609 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1149 . -286) 97467) ((-1106 . -309) 97405) ((-1095 . -235) 97389) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97366) ((-96 . -102) T) ((-648 . -848) 97350) ((-1128 . 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. -145) 95043) ((-495 . -1034) 94986) ((-1128 . -1130) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -610) 94952) ((-502 . -610) 94934) ((-1281 . -1052) T) ((-379 . -1054) T) ((-1022 . -1093) 94912) ((-55 . -1034) 94894) ((-897 . -34) T) ((-482 . -309) 94832) ((-590 . -102) T) ((-1149 . -611) 94793) ((-1149 . -610) 94725) ((-1165 . -846) 94704) ((-45 . -102) T) ((-1118 . -846) 94683) ((-813 . -102) T) ((-1230 . -25) T) ((-1230 . -21) T) ((-851 . -25) T) ((-44 . -367) 94667) ((-851 . -21) T) ((-727 . -452) 94618) ((-1280 . -610) 94600) ((-1049 . -309) 94538) ((-666 . -1076) T) ((-603 . -1076) T) ((-390 . -1093) T) ((-570 . -25) T) ((-570 . -21) T) ((-180 . -1076) T) ((-161 . -1076) T) ((-156 . -1076) T) ((-154 . -1076) T) ((-618 . -1093) T) ((-694 . -882) 94520) ((-1257 . -1208) T) ((-227 . -309) 94458) ((-144 . -368) T) ((-1042 . -611) 94400) ((-1042 . -610) 94343) ((-313 . -905) NIL) ((-1215 . -840) T) ((-694 . 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92984) ((-1280 . -382) 92963) ((-815 . -846) T) ((-1259 . -1093) T) ((-1152 . -229) 92910) ((-386 . -846) 92889) ((-1249 . -1196) 92855) ((-1249 . -1193) 92821) ((-1242 . -1193) 92787) ((-515 . -131) T) ((-1242 . -1196) 92753) ((-1221 . -1193) 92719) ((-1221 . -1196) 92685) ((-1249 . -35) 92651) ((-1249 . -95) 92617) ((-632 . -610) 92586) ((-604 . -610) 92555) ((-225 . -846) T) ((-1242 . -95) 92521) ((-1242 . -35) 92487) ((-1241 . -1105) T) ((-1113 . -643) 92474) ((-1221 . -95) 92440) ((-1220 . -1105) T) ((-591 . -151) 92422) ((-1073 . -349) 92401) ((-174 . -290) T) ((-117 . -377) 92378) ((-117 . -338) 92355) ((-1221 . -35) 92321) ((-866 . -307) T) ((-313 . -790) NIL) ((-313 . -787) NIL) ((-316 . -722) 92170) ((-313 . -722) T) ((-474 . -363) 92149) ((-359 . -349) 92128) ((-353 . -349) 92107) ((-345 . -349) 92086) ((-316 . -473) 92065) ((-1241 . -23) T) ((-1220 . -23) T) ((-714 . -1105) T) ((-710 . -131) T) ((-648 . -102) T) ((-477 . -713) 92030) ((-45 . -282) 91980) ((-105 . -1093) T) 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. -363) T) ((-352 . -329) 90122) ((-352 . -363) T) ((-344 . -329) 90106) ((-344 . -363) T) ((-487 . -102) T) ((-1269 . -38) 90076) ((-546 . -846) T) ((-523 . -682) 90026) ((-217 . -102) T) ((-1020 . -1034) 89906) ((-999 . -111) 89835) ((-1167 . -969) 89804) ((-1166 . -969) 89766) ((-520 . -151) 89750) ((-1073 . -370) 89729) ((-351 . -610) 89711) ((-322 . -21) T) ((-354 . -1034) 89688) ((-322 . -25) T) ((-1160 . -969) 89657) ((-1119 . -969) 89624) ((-76 . -610) 89606) ((-694 . -307) T) ((-169 . -846) 89585) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89572) ((-86 . -610) 89554) ((-694 . -1018) T) ((-672 . -846) T) ((-1241 . -131) T) ((-1220 . -131) T) ((-897 . -1006) 89538) ((-832 . -21) T) ((-48 . -1034) 89481) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1279 . -1052) T) ((-548 . -102) T) ((-1277 . -1052) T) ((-649 . -722) T) ((-1097 . -615) 89384) ((-999 . -613) 89314) ((-1280 . -1051) 89298) ((-1230 . -846) 89277) ((-811 . -411) 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. -1212) 81333) ((-727 . -309) 81320) ((-696 . -613) 81292) ((-398 . -610) 81274) ((-670 . -514) 81207) ((-659 . -25) T) ((-659 . -21) T) ((-454 . -555) 81138) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -613) 81120) ((-116 . -613) 81092) ((-1259 . -610) 81074) ((-1214 . -846) T) ((-1202 . -1105) T) ((-1202 . -23) T) ((-1160 . -309) 80959) ((-1119 . -309) 80946) ((-1073 . -713) 80814) ((-862 . -643) 80774) ((-939 . -976) 80758) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80709) ((-707 . -1105) T) ((-707 . -23) T) ((-696 . -1045) T) ((-642 . -1093) 80687) ((-629 . -1093) T) ((-580 . -1212) T) ((-518 . -1212) T) ((-696 . -233) T) ((-629 . -607) 80662) ((-580 . -555) T) ((-518 . -555) T) ((-359 . -713) 80614) ((-339 . -1051) 80598) ((-353 . -713) 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. -286) 59868) ((-294 . -1208) T) ((-1049 . -610) 59830) ((-1049 . -611) 59791) ((-1020 . -1105) T) ((-169 . -102) T) ((-275 . -846) T) ((-1158 . -1093) T) ((-814 . -610) 59773) ((-1106 . -288) 59750) ((-1095 . -229) 59734) ((-999 . -307) T) ((-795 . -713) 59718) ((-359 . -1051) 59670) ((-354 . -1105) T) ((-353 . -1051) 59622) ((-414 . -610) 59604) ((-385 . -610) 59586) ((-345 . -1051) 59538) ((-227 . -610) 59470) ((-1073 . -111) 59366) ((-1020 . -23) T) ((-108 . -1051) 59316) ((-894 . -102) T) ((-837 . -102) T) ((-804 . -102) T) ((-765 . -102) T) ((-672 . -102) T) ((-474 . -452) 59295) ((-418 . -172) T) ((-359 . -111) 59233) ((-353 . -111) 59171) ((-345 . -111) 59109) ((-251 . -231) 59078) ((-250 . -231) 59047) ((-354 . -23) T) ((-71 . -1208) T) ((-225 . -38) 59012) ((-108 . -111) 58946) ((-40 . -25) T) ((-40 . -21) T) ((-665 . -716) T) ((-169 . -284) 58924) ((-48 . -1105) T) ((-917 . -25) T) ((-767 . -25) T) ((-1143 . -489) 58861) ((-485 . -1093) T) ((-1281 . -643) 58835) ((-1230 . 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|Conduit| |ContinuedFraction| |Contour| |CoordinateSystems| + |OneDimensionalArrayFunctions2| |OneDimensionalArray| + |TwoDimensionalArray| |Asp10| |Asp12| |Asp19| |Asp1| |Asp20| |Asp24| + |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| + |Asp41| |Asp42| |Asp49| |Asp4| |Asp50| |Asp55| |Asp6| |Asp73| |Asp74| + |Asp77| |Asp78| |Asp7| |Asp80| |Asp8| |Asp9| |AssociatedEquations| + |ArrayStack| |AbstractSyntaxCategory&| |AbstractSyntaxCategory| + |ArcTrigonometricFunctionCategory&| |ArcTrigonometricFunctionCategory| + |AttributeAst| |AttributeButtons| |AttributeRegistry| |Automorphism| + |BalancedFactorisation| |BasicType&| |BasicType| |BalancedBinaryTree| + |BezoutMatrix| |BasicFunctions| |BagAggregate&| |BagAggregate| + |BinaryExpansion| |Binding| |Bits| |BiModule| |Boolean| + |BasicOperatorFunctions1| |BasicOperator| |BoundIntegerRoots| + |BalancedPAdicInteger| |BalancedPAdicRational| + |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| + |BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate| + |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| + |BinaryTree| |ByteBuffer| |Byte| |ByteOrder| + |CancellationAbelianMonoid| |CachableSet| |CapsuleAst| + |CardinalNumber| |CartesianTensorFunctions2| |CartesianTensor| + |CaseAst| |CategoryAst| |CategoryConstructor| |Category| + |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory| + |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage| + |CharacteristicZero| |ChangeOfVariable| + |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| + |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| + |CollectAst| |ComplexRootPackage| |ColonAst| |Color| + |CombinatorialFunction| |IntegerCombinatoricFunctions| + |CombinatorialOpsCategory| |CommaAst| |Commutator| |CommonOperators| + |CommuteUnivariatePolynomialCategory| |ComplexCategory&| + |ComplexCategory| |ComplexFactorization| |ComplexFunctions2| |Complex| + |ComplexPattern| |SubSpaceComponentProperty| |CommutativeRing| + |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems| |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch| - |CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools| - |Constructor| |ConstructorCall| |ConstructorCategory&| |ConstructorCategory| - |ConstructorKind| |ComplexTrigonometricManipulations| - |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage| - |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| - |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| - |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| - |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| - |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| - |d03fafAnnaType| |DataArray| |Database| |DoubleResultantPackage| - |DistinctDegreeFactorize| |DecimalExpansion| |DefinitionAst| - |ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration| - |DegreeReductionPackage| |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| - |DoubleFloat| |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| - |Dictionary&| |Dictionary| |DifferentialExtension&| |DifferentialExtension| + |CRApackage| |CoerceAst| |ComplexRootFindingPackage| + |CyclicStreamTools| |ConstructorCall| |ConstructorCategory&| + |ConstructorCategory| |ConstructorKind| |Constructor| + |ComplexTrigonometricManipulations| |CoerceVectorMatrixPackage| + |CycleIndicators| |CyclotomicPolynomialPackage| |d01AgentsPackage| + |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| + |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| + |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType| + |d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| + |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| + |d03eefAnnaType| |d03fafAnnaType| |DataArray| |Database| + |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion| + |DefinitionAst| |ElementaryFunctionDefiniteIntegration| + |RationalFunctionDefiniteIntegration| |DegreeReductionPackage| + |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat| + |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| |Dictionary&| + |Dictionary| |DifferentialExtension&| |DifferentialExtension| |DifferentialRing&| |DifferentialRing| |DictionaryOperations&| - |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| - |DirectProductCategory| |DirectProduct| |DirectProductFunctions2| - |DisplayPackage| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| - |DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| - |Domain| |DomainConstructor| |DirectProductMatrixModule| |DirectProductModule| - |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| - |DequeueAggregate| |TopLevelDrawFunctions| + |DictionaryOperations| |DiophantineSolutionPackage| + |DirectProductCategory&| |DirectProductCategory| + |DirectProductFunctions2| |DirectProduct| |DisplayPackage| + |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList| + |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| + |Domain| |DomainConstructor| |DirectProductMatrixModule| + |DirectProductModule| |DifferentialPolynomialCategory&| + |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| - |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| - |TopLevelDrawFunctionsForPoints| |DrawOption| |DrawOptionFunctions0| - |DrawOptionFunctions1| |DifferentialSparseMultivariatePolynomial| + |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| + |DrawNumericHack| |TopLevelDrawFunctions| + |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| + |DrawOptionFunctions1| |DrawOption| + |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| - |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| + |ExtAlgBasis| |ElementaryFunction| + |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElaboratedExpression| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| - |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| - |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| - |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| - |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| - |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| - |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| - |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| - |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| - |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| - |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| - |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| - |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| - |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| - |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| - |FortranCodePackage1| |FiniteDivisor| |FiniteDivisorFunctions2| - |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| - |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| - |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| - |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| + |EllipticFunctionsUnivariateTaylorSeries| |Eltable| + |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| + |EntireRing| |Environment| |EigenPackage| |EquationFunctions2| + |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| + |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| + |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| + |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| + |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| + |Evalable&| |Evalable| |EvaluateCycleIndicators| |ExitAst| |Exit| + |ExponentialExpansion| |ExpressionFunctions2| + |ExpressionToUnivariatePowerSeries| |Expression| + |ExpressionSpaceODESolver| |ExpressionTubePlot| + |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| + |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| + |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| + |FiniteAbelianMonoidRing| |FlexibleArray| + |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| + |FortranCode| |FourierComponent| |FortranCodePackage1| + |FiniteDivisorFunctions2| |FiniteDivisorCategory&| + |FiniteDivisorCategory| |FiniteDivisor| |FullyEvalableOver&| + |FullyEvalableOver| |FortranExpression| + |FunctionFieldCategoryFunctions2| |FunctionFieldCategory&| + |FunctionFieldCategory| |FiniteFieldCyclicGroup| + |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| - |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| - |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| - |FiniteFieldNormalBasisExtensionByPolynomial| - |FiniteFieldNormalBasisExtension| |FiniteFieldExtensionByPolynomial| - |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| + |FiniteFieldHomomorphisms| |FiniteFieldCategory&| + |FiniteFieldCategory| |FunctionFieldIntegralBasis| + |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| + |FiniteFieldNormalBasisExtension| |FiniteField| + |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| + |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| - |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory| - |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| - |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&| - |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| - |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| - |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| - |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| - |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoid| - |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| - |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat| - |ScriptFormulaFormat1| |FortranPackage| |FortranProgramCategory| - |FortranFunctionCategory| |FortranProgram| |FullPartialFractionExpansion| - |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| - |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| - |Factored| |FactoredFunctions2| |Fraction| |FractionFunctions2| - |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| - |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| + |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| + |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| + |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| + |FiniteLinearAggregateFunctions2| |FiniteLinearAggregate&| + |FiniteLinearAggregate| |FreeLieAlgebra| |FiniteLinearAggregateSort| + |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| + |FloatingComplexPackage| |Float| |FloatingRealPackage| |FreeModule1| + |FreeModuleCat| |FortranMatrixCategory| + |FortranMatrixFunctionCategory| |FreeModule| |FreeMonoid| + |FortranMachineTypeCategory| |FileName| |FileNameCategory| + |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| + |ScriptFormulaFormat1| |ScriptFormulaFormat| |FortranProgramCategory| + |FortranFunctionCategory| |FortranPackage| |FortranProgram| + |FullPartialFractionExpansion| |FullyPatternMatchable| + |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| + |FloatingPointSystem&| |FloatingPointSystem| |FactoredFunctions2| + |FractionFunctions2| |Fraction| |FramedAlgebra&| |FramedAlgebra| + |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdealFunctions2| + |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| - |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&| - |FunctionSpace| |FunctionSpaceFunctions2| - |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| - |FiniteSetAggregate&| |FiniteSetAggregate| |FiniteSetAggregateFunctions2| - |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| + |FramedNonAssociativeAlgebra| |Factored| |FactoredFunctionUtilities| + |FunctionSpaceToExponentialExpansion| |FunctionSpaceFunctions2| + |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregateFunctions2| + |FiniteSetAggregate&| |FiniteSetAggregate| + |FunctionSpaceComplexIntegration| |FourierSeries| + |FunctionSpaceIntegration| |FunctionSpace&| |FunctionSpace| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| - |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| - |FunctionCalled| |FunctionDescriptor| |FortranVectorCategory| - |FortranVectorFunctionCategory| |GaloisGroupFactorizer| - |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| - |GaloisGroupUtilities| |GaussianFactorizationPackage| |GroebnerPackage| - |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| - |GroebnerInternalPackage| |GcdDomain&| |GcdDomain| - |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| - |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| + |FunctionSpaceUnivariatePolynomialFactor| |FortranTemplate| + |FortranType| |FunctionCalled| |FunctionDescriptor| + |FortranVectorCategory| |FortranVectorFunctionCategory| + |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| + |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| + |GaussianFactorizationPackage| |EuclideanGroebnerBasisPackage| + |GroebnerFactorizationPackage| |GroebnerInternalPackage| + |GroebnerPackage| |GcdDomain&| |GcdDomain| + |GenericNonAssociativeAlgebra| + |GeneralDistributedMultivariatePolynomial| |GenExEuclid| + |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| - |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| - |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| - |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| - |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| - |Pi| |HasAst| |HashTable| |HallBasis| - |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| - |HeadAst| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| - |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname| - |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| - |InnerAlgebraicNumber| |IndexedOneDimensionalArray| + |GeneralModulePolynomial| |GosperSummationMethod| + |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| + |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| + |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| + |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HasAst| |HashTable| + |HallBasis| |HomogeneousDistributedMultivariatePolynomial| + |HomogeneousDirectProduct| |HeadAst| |Heap| + |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| + |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| + |Hostname| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| + |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| - |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| - |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| - |Identifier| |IndexedDirectProductAbelianGroup| - |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| - |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| - |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable| - |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField| - |InnerIndexedTwoDimensionalArray| |IndexedList| - |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| - |IndexedMatrix| |ImportAst| |InAst| |InputByteConduit&| |InputByteConduit| + |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| + |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| + |IdealDecompositionPackage| |Identifier| + |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| + |IndexedDirectProductCategory| + |IndexedDirectProductOrderedAbelianMonoid| + |IndexedDirectProductOrderedAbelianMonoidSup| + |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| + |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| + |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| + |InnerMatrixLinearAlgebraFunctions| + |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| + |InAst| |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions| |InputBinaryFile| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |InetClientStreamSocket| - |Infinity| |InputForm| |InputFormFunctions1| + |Infinity| |InputFormFunctions1| |InputForm| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| - |IntegerNumberSystem| |Integer| |Int16| |Int32| |Int8| |InnerTable| - |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| - |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| - |IntegerFactorizationPackage| |IntegrationFunctionsTable| - |GenusZeroIntegration| |IntegerNumberTheoryFunctions| - |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| + |IntegerNumberSystem| |Int16| |Int32| |Int8| |InnerTable| + |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| + |IntervalCategory| |IntegralDomain&| |IntegralDomain| + |ElementaryIntegration| |IntegerFactorizationPackage| + |IntegrationFunctionsTable| |GenusZeroIntegration| + |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| + |TranscendentalHermiteIntegration| |Integer| |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| - |TranscendentalIntegration| |InverseLaplaceTransform| |InputOutputByteConduit| - |InputOutputBinaryFile| |IOMode| |IP4Address| |InnerPAdicInteger| - |InnerPrimeField| |InternalPrintPackage| |IntegrationResult| - |IntegrationResultFunctions2| |IntegrationResultToFunction| |IntegerRoots| - |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| - |IrrRepSymNatPackage| |InternalRationalUnivariateRepresentationPackage| - |IsAst| |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| - |InnerTaylorSeries| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| - |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| - |IndexedAggregate&| |IndexedAggregate| |JavaBytecode| |JoinAst| - |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| - |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| - |Kovacic| |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| - |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| |LaplaceTransform| - |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| - |LetAst| |LieExponentials| |LexTriangularPackage| |LiouvillianFunction| - |LiouvillianFunctionCategory| |LinGroebnerPackage| |Library| - |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| |PowerSeriesLimitPackage| - |RationalFunctionLimitPackage| |LinearDependence| |LinearlyExplicitRingOver| - |List| |ListFunctions2| |ListToMap| |ListFunctions3| |Literal| - |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| - |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| - |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| + |TranscendentalIntegration| |InverseLaplaceTransform| + |InputOutputByteConduit| |InputOutputBinaryFile| |IOMode| |IP4Address| + |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| + |IntegrationResultToFunction| |IntegrationResultFunctions2| + |IntegrationResult| |IntegerRoots| |IrredPolyOverFiniteField| + |IntegrationResultRFToFunction| |IrrRepSymNatPackage| + |InternalRationalUnivariateRepresentationPackage| |IsAst| + |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| + |InnerTaylorSeries| |InfiniteTupleFunctions2| + |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| + |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| + |JavaBytecode| |JoinAst| |AssociatedJordanAlgebra| |KeyedAccessFile| + |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| + |CoercibleTo| |ConvertibleTo| |Kovacic| |CoercibleFrom| + |KleeneTrivalentLogic| |ConvertibleFrom| |LeftAlgebra&| |LeftAlgebra| + |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| + |LazardSetSolvingPackage| |LeadingCoefDetermination| |LetAst| + |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| + |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| + |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| + |RationalFunctionLimitPackage| |LinearDependence| + |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| + |ListFunctions3| |List| |Literal| |ListMultiDictionary| |LeftModule| + |ListMonoidOps| |LinearAggregate&| |LinearAggregate| + |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| - |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| + |LinearOrdinaryDifferentialOperator| + |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| - |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| - |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| - |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| - |MacroAst| |Magma| |MappingPackageInternalHacks1| - |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| - |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| - |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| + |ListAggregate| |LinearSystemMatrixPackage1| + |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| + |LieSquareMatrix| |ConstructAst| |LyndonWord| |LazyStreamAggregate&| + |LazyStreamAggregate| |ThreeDimensionalMatrix| |MacroAst| |Magma| + |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| + |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| + |MappingPackage2| |MappingPackage3| |MatrixCategoryFunctions2| + |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| - |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| - |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| - |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| - |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| - |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| - |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| - |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| - |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| - |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| - |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| - |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |Multiset| - |MultisetAggregate| |MoreSystemCommands| |MergeThing| - |MultivariateTaylorSeriesCategory| |MultivariateFactorize| - |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| + |MultiVariableCalculusFunctions| |MatrixCommonDenominator| + |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| + |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| + |MakeBinaryCompiledFunction| |MakeCachableSet| + |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| + |MakeUnaryCompiledFunction| |MultivariateLifting| + |MonogenicLinearOperator| |MultipleMap| |MathMLFormat| |ModularField| + |ModMonic| |ModuleMonomial| |ModuleOperator| |ModularRing| |Module&| + |Module| |MoebiusTransform| |Monad&| |Monad| |MonadWithUnit&| + |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| + |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| + |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| + |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| + |MonoidRingFunctions2| |MonoidRing| |MultisetAggregate| |Multiset| + |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| + |MultivariateFactorize| |MultivariateSquareFree| + |NonAssociativeAlgebra&| |NonAssociativeAlgebra| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| - |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| - |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| - |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| - |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| - |NumericComplexEigenPackage| |NumericContinuedFraction| - |NonCommutativeOperatorDivision| |NetworkClientSocket| - |NumberFieldIntegralBasis| |NumericalIntegrationProblem| - |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| - |None| |NoneFunctions1| |NormInMonogenicAlgebra| |NormalizationPackage| + |NagFittingPackage| |NagOptimisationPackage| + |NagMatrixOperationsPackage| |NagEigenPackage| + |NagLinearEquationSolvingPackage| |NagLapack| + |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| + |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| + |NonAssociativeRing| |NumericComplexEigenPackage| + |NumericContinuedFraction| |NonCommutativeOperatorDivision| + |NetworkClientSocket| |NumberFieldIntegralBasis| + |NumericalIntegrationProblem| |NonLinearSolvePackage| + |NonNegativeInteger| |NonLinearFirstOrderODESolver| |NoneFunctions1| + |None| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| - |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| - |NewSparseUnivariatePolynomialFunctions2| |NumberTheoreticPolynomialFunctions| + |NewSparseMultivariatePolynomial| + |NewSparseUnivariatePolynomialFunctions2| + |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| - |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| - |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| - |OrderedAbelianMonoid| |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| - |OctonionCategory&| |OctonionCategory| |OrderedCancellationAbelianMonoid| - |Octonion| |OctonionCategoryFunctions2| + |NumericalIntegrationCategory| + |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| + |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| + |OrderedCancellationAbelianMonoid| |OctonionCategory&| + |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| - |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| |ODEIntegration| - |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| |PrimitiveRatDE| - |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| - |RationalRicDE| |SystemODESolver| |ODETools| |OrderedDirectProduct| + |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| + |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| + |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| + |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| + |SystemODESolver| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| - |OrderlyDifferentialVariable| |OrderedFreeMonoid| |OrderedIntegralDomain| - |OpenMath| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| - |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| - |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| - |OpenMathServerPackage| |OnePointCompletion| |OnePointCompletionFunctions2| - |Operator| |OperatorCategory&| |OperatorCategory| |OperationsQuery| + |OrderlyDifferentialVariable| |OrderedFreeMonoid| + |OrderedIntegralDomain| |OpenMathConnection| |OpenMathDevice| + |OpenMathEncoding| |OpenMathErrorKind| |OpenMathError| + |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMath| + |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| + |OnePointCompletionFunctions2| |OnePointCompletion| + |OperatorCategory&| |OperatorCategory| |Operator| |OperationsQuery| |OperatorSignature| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| - |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| - |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| - |OrderedSet| |UnivariateSkewPolynomialCategory&| - |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| - |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| - |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| - |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputBinaryFile| - |OutputForm| |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| - |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| - |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Pair| + |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| + |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| + |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| + |UnivariateSkewPolynomialCategory| + |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| + |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| + |OrderedSemiGroup| |OrdSetInts| |OutputByteConduit&| + |OutputByteConduit| |OutputBinaryFile| |OutputForm| |OutputPackage| + |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| + |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| + |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| - |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| - |Parser| |ParametricSurfaceFunctions2| |ParametricSurface| - |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| - |PatternMatchable| |PatternMatch| |PatternMatchResult| - |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| - |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| + |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| + |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| + |ParametricSurface| |PartitionsAndPermutations| |Patternable| + |PatternMatchListResult| |PatternMatchable| |PatternMatch| + |PatternMatchResultFunctions2| |PatternMatchResult| + |PatternFunctions1| |PatternFunctions2| |Pattern| + |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| - |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| - |PrimeField| |PolynomialFactorizationByRecursion| + |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| + |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| - |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| - |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| - |PermutationGroupExamples| |PolyGroebner| |PositiveInteger| |PiCoercions| - |PrincipalIdealDomain| |PolynomialInterpolation| - |PolynomialInterpolationAlgorithms| |ParametricLinearEquations| |Plot| - |PlotFunctions1| |Plot3D| |PlotTools| |PatternMatchAssertions| - |FunctionSpaceAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| + |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| + |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| + |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| + |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| + |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| + |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| + |PlotTools| |FunctionSpaceAssertions| |PatternMatchAssertions| + |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| - |AttachPredicates| |FunctionSpaceAttachPredicates| - |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| - |PolynomialNumberTheoryFunctions| |Point| |PolToPol| - |RealPolynomialUtilitiesPackage| |Polynomial| |PolynomialFunctions2| - |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| - |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| - |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| |PolynomialRing| - |PrecomputedAssociatedEquations| |PrimitiveArray| |PrimitiveArrayFunctions2| - |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| - |PrintPackage| |Product| |Property| |PropositionalFormula| - |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| - |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| - |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| - |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| - |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| - |PartialTranscendentalFunctions| |PushVariables| - |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| - |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategory&| - |QuotientFieldCategory| |QuotientFieldCategoryFunctions2| |QuadraticForm| - |QuasiquoteAst| |QueueAggregate| |Quaternion| |QuaternionCategory&| - |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| |RadicalCategory&| - |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| - |RandomNumberSource| |RationalFactorize| |RationalRetractions| - |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| - |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| - |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| - |ReducedDivisor| |ReduceAst| |RealConstant| |RealZeroPackage| - |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| - |Reference| |RegularTriangularSet| |RadicalEigenPackage| - |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| + |FunctionSpaceAttachPredicates| |AttachPredicates| + |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| + |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| + |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| + |PolynomialToUnivariatePolynomial| |PolynomialCategory&| + |PolynomialCategory| |PolynomialCategoryQuotientFunctions| + |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| + |PortNumber| |PlottablePlaneCurveCategory| + |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| + |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| + |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| + |Property| |PropositionalFormula| |PropositionalLogic| + |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| + |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| + |PlottableSpaceCurveCategory| |PolynomialSetCategory&| + |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| + |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| + |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| + |PushVariables| |PAdicWildFunctionFieldIntegralBasis| + |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| + |QueryEquation| |QuotientFieldCategoryFunctions2| + |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| + |QuasiquoteAst| |QueueAggregate| |QuaternionCategory&| + |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| + |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| + |RadixExpansion| |RadixUtilities| |RandomNumberSource| + |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| + |RecursiveAggregate| |RealClosedField&| |RealClosedField| + |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| + |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| + |ReduceAst| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| + |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| + |RegularTriangularSet| |RepresentationPackage1| + |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| - |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| - |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain| - |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| - |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| - |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| - |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| - |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| + |RandomFloatDistributions| |RationalFunctionFactor| + |RationalFunctionFactorizer| |RationalFunction| |RGBColorModel| + |RGBColorSpace| |RegularChain| |RandomIntegerDistributions| |Ring&| + |Ring| |RationalInterpolation| |RectangularMatrixCategory&| + |RectangularMatrixCategory| |RectangularMatrix| + |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| + |RealNumberSystem&| |RealNumberSystem| + |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| + |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| - |RegularTriangularSetGcdPackage| |RestrictAst| |RewriteRule| |RuleCalled| - |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtension| - |SimpleAlgebraicExtensionAlgFactor| |SAERationalFunctionAlgFactor| - |SingletonAsOrderedSet| |SpadSyntaxCategory| |SortedCache| |Scope| + |RegularTriangularSetGcdPackage| |RestrictAst| |RuleCalled| + |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| + |SimpleAlgebraicExtensionAlgFactor| |SimpleAlgebraicExtension| + |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| + |SpadSyntaxCategory| |SortedCache| |Scope| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| - |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| |SegmentAst| - |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| - |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| - |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| - |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| - |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| - |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| - |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| - |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| - |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| - |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| - |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| - |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| - |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| - |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| + |SequentialDifferentialVariable| |SegmentFunctions2| |SegmentAst| + |SegmentBindingFunctions2| |SegmentBinding| |SegmentCategory| + |Segment| |SegmentExpansionCategory| |SequenceAst| |SetAggregate&| + |SetAggregate| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| + |Set| |SExpressionCategory| |SExpression| |SExpressionOf| + |SimpleFortranProgram| |SquareFreeQuasiComponentPackage| + |SquareFreeRegularTriangularSetGcdPackage| + |SquareFreeRegularTriangularSetCategory| + |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| + |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |SignatureAst| + |ElementaryFunctionSign| |RationalFunctionSign| |Signature| + |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| + |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| + |SmithNormalForm| |SparseMultivariatePolynomial| + |SparseMultivariateTaylorSeries| + |SquareFreeNormalizedTriangularSetCategory| + |PolynomialSolveByFormulas| |RadicalSolvePackage| + |TransSolvePackageService| |TransSolvePackage| |SortPackage| + |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| |SpadAstExports| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| - |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| - |SparseTable| |StepThrough| |StreamInfiniteProduct| |Stream| - |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StringCategory| - |String| |StringTable| |StreamTaylorSeriesOperations| - |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| - |SubResultantPackage| |SubSpace| |SuchThat| |SuchThatAst| - |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| - |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| - |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| + |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| + |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| + |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |Stream| + |StringCategory| |String| |StringTable| |StreamTaylorSeriesOperations| + |StreamTranscendentalFunctionsNonCommutative| + |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| + |SuchThat| |SuchThatAst| |SparseUnivariateLaurentSeries| + |FunctionSpaceSum| |RationalFunctionSum| + |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| + |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| - |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemInteger| - |SystemNonNegativeInteger| |SystemSolvePackage| |System| |TableauxBumpers| - |Table| |Tableau| |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat| |TexFormat1| - |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| + |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| + |SystemInteger| |SystemNonNegativeInteger| |SystemSolvePackage| + |System| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| + |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| + |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| + |TopLevelThreeSpace| |TranscendentalFunctionCategory&| + |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| |TriangularMatrixOperations| - |TranscendentalManipulations| |TaylorSeries| |TriangularSetCategory&| - |TriangularSetCategory| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| - |Type| |TypeAst| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| - |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UInt16| |UInt32| - |UInt8| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| - |UnivariateLaurentSeriesCategory| + |TranscendentalManipulations| |TriangularSetCategory&| + |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| + |Tuple| |TwoFactorize| |TypeAst| |Type| |UserDefinedPartialOrdering| + |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt8| + |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| - |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| |UniversalSegment| - |UniversalSegmentFunctions2| |UnivariatePolynomial| - |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| + |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| + |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| + |UnivariatePolynomialFunctions2| + |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| - |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialCategory&| - |UnivariatePolynomialCategory| |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| + |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| - |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| - |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| + |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| + |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| - |UnivariatePuiseuxSeriesConstructor| - |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| - |UnaryRecursiveAggregate| |UnivariateTaylorSeries| + |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| + |UnivariatePuiseuxSeriesWithExponentialSingularity| + |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| - |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesODESolver| - |UTSodetools| |UnionType| |Variable| |VectorCategory&| |VectorCategory| - |Vector| |VectorFunctions2| |ViewportPackage| |TwoDimensionalViewport| - |ThreeDimensionalViewport| |ViewDefaultsPackage| |Void| |VectorSpace&| - |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| - |WhereAst| |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| - |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| - |ExtensionField| |XFreeAlgebra| |XPBWPolynomial| |XPolynomial| - |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| + |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| + |UnivariateTaylorSeriesODESolver| |UTSodetools| |UnionType| |Variable| + |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| + |TwoDimensionalViewport| |ThreeDimensionalViewport| + |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| + |VectorSpace| |WeierstrassPreparation| + |WildFunctionFieldIntegralBasis| |WhereAst| |WhileAst| + |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| + |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| + |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| + |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| - |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| - |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |size?| - |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| - |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| - |rightRank| |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| - |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| - |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| - |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| - |radicalOfLeftTraceForm| |showTypeInOutput| |obj| |dom| |objectOf| |domainOf| - |any| |applyRules| |localUnquote| |arbitrary| |setColumn!| |setRow!| - |oneDimensionalArray| |associatedSystem| |uncouplingMatrices| - |associatedEquations| |arrayStack| |setButtonValue| |setAttributeButtonStep| - |resetAttributeButtons| |getButtonValue| |decrease| |increase| |morphism| - |balancedFactorisation| |mapDown!| |mapUp!| |setleaves!| |balancedBinaryTree| - |sylvesterMatrix| |bezoutMatrix| |bezoutResultant| |bezoutDiscriminant| - |bfEntry| |bfKeys| |inspect| |extract!| |bag| |binding| |test| |setProperties| - |setProperty| |deleteProperty!| |has?| |comparison| |equality| |nary?| - |unary?| |nullary?| |properties| |derivative| |constantOperator| - |constantOpIfCan| |integerBound| |setright!| |setleft!| - |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| - |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| |byte| - |setLength!| |capacity| |byteBuffer| |unknownEndian| |bigEndian| - |littleEndian| |subtractIfCan| |setPosition| - |generalizedContinuumHypothesisAssumed| - |generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel| - |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |parents| - |principalAncestors| |exportedOperators| |alphanumeric| |alphabetic| - |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?| |upperCase?| - |alphabetic?| |hexDigit?| |digit?| |escape| |char| |ord| |mkIntegral| - |radPoly| |rootPoly| |goodPoint| |chvar| |removeDuplicates| |find| |e| - |clipParametric| |clipWithRanges| |numberOfHues| |yellow| |iifact| |iibinom| - |iiperm| |iipow| |iidsum| |iidprod| |ipow| |factorial| |multinomial| - |permutation| |stirling1| |stirling2| |summation| |factorials| |mkcomm| - |polarCoordinates| |complex| |imaginary| |solid| |solid?| |denominators| - |numerators| |convergents| |approximants| |reducedForm| |partialQuotients| - |partialDenominators| |partialNumerators| |reducedContinuedFraction| |push| - |bindings| |cartesian| |polar| |cylindrical| |spherical| |parabolic| - |parabolicCylindrical| |paraboloidal| |ellipticCylindrical| - |prolateSpheroidal| |oblateSpheroidal| |bipolar| |bipolarCylindrical| - |toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros| - |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| - |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| - |computeCycleLength| |computeCycleEntry| |findConstructor| |arguments| - |operations| |dualSignature| |kind| |package| |domain| |category| |coerceP| - |powerSum| |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath| - |SFunction| |skewSFunction| |cyclotomicDecomposition| - |cyclotomicFactorization| |rangeIsFinite| |functionIsContinuousAtEndPoints| - |functionIsOscillatory| |changeName| |exprHasWeightCosWXorSinWX| - |exprHasAlgebraicWeight| |exprHasLogarithmicWeights| - |combineFeatureCompatibility| |sparsityIF| |stiffnessAndStabilityFactor| - |stiffnessAndStabilityOfODEIF| |systemSizeIF| |expenseOfEvaluationIF| - |accuracyIF| |intermediateResultsIF| |subscriptedVariables| |central?| - |elliptic?| |qsetelt| |doubleResultant| |distdfact| |separateDegrees| - |trace2PowMod| |tracePowMod| |irreducible?| |decimal| |innerint| - |exteriorDifferential| |totalDifferential| |homogeneous?| |leadingBasisTerm| - |ignore?| |computeInt| |checkForZero| |logGamma| |hypergeometric0F1| |rotatez| - |rotatey| |rotatex| |identity| |dictionary| |dioSolve| |directProduct| - |newLine| |copies| |say| |sayLength| |setnext!| |setprevious!| |next| - |previous| |datalist| |shanksDiscLogAlgorithm| |showSummary| |reflect| |reify| - |constructor| |separant| |initial| |leader| |isobaric?| |weights| - |differentialVariables| |extractBottom!| |extractTop!| |insertBottom!| - |insertTop!| |bottom!| |top!| |dequeue| |makeObject| |recolor| |drawComplex| - |drawComplexVectorField| |setRealSteps| |setImagSteps| |setClipValue| |draw| - |option?| |range| |colorFunction| |curveColor| |pointColor| |clip| - |clipBoolean| |style| |toScale| |pointColorPalette| |curveColorPalette| - |var1Steps| |var2Steps| |space| |tubePoints| |tubeRadius| |option| |weight| - |makeVariable| |finiteBound| |sortConstraints| |sumOfSquares| |splitLinear| - |simpleBounds?| |linearMatrix| |linearPart| |nonLinearPart| |quadratic?| - |changeNameToObjf| |optAttributes| |Nul| |exponents| |iisqrt2| |iisqrt3| - |iiexp| |iilog| |iisin| |iicos| |iitan| |iicot| |iisec| |iicsc| |iiasin| - |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| |iisinh| |iicosh| |iitanh| - |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| |iiatanh| |iiacoth| |iiasech| - |iiacsch| |specialTrigs| |localReal?| |rischNormalize| |realElementary| - |validExponential| |rootNormalize| |tanQ| |callForm?| |getIdentifier| - |getConstant| |type| |select!| |delete!| |sn| |cn| |dn| |sncndn| |qsetelt!| - |categoryFrame| |currentEnv| |setProperties!| |getProperties| |setProperty!| - |getProperty| |scopes| |eigenvalues| |eigenvector| |generalizedEigenvector| - |generalizedEigenvectors| |eigenvectors| |factorAndSplit| |rightOne| |leftOne| - |rightZero| |leftZero| |swap| |error| |minPoly| |freeOf?| |operators| |tower| - |kernels| |mainKernel| |distribute| |subst| |functionIsFracPolynomial?| - |problemPoints| |zerosOf| |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| - |ocf2ocdf| |socf2socdf| |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| - |numberOfOperations| |edf2efi| |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| - |vedf2vef| |df2st| |f2st| |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| - |measure2Result| |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| - |fi2df| |mat| |neglist| |multiEuclidean| |extendedEuclidean| |euclideanSize| - |sizeLess?| |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| - |tubePlot| |exponentialOrder| |completeEval| |lowerPolynomial| - |raisePolynomial| |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| - |binomThmExpt| |pomopo!| |mapExponents| |linearAssociatedLog| - |linearAssociatedOrder| |linearAssociatedExp| |createNormalElement| - |setLabelValue| |getCode| |printCode| |code| |operation| |common| - |printStatement| |save| |stop| |block| |cond| |returns| |call| |comment| - |continue| |goto| |repeatUntilLoop| |whileLoop| |forLoop| |sin?| |zeroVector| - |zeroSquareMatrix| |identitySquareMatrix| |lSpaceBasis| |finiteBasis| - |principal?| |divisor| |useNagFunctions| |rationalPoints| |nonSingularModel| - |algSplitSimple| |hyperelliptic| |elliptic| |integralDerivationMatrix| - |integralRepresents| |integralCoordinates| |yCoordinates| - |inverseIntegralMatrixAtInfinity| |integralMatrixAtInfinity| - |inverseIntegralMatrix| |integralMatrix| |reduceBasisAtInfinity| - |normalizeAtInfinity| |complementaryBasis| |integral?| |integralAtInfinity?| - |integralBasisAtInfinity| |ramified?| |ramifiedAtInfinity?| |singular?| - |singularAtInfinity?| |branchPoint?| |branchPointAtInfinity?| |rationalPoint?| - |absolutelyIrreducible?| |genus| |getZechTable| |createZechTable| - |createMultiplicationTable| |createMultiplicationMatrix| - |createLowComplexityTable| |createLowComplexityNormalBasis| - |representationType| |createPrimitiveElement| |tableForDiscreteLogarithm| - |factorsOfCyclicGroupSize| |sizeMultiplication| |getMultiplicationMatrix| - |getMultiplicationTable| |primitive?| |numberOfIrreduciblePoly| - |numberOfPrimitivePoly| |numberOfNormalPoly| |createIrreduciblePoly| - |createPrimitivePoly| |createNormalPoly| |createNormalPrimitivePoly| - |createPrimitiveNormalPoly| |nextIrreduciblePoly| |nextPrimitivePoly| - |nextNormalPoly| |nextNormalPrimitivePoly| |nextPrimitiveNormalPoly| - |leastAffineMultiple| |reducedQPowers| |rootOfIrreduciblePoly| |write!| - |read!| |iomode| |close!| |reopen!| |open| |rightUnit| |leftUnit| - |rightMinimalPolynomial| |leftMinimalPolynomial| |associatorDependence| - |lieAlgebra?| |jordanAlgebra?| |noncommutativeJordanAlgebra?| - |jordanAdmissible?| |lieAdmissible?| |jacobiIdentity?| |powerAssociative?| - |alternative?| |flexible?| |rightAlternative?| |leftAlternative?| - |antiAssociative?| |associative?| |antiCommutative?| |commutative?| - |rightCharacteristicPolynomial| |leftCharacteristicPolynomial| |rightNorm| - |leftNorm| |rightTrace| |leftTrace| |someBasis| |sort!| |copyInto!| |sorted?| - |LiePoly| |quickSort| |heapSort| |shellSort| |outputSpacing| |outputGeneral| - |outputFixed| |outputFloating| |exp1| |log10| |log2| |rationalApproximation| - |relerror| |complexSolve| |complexRoots| |realRoots| |leadingTerm| |writable?| - |readable?| |exists?| |extension| |directory| |filename| |shallowExpand| - |deepExpand| |clearFortranOutputStack| |showFortranOutputStack| - |popFortranOutputStack| |pushFortranOutputStack| |topFortranOutputStack| - |setFormula!| |formula| |linkToFortran| |setLegalFortranSourceExtensions| - |fracPart| |polyPart| |fullPartialFraction| |primeFrobenius| |discreteLog| - |decreasePrecision| |increasePrecision| |bits| |unitNormalize| |unit| - |flagFactor| |sqfrFactor| |primeFactor| |nthFlag| |nthExponent| - |irreducibleFactor| |nilFactor| |regularRepresentation| |traceMatrix| - |randomLC| |minimize| |module| |rightRegularRepresentation| - |leftRegularRepresentation| |rightTraceMatrix| |leftTraceMatrix| - |rightDiscriminant| |leftDiscriminant| |represents| |mergeFactors| |isMult| - |applyQuote| |ground| |ground?| |exprToXXP| |exprToUPS| |exprToGenUPS| - |localAbs| |universe| |complement| |cardinality| |internalIntegrate0| - |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| |newReduc| |logical?| - |character?| |doubleComplex?| |complex?| |double?| |ffactor| |qfactor| - |UP2ifCan| |anfactor| |fortranCharacter| |fortranDoubleComplex| - |fortranComplex| |fortranLogical| |fortranInteger| |fortranDouble| - |fortranReal| |external?| |scalarTypeOf| |fortranCarriageReturn| - |fortranLiteral| |fortranLiteralLine| |processTemplate| |makeFR| - |musserTrials| |stopMusserTrials| |numberOfFactors| |modularFactor| - |useSingleFactorBound?| |useSingleFactorBound| |useEisensteinCriterion?| - |useEisensteinCriterion| |eisensteinIrreducible?| - |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| - |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| - |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| - |factorsOfDegree| |pascalTriangle| |rangePascalTriangle| |sizePascalTriangle| - |fillPascalTriangle| |safeCeiling| |safeFloor| |safetyMargin| |sumSquares| - |euclideanNormalForm| |euclideanGroebner| |factorGroebnerBasis| - |groebnerFactorize| |credPol| |redPol| |gbasis| |critT| |critM| |critB| - |critBonD| |critMTonD1| |critMonD1| |redPo| |hMonic| |updatF| |sPol| |updatD| - |minGbasis| |lepol| |prinshINFO| |prindINFO| |fprindINFO| |prinpolINFO| - |prinb| |critpOrder| |makeCrit| |virtualDegree| |lcm| - |conditionsForIdempotents| |genericRightDiscriminant| |genericRightTraceForm| - |genericLeftDiscriminant| |genericLeftTraceForm| |genericRightNorm| - |genericRightTrace| |genericRightMinimalPolynomial| |rightRankPolynomial| - |genericLeftNorm| |genericLeftTrace| |genericLeftMinimalPolynomial| - |leftRankPolynomial| |generic| |rightUnits| |leftUnits| |compBound| |tablePow| - |solveid| |testModulus| |HenselLift| |completeHensel| |multMonom| |build| - |leadingIndex| |leadingExponent| |GospersMethod| |nextSubsetGray| - |firstSubsetGray| |clipPointsDefault| |drawToScale| |adaptive| |figureUnits| - |putColorInfo| |appendPoint| |component| |ranges| |pointLists| - |makeGraphImage| |graphImage| |groebSolve| |testDim| |genericPosition| |lfunc| - |inHallBasis?| |reorder| |parameters| |headAst| |heap| |gcdprim| |gcdcofact| - |gcdcofactprim| |lintgcd| |hex| |parts| |count| |every?| |any?| |map!| |host| - |trueEqual| |factorList| |listConjugateBases| |matrixGcd| |divideIfCan!| - |leastPower| |idealiser| |idealiserMatrix| |moduleSum| |mapUnivariate| - |mapUnivariateIfCan| |mapMatrixIfCan| |mapBivariate| |fullDisplay| - |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal| - |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?| - |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp| - |contract| |leadingSupport| |shrinkable| |physicalLength!| |physicalLength| - |flexibleArray| |elseBranch| |thenBranch| |generalizedInverse| |imports| - |sequence| |iterationVar| |readBytes!| |readUInt32!| |readInt32!| - |readUInt16!| |readInt16!| |readUInt8!| |readInt8!| |readByte!| |setFieldInfo| - |pol| |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup| |normal?| |basis| - |normalElement| |minimalPolynomial| |position!| |eof?| |inputBinaryFile| - |increment| |incrementBy| |charpol| |solve1| |innerEigenvectors| |compile| - |declare| |parseString| |unparse| |flatten| |lambda| |binary| |packageCall| - |interpret| |innerSolve1| |innerSolve| |makeEq| |modularGcdPrimitive| - |modularGcd| |reduction| |signAround| |invmod| |powmod| |mulmod| |submod| - |addmod| |mask| |dec| |inc| |symmetricRemainder| |positiveRemainder| |bit?| - |algint| |algintegrate| |palgintegrate| |palginfieldint| |bitLength| |bitCoef| - |bitTruth| |contains?| |inf| |qinterval| |interval| |unit?| |associates?| - |unitCanonical| |unitNormal| |lfextendedint| |lflimitedint| |lfinfieldint| - |lfintegrate| |lfextlimint| |BasicMethod| |PollardSmallFactor| |showTheFTable| - |clearTheFTable| |fTable| |showAttributes| |entry| |palgint0| |palgextint0| - |palglimint0| |palgRDE0| |palgLODE0| |chineseRemainder| |divisors| |eulerPhi| - |fibonacci| |harmonic| |jacobi| |moebiusMu| |numberOfDivisors| |sumOfDivisors| - |sumOfKthPowerDivisors| |HermiteIntegrate| |palgint| |palgextint| |palglimint| - |palgRDE| |palgLODE| |splitConstant| |pmComplexintegrate| |pmintegrate| - |infieldint| |extendedint| |limitedint| |integerIfCan| |internalIntegrate| - |infieldIntegrate| |limitedIntegrate| |extendedIntegrate| |varselect| |kmax| - |ksec| |vark| |removeConstantTerm| |mkPrim| |intPatternMatch| |primintegrate| - |expintegrate| |tanintegrate| |primextendedint| |expextendedint| - |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| - |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| - |inverseLaplace| |inputOutputBinaryFile| |bothWays| |input| |resolve| |bytes| - |ip4Address| |iprint| |elem?| |notelem| |logpart| |ratpart| |mkAnswer| - |perfectNthPower?| |perfectNthRoot| |approxNthRoot| |perfectSquare?| - |perfectSqrt| |approxSqrt| |generateIrredPoly| |complexExpand| - |complexIntegrate| |dimensionOfIrreducibleRepresentation| - |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| - |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| - |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| - |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| - |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| GF2FG FG2F F2FG - |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| - |indices| |index?| |entries| |categories| |search| |key?| |symbolIfCan| - |kernel| |argument| |constantKernel| |constantIfCan| |kovacic| |true| - |unknown| |false| |laplace| |trailingCoefficient| |normalizeIfCan| |polCase| - |distFact| |identification| |LyndonCoordinates| |LyndonBasis| - |zeroDimensional?| |fglmIfCan| |groebner| |lexTriangular| - |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| |Si| |Ei| - |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| |anticoord| - |intcompBasis| |choosemon| |transform| |pack!| |library| |complexLimit| - |limit| |linearlyDependent?| |linearDependence| |solveLinear| |reducedSystem| - |setDifference| |setIntersection| |setUnion| |append| |null| |nil| - |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| - |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |makeMulti| |makeTerm| - |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| - |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ - |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| - |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| - |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| - |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| - |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| - |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| - |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| - |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| - |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| - |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| - |rightScalarTimes!| |times!| |power!| |nothing| |just| |gradient| |divergence| - |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| - |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| - |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| - |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| - |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| - |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| - |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| - |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| - |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| - |derivationCoordinates| |generator| |one?| |splitSquarefree| |normalDenom| - |reshape| |totalfract| |pushdterm| |pushucoef| |pushuconst| - |numberOfMonomials| |multiset| |systemCommand| |mergeDifference| - |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| - |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |c02aff| |c02agf| |c05adf| - |c05nbf| |c05pbf| |c06eaf| |c06ebf| |c06ecf| |c06ekf| |c06fpf| |c06fqf| - |c06frf| |c06fuf| |c06gbf| |c06gcf| |c06gqf| |c06gsf| |d01ajf| |d01akf| - |d01alf| |d01amf| |d01anf| |d01apf| |d01aqf| |d01asf| |d01bbf| |d01fcf| - |d01gaf| |d01gbf| |d02bbf| |d02bhf| |d02cjf| |d02ejf| |d02gaf| |d02gbf| - |d02kef| |d02raf| |d03edf| |d03eef| |d03faf| |e01baf| |e01bef| |e01bff| - |e01bgf| |e01bhf| |e01daf| |e01saf| |e01sbf| |e01sef| |e01sff| |e02adf| - |e02aef| |e02agf| |e02ahf| |e02ajf| |e02akf| |e02baf| |e02bbf| |e02bcf| - |e02bdf| |e02bef| |e02daf| |e02dcf| |e02ddf| |e02def| |e02dff| |e02gaf| - |e02zaf| |e04dgf| |e04fdf| |e04gcf| |e04jaf| |e04mbf| |e04naf| |e04ucf| - |e04ycf| |f01brf| |f01bsf| |f01maf| |f01mcf| |f01qcf| |f01qdf| |f01qef| - |f01rcf| |f01rdf| |f01ref| |f02aaf| |f02abf| |f02adf| |f02aef| |f02aff| - |f02agf| |f02ajf| |f02akf| |f02awf| |f02axf| |f02bbf| |f02bjf| |f02fjf| - |f02wef| |f02xef| |f04adf| |f04arf| |f04asf| |f04atf| |f04axf| |f04faf| - |f04jgf| |f04maf| |f04mbf| |f04mcf| |f04qaf| |f07adf| |f07aef| |f07fdf| - |f07fef| |s01eaf| |s13aaf| |s13acf| |s13adf| |s14aaf| |s14abf| |s14baf| - |s15adf| |s15aef| |s17acf| |s17adf| |s17aef| |s17aff| |s17agf| |s17ahf| - |s17ajf| |s17akf| |s17dcf| |s17def| |s17dgf| |s17dhf| |s17dlf| |s18acf| - |s18adf| |s18aef| |s18aff| |s18dcf| |s18def| |s19aaf| |s19abf| |s19acf| - |s19adf| |s20acf| |s20adf| |s21baf| |s21bbf| |s21bcf| |s21bdf| - |fortranCompilerName| |fortranLinkerArgs| |aspFilename| |dimensionsOf| - |checkPrecision| |restorePrecision| |antiCommutator| |commutator| |associator| - |complexEigenvalues| |complexEigenvectors| |isConnected?| |connectTo| |shift| - |normalizedAssociate| |normalize| |outputArgs| |normInvertible?| |normFactors| - |npcoef| |listexp| |characteristicPolynomial| |realEigenvalues| - |realEigenvectors| |halfExtendedResultant2| |halfExtendedResultant1| - |extendedResultant| |subResultantsChain| |lazyPseudoQuotient| - |lazyPseudoRemainder| |bernoulliB| |eulerE| |numeric| |complexNumeric| - |numericIfCan| |complexNumericIfCan| |FormatArabic| |ScanArabic| |FormatRoman| - |ScanRoman| |ScanFloatIgnoreSpaces| |ScanFloatIgnoreSpacesIfCan| - |numericalIntegration| |rk4| |rk4a| |rk4qc| |rk4f| |aromberg| |asimpson| - |atrapezoidal| |romberg| |simpson| |trapezoidal| |rombergo| |simpsono| - |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| |imagi| |octon| |ODESolve| - |constDsolve| |showTheIFTable| |clearTheIFTable| |keys| |iFTable| - |showIntensityFunctions| |expint| |diff| |algDsolve| |denomLODE| - |indicialEquations| |indicialEquation| |denomRicDE| |leadingCoefficientRicDE| - |constantCoefficientRicDE| |changeVar| |ratDsolve| - |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| - |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| - |factors| |nthFactor| |nthExpon| |overlap| |hcrf| |hclf| |lexico| |OMmakeConn| - |OMcloseConn| |OMconnInDevice| |OMconnOutDevice| |OMconnectTCP| |OMbindTCP| - |OMopenFile| |OMopenString| |OMclose| |OMsetEncoding| |OMputApp| |OMputAtp| - |OMputAttr| |OMputBind| |OMputBVar| |OMputError| |OMputObject| |OMputEndApp| - |OMputEndAtp| |OMputEndAttr| |OMputEndBind| |OMputEndBVar| |OMputEndError| - |OMputEndObject| |OMputInteger| |OMputFloat| |OMputVariable| |OMputString| - |OMputSymbol| |OMgetApp| |OMgetAtp| |OMgetAttr| |OMgetBind| |OMgetBVar| - |OMgetError| |OMgetObject| |OMgetEndApp| |OMgetEndAtp| |OMgetEndAttr| - |OMgetEndBind| |OMgetEndBVar| |OMgetEndError| |OMgetEndObject| |OMgetInteger| - |OMgetFloat| |OMgetVariable| |OMgetString| |OMgetSymbol| |OMgetType| - |OMencodingBinary| |OMencodingSGML| |OMencodingXML| |OMencodingUnknown| - |omError| |errorInfo| |errorKind| |OMReadError?| |OMUnknownSymbol?| - |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread| |OMreadFile| - |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?| |OMsupportsSymbol?| - |OMunhandledSymbol| |OMreceive| |OMsend| |OMserve| |infinity| |makeop| - |opeval| |evaluateInverse| |evaluate| |conjug| |adjoint| |arity| |getDatabase| - |numericalOptimization| |optimize| |goodnessOfFit| |whatInfinity| |infinite?| - |finite?| |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex| - |min| |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient| - |rightRemainder| |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| - |leftExactQuotient| |leftRemainder| |leftQuotient| |times| |apply| - |monicLeftDivide| |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| - |laguerreL| |legendreP| |outputList| |writeBytes!| |writeUInt8!| |writeInt8!| - |writeByte!| |isOpen?| |outputBinaryFile| |quo| |rem| |div| >= > ~= - |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren| |bracket| - |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper| |presub| - |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| |infix?| - |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| |hspace| - |superHeight| |subHeight| |height| |width| |doubleFloatFormat| |messagePrint| - |message| |members| |padecf| |pade| |root| |quotientByP| |moduloP| |modulus| - |digits| |continuedFraction| |pair| |light| |pastel| |bright| |dim| |dark| - |getSyntaxFormsFromFile| |surface| |coordinate| |partitions| |conjugates| - |shuffle| |shufflein| |sequences| |permutations| |lists| |atoms| |makeResult| - |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| |getMatch| |failed| - |failed?| |optpair| |getBadValues| |resetBadValues| |hasTopPredicate?| - |topPredicate| |setTopPredicate| |patternVariable| |withPredicates| - |setPredicates| |predicates| |hasPredicate?| |optional?| |multiple?| - |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| |satisfy?| - |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| |PDESolve| - |leftFactor| |rightFactorCandidate| |measure| D |ptree| |coerceImages| - |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| - |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| - |cycles| |cycle| |initializeGroupForWordProblem| <= < |movedPoints| - |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| - |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| - |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| - |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| - |charthRoot| |conditionP| |solveLinearPolynomialEquation| - |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| - |gcdPolynomial| |torsion?| |torsionIfCan| |getGoodPrime| |badNum| |mix| - |doubleDisc| |polyred| |padicFraction| |padicallyExpand| - |numberOfFractionalTerms| |nthFractionalTerm| |firstNumer| |firstDenom| - |compactFraction| |partialFraction| |gcdPrimitive| |symmetricGroup| - |alternatingGroup| |abelianGroup| |cyclicGroup| |dihedralGroup| |mathieu11| - |mathieu12| |mathieu22| |mathieu23| |mathieu24| |janko2| |rubiksGroup| - |youngGroup| |lexGroebner| |totalGroebner| |expressIdealMember| - |principalIdeal| |LagrangeInterpolation| |psolve| |wrregime| |rdregime| - |bsolve| |dmp2rfi| |se2rfi| |pr2dmp| |hasoln| |ParCondList| |redpps| |B1solve| - |factorset| |maxrank| |minrank| |minset| |nextSublist| |overset?| |ParCond| - |redmat| |regime| |sqfree| |inconsistent?| |debug| |numFunEvals| |setAdaptive| - |adaptive?| |setScreenResolution| |screenResolution| |setMaxPoints| - |maxPoints| |setMinPoints| |minPoints| |parametric?| |plotPolar| |debug3D| - |numFunEvals3D| |setAdaptive3D| |adaptive3D?| |setScreenResolution3D| - |screenResolution3D| |setMaxPoints3D| |maxPoints3D| |setMinPoints3D| - |minPoints3D| |tValues| |tRange| |plot| |pointPlot| |calcRanges| |assert| - |optional| |multiple| |fixPredicate| |patternMatch| |patternMatchTimes| - |bernoulli| |chebyshevT| |chebyshevU| |cyclotomic| |euler| |fixedDivisor| - |laguerre| |legendre| |dmpToHdmp| |hdmpToDmp| |pToHdmp| |hdmpToP| |dmpToP| - |pToDmp| |sylvesterSequence| |sturmSequence| |boundOfCauchy| - |sturmVariationsOf| |lazyVariations| |content| |primitiveMonomials| - |totalDegree| |minimumDegree| |monomials| |isPlus| |isTimes| |isExpt| - |isPower| |rroot| |qroot| |froot| |nthr| |port| |firstUncouplingMatrix| - |integral| |primitiveElement| |nextPrime| |prevPrime| |primes| |print| - |selectsecond| |selectfirst| |makeprod| |property| |equivOperands| |equiv?| - |impliesOperands| |implies?| |orOperands| |or?| |andOperands| |and?| - |notOperand| |not?| |variable?| |term| |term?| |equiv| |implies| |or| |and| - |merge!| |max| |resultantEuclidean| |semiResultantEuclidean2| - |semiResultantEuclidean1| |indiceSubResultant| |indiceSubResultantEuclidean| - |semiIndiceSubResultantEuclidean| |degreeSubResultant| - |degreeSubResultantEuclidean| |semiDegreeSubResultantEuclidean| - |lastSubResultantEuclidean| |semiLastSubResultantEuclidean| - |subResultantGcdEuclidean| |semiSubResultantGcdEuclidean2| - |semiSubResultantGcdEuclidean1| |discriminantEuclidean| - |semiDiscriminantEuclidean| |chainSubResultants| |schema| |resultantReduit| - |resultantReduitEuclidean| |semiResultantReduitEuclidean| |divide| |Lazard| - |Lazard2| |nextsousResultant2| |resultantnaif| |resultantEuclideannaif| - |semiResultantEuclideannaif| |pdct| |powers| |partition| |complete| |pole?| - |monomial| |leadingMonomial| |zRange| |yRange| |xRange| |listBranches| - |triangular?| |rewriteIdealWithRemainder| |rewriteIdealWithHeadRemainder| - |remainder| |headRemainder| |roughUnitIdeal?| |roughEqualIdeals?| - |roughSubIdeal?| |roughBase?| |trivialIdeal?| |sort| |collectUpper| |collect| - |collectUnder| |mainVariable?| |mainVariables| |removeSquaresIfCan| - |unprotectedRemoveRedundantFactors| |removeRedundantFactors| - |certainlySubVariety?| |possiblyNewVariety?| |probablyZeroDim?| - |selectPolynomials| |selectOrPolynomials| |selectAndPolynomials| - |quasiMonicPolynomials| |univariate?| |univariatePolynomials| |linear?| - |linearPolynomials| |bivariate?| |bivariatePolynomials| - |removeRoughlyRedundantFactorsInPols| |removeRoughlyRedundantFactorsInPol| - |interReduce| |roughBasicSet| |crushedSet| - |rewriteSetByReducingWithParticularGenerators| - |rewriteIdealWithQuasiMonicGenerators| |squareFreeFactors| - |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInContents| - |removeRedundantFactorsInContents| |removeRedundantFactorsInPols| - |irreducibleFactors| |lazyIrreducibleFactors| - |removeIrreducibleRedundantFactors| |normalForm| |changeBase| - |companionBlocks| |xCoord| |yCoord| |zCoord| |rCoord| |thetaCoord| |phiCoord| - |color| |hue| |shade| |nthRootIfCan| |expIfCan| |logIfCan| |sinIfCan| - |cosIfCan| |tanIfCan| |cotIfCan| |secIfCan| |cscIfCan| |asinIfCan| |acosIfCan| - |atanIfCan| |acotIfCan| |asecIfCan| |acscIfCan| |sinhIfCan| |coshIfCan| - |tanhIfCan| |cothIfCan| |sechIfCan| |cschIfCan| |asinhIfCan| |acoshIfCan| - |atanhIfCan| |acothIfCan| |asechIfCan| |acschIfCan| |pushdown| |pushup| - |reducedDiscriminant| |idealSimplify| |definingInequation| |definingEquations| - |setStatus| |quasiAlgebraicSet| |radicalSimplify| |random| |denominator| - |numerator| |denom| |numer| |quadraticForm| |back| |front| |rotate!| - |dequeue!| |enqueue!| |quatern| |imagK| |imagJ| |imagI| |conjugate| |queue| - |nthRoot| |fractRadix| |wholeRadix| |cycleRagits| |prefixRagits| |fractRagits| - |wholeRagits| |radix| |randnum| |reseed| |seed| |rational| |rational?| - |rationalIfCan| |setvalue!| |setchildren!| |node?| |child?| |distance| - |leaves| |nodes| |rename| |rename!| |mainValue| |mainDefiningPolynomial| - |mainForm| |sqrt| |rischDE| |rischDEsys| |monomRDE| |baseRDE| |polyRDE| - |monomRDEsys| |baseRDEsys| |weighted| |rdHack1| |operator| |midpoint| - |midpoints| |realZeros| |mainCharacterization| |algebraicOf| |ReduceOrder| = - |setref| |deref| |ref| |radicalEigenvectors| |radicalEigenvector| - |radicalEigenvalues| |eigenMatrix| |normalise| |gramschmidt| - |orthonormalBasis| |antisymmetricTensors| |createGenericMatrix| - |symmetricTensors| |tensorProduct| |permutationRepresentation| - |completeEchelonBasis| |createRandomElement| |cyclicSubmodule| - |standardBasisOfCyclicSubmodule| |areEquivalent?| |isAbsolutelyIrreducible?| - |meatAxe| |scanOneDimSubspaces| |double| |expt| |lift| |showArrayValues| - |showScalarValues| |solveRetract| |variables| |mainVariable| |univariate| - |multivariate| |uniform01| |normal01| |exponential1| |chiSquare1| |normal| - |exponential| |chiSquare| F |t| |factorFraction| |componentUpperBound| |blue| - |green| |red| |whitePoint| |uniform| |binomial| |poisson| |geometric| - |ridHack1| |interpolate| |nullSpace| |nullity| |rank| |rowEchelon| |column| - |row| |qelt| |ncols| |nrows| |maxColIndex| |minColIndex| |maxRowIndex| - |minRowIndex| |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| - |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart| - |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right| - |left| |roman| |recoverAfterFail| |showTheRoutinesTable| |deleteRoutine!| - |getExplanations| |getMeasure| |changeMeasure| |changeThreshhold| - |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| - |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| - |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| - |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| - |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| - |subResultantChain| |halfExtendedSubResultantGcd2| - |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| - |exactQuotient| |primPartElseUnitCanonical!| |primPartElseUnitCanonical| - |retract| |retractIfCan| |lazyResidueClass| |monicModulo| |lazyPseudoDivide| - |lazyPremWithDefault| |lazyPquo| |lazyPrem| |pquo| |prem| |supRittWu?| - |RittWuCompare| |mainMonomials| |mainCoefficients| |leastMonomial| - |mainMonomial| |quasiMonic?| |monic?| |leadingCoefficient| |deepestInitial| - |iteratedInitials| |deepestTail| |head| |mdeg| |mvar| |iterators| - |relativeApprox| |rootOf| |allRootsOf| |definingPolynomial| |positive?| - |negative?| |zero?| |augment| |lastSubResultant| |lastSubResultantElseSplit| - |invertibleSet| |invertible?| |invertibleElseSplit?| - |purelyAlgebraicLeadingMonomial?| |algebraicCoefficients?| - |purelyTranscendental?| |purelyAlgebraic?| |prepareSubResAlgo| - |internalLastSubResultant| |integralLastSubResultant| |toseLastSubResultant| - |toseInvertible?| |toseInvertibleSet| |toseSquareFreePart| |expression| - |quotedOperators| |pattern| |suchThat| |rule| |rules| |ruleset| |rur| |create| - |clearCache| |cache| |enterInCache| |currentCategoryFrame| |currentScope| - |pushNewContour| |findBinding| |contours| |structuralConstants| |coordinates| - |bounds| |equation| |incr| |high| |low| |hi| |lo| BY |body| |union| |subset?| - |symmetricDifference| |difference| |intersect| |set| |brace| |part?| |latex| - |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| - |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| - |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| - |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| - |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| - |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| - |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| - |removeSuperfluousCases| |prepareDecompose| |branchIfCan| |startTableGcd!| - |stopTableGcd!| |startTableInvSet!| |stopTableInvSet!| - |stosePrepareSubResAlgo| |stoseInternalLastSubResultant| - |stoseIntegralLastSubResultant| |stoseLastSubResultant| - |stoseInvertible?sqfreg| |stoseInvertibleSetsqfreg| |stoseInvertible?reg| - |stoseInvertibleSetreg| |stoseInvertible?| |stoseInvertibleSet| - |stoseSquareFreePart| |coleman| |inverseColeman| |listYoungTableaus| - |makeYoungTableau| |nextColeman| |nextLatticePermutation| |nextPartition| - |numberOfImproperPartitions| |subSet| |unrankImproperPartitions0| - |unrankImproperPartitions1| |subresultantSequence| |SturmHabichtSequence| - |SturmHabichtCoefficients| |SturmHabicht| |countRealRoots| - |SturmHabichtMultiple| |countRealRootsMultiple| |source| |target| |signature| - |signatureAst| |Or| |And| |Not| |xor| |not| |depth| |top| |pop!| |push!| - |minordet| |determinant| |diagonalProduct| |trace| |diagonal| |diagonalMatrix| - |scalarMatrix| |hermite| |completeHermite| |smith| |completeSmith| - |diophantineSystem| |csubst| |particularSolution| |mapSolve| |linear| - |quadratic| |cubic| |quartic| |aLinear| |aQuadratic| |aCubic| |aQuartic| - |radicalSolve| |radicalRoots| |contractSolve| |decomposeFunc| |unvectorise| - |bubbleSort!| |insertionSort!| |check| |objects| |lprop| |llprop| |lllp| - |lllip| |lp| |mesh?| |mesh| |polygon?| |polygon| |closedCurve?| |closedCurve| - |curve?| |curve| |point?| |enterPointData| |composites| |components| - |numberOfComposites| |numberOfComponents| |create3Space| |parse| - |outputAsFortran| |outputAsScript| |outputAsTex| |abs| |Beta| |digamma| - |polygamma| |Gamma| |besselJ| |besselY| |besselI| |besselK| |airyAi| |airyBi| - |subNode?| |infLex?| |setEmpty!| |setStatus!| |setCondition!| |setValue!| - |copy| |status| |value| |empty?| |splitNodeOf!| |remove!| |remove| - |subNodeOf?| |nodeOf?| |result| |conditions| |updateStatus!| - |extractSplittingLeaf| |squareMatrix| |transpose| |rightTrim| |leftTrim| - |trim| |split| |position| |replace| |match?| |match| |substring?| |suffix?| - |prefix?| |upperCase!| |upperCase| |lowerCase!| |lowerCase| |KrullNumber| - |numberOfVariables| |algebraicDecompose| |transcendentalDecompose| - |internalDecompose| |decompose| |upDateBranches| |printInfo| |preprocess| - |internalZeroSetSplit| |internalAugment| |stack| |possiblyInfinite?| - |explicitlyFinite?| |nextItem| |init| |infiniteProduct| |evenInfiniteProduct| - |oddInfiniteProduct| |generalInfiniteProduct| |filterUntil| |filterWhile| - |generate| |showAll?| |showAllElements| |output| |cons| |delay| |findCycle| - |repeating?| |repeating| |exquo| |recip| |integers| |oddintegers| |int| - |mapmult| |deriv| |gderiv| |compose| |addiag| |lazyIntegrate| |nlde| |powern| - |mapdiv| |lazyGintegrate| |power| |sincos| |sinhcosh| |asin| |acos| |atan| - |acot| |asec| |acsc| |sinh| |cosh| |tanh| |coth| |sech| |csch| |asinh| |acosh| - |atanh| |acoth| |asech| |acsch| |subresultantVector| |primitivePart| - |pointData| |parent| |level| |extractProperty| |extractClosed| |extractIndex| - |extractPoint| |traverse| |defineProperty| |closeComponent| |modifyPoint| - |addPointLast| |addPoint2| |addPoint| |merge| |deepCopy| |shallowCopy| - |numberOfChildren| |children| |child| |birth| |internal?| |root?| |leaf?| - |rhs| |lhs| |construct| |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT - LT |list| |string| |argscript| |superscript| |subscript| |script| |scripts| - |scripted?| |name| |resetNew| |symFunc| |symbolTableOf| |argumentListOf| - |returnTypeOf| |printHeader| |returnType!| |argumentList!| |endSubProgram| - |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| - |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| - |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| - |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| - |solve| |triangularSystems| |loadNativeModule| |nativeModuleExtension| - |hostByteOrder| |hostPlatform| |rootDirectory| |bumprow| |bumptab| |bumptab1| - |untab| |bat1| |bat| |tab1| |tab| |lex| |slex| |inverse| |maxrow| |mr| - |tableau| |listOfLists| |tanSum| |tanAn| |tanNa| |table| |initTable!| - |printInfo!| |startStats!| |printStats!| |clearTable!| |usingTable?| - |printingInfo?| |makingStats?| |extractIfCan| |insert!| |interpretString| - |stripCommentsAndBlanks| |setPrologue!| |setTex!| |setEpilogue!| |prologue| - |new| |tex| |epilogue| |display| |endOfFile?| |readIfCan!| |readLineIfCan!| - |readLine!| |writeLine!| |sign| |nonQsign| |direction| |createThreeSpace| |pi| - |cyclicParents| |cyclicEqual?| |cyclicEntries| |cyclicCopy| |tree| |cyclic?| - |cos| |cot| |csc| |sec| |sin| |tan| |complexNormalize| |complexElementary| - |trigs| |real| |imag| |real?| |complexForm| |UpTriBddDenomInv| - |LowTriBddDenomInv| |simplify| |htrigs| |simplifyExp| |simplifyLog| - |expandPower| |expandLog| |cos2sec| |cosh2sech| |cot2trig| |coth2trigh| - |csc2sin| |csch2sinh| |sec2cos| |sech2cosh| |sin2csc| |sinh2csch| |tan2trig| - |tanh2trigh| |tan2cot| |tanh2coth| |cot2tan| |coth2tanh| |removeCosSq| - |removeSinSq| |removeCoshSq| |removeSinhSq| |expandTrigProducts| |fintegrate| - |coefficient| |coHeight| |extendIfCan| |algebraicVariables| - |zeroSetSplitIntoTriangularSystems| |zeroSetSplit| |reduceByQuasiMonic| - |collectQuasiMonic| |removeZero| |initiallyReduce| |headReduce| - |stronglyReduce| |rewriteSetWithReduction| |autoReduced?| |initiallyReduced?| - |headReduced?| |stronglyReduced?| |reduced?| |normalized?| |quasiComponent| - |initials| |basicSet| |infRittWu?| |getCurve| |listLoops| |closed?| |open?| - |setClosed| |tube| |point| |unitVector| |cosSinInfo| |loopPoints| |select| - |generalTwoFactor| |generalSqFr| |twoFactor| |setOrder| |getOrder| |less?| - |userOrdered?| |largest| |more?| |setVariableOrder| |getVariableOrder| - |resetVariableOrder| |prime?| |sample| |bitior| |bitand| |rationalFunction| - |taylorIfCan| |taylor| |removeZeroes| |taylorRep| |factor| |factorSquareFree| - |henselFact| |hasHi| |segment| SEGMENT |fmecg| |commonDenominator| - |clearDenominator| |splitDenominator| |monicRightFactorIfCan| - |rightFactorIfCan| |leftFactorIfCan| |monicDecomposeIfCan| - |monicCompleteDecompose| |divideIfCan| |noKaratsuba| |karatsubaOnce| - |karatsuba| |separate| |pseudoDivide| |pseudoQuotient| |composite| - |subResultantGcd| |resultant| |discriminant| |pseudoRemainder| |shiftLeft| - |shiftRight| |karatsubaDivide| |monicDivide| |divideExponents| |unmakeSUP| - |makeSUP| |vectorise| |eval| |extend| |approximate| |truncate| |order| - |center| |terms| |squareFreePart| |BumInSepFFE| |multiplyExponents| - |laurentIfCan| |laurent| |laurentRep| |rationalPower| |puiseux| |dominantTerm| - |limitPlus| |split!| |setlast!| |setrest!| |setelt| |setfirst!| |cycleSplit!| - |concat!| |cycleTail| |cycleLength| |cycleEntry| |third| |second| |tail| - |last| |rest| |elt| |first| |concat| |invmultisect| |multisect| |revert| - |generalLambert| |evenlambert| |oddlambert| |lambert| |lagrange| - |differentiate| |univariatePolynomial| |integrate| ** |polynomial| - |multiplyCoefficients| |quoByVar| |coefficients| |series| |stFunc1| |stFunc2| - |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| |mpsode| UP2UTS UTS2UP - LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| |outerProduct| |dot| - - |zero| + |vector| |scan| |reduce| |graphCurves| |drawCurves| |update| |show| - |scale| |connect| |region| |points| |units| |getGraph| |putGraph| |graphs| - |graphStates| |graphState| |makeViewport2D| |viewport2D| |getPickedPoints| - |key| |close| |write| |colorDef| |reset| |intensity| |lighting| |clipSurface| - |showClipRegion| |showRegion| |hitherPlane| |eyeDistance| |perspective| - |translate| |zoom| |rotate| |drawStyle| |outlineRender| |diagonals| |axes| - |controlPanel| |viewpoint| |dimensions| |title| |resize| |move| |options| - |modifyPointData| |subspace| |makeViewport3D| |viewport3D| |viewDeltaYDefault| - |viewDeltaXDefault| |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| - |pointColorDefault| |lineColorDefault| |axesColorDefault| |unitsColorDefault| - |pointSizeDefault| |viewPosDefault| |viewSizeDefault| |viewDefaults| - |viewWriteDefault| |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| - |tubePointsDefault| |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| - |sts2stst| |clikeUniv| |weierstrass| |qqq| |integralBasis| - |localIntegralBasis| |qualifier| |mainExpression| |condition| - |changeWeightLevel| |characteristicSerie| |characteristicSet| |medialSet| - |Hausdorff| |Frobenius| |transcendenceDegree| |extensionDegree| - |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| |mirror| - |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| - |LiePolyIfCan| |coerce| |trunc| |degree| / |quasiRegular| |quasiRegular?| - |constant| |constant?| |coef| |mindeg| |maxdeg| |#| |map| |reductum| * - |RemainderList| |unexpand| |expand| Y |triangSolve| |univariateSolve| - |realSolve| |positiveSolve| |squareFree| |convert| |linearlyDependentOverZ?| - |linearDependenceOverZ| |solveLinearlyOverQ| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| - |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| + |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| + |Record| |Union| |exponentialOrder| |cRationalPower| |back| + |writeUInt8!| |fintegrate| |stop| |fprindINFO| + |solveLinearPolynomialEquation| |f01maf| |SturmHabichtSequence| + |completeEval| |cPower| |front| |writeInt8!| |coefficient| + |prinpolINFO| |factorSquareFreePolynomial| |f01mcf| + |SturmHabichtCoefficients| |lowerPolynomial| |seriesToOutputForm| + |rotate!| |writeByte!| |coHeight| |prinb| |factorPolynomial| |f01qcf| + |SturmHabicht| |shift| |raisePolynomial| |iCompose| |dequeue!| + |isOpen?| |extendIfCan| |critpOrder| |squareFreePolynomial| |f01qdf| + |countRealRoots| |normalDeriv| |vector| |taylorQuoByVar| |enqueue!| + |outputBinaryFile| |algebraicVariables| |makeCrit| |gcdPolynomial| + |f01qef| |SturmHabichtMultiple| |ran| |compile| |iExquo| |quatern| + |blankSeparate| |zeroSetSplitIntoTriangularSystems| |virtualDegree| + |f01rcf| |torsion?| |varList| |countRealRootsMultiple| + |highCommonTerms| |getStream| |imagK| |semicolonSeparate| + |zeroSetSplit| |property| |conditionsForIdempotents| |torsionIfCan| + |f01rdf| |signatureAst| |optimize| |mapCoef| |differentiate| |getRef| + |imagJ| |commaSeparate| |reduceByQuasiMonic| + |genericRightDiscriminant| |getGoodPrime| |f01ref| |pop!| |makeSeries| + |imagI| |pile| |collectQuasiMonic| |nand| |genericRightTraceForm| + |badNum| |f02aaf| |push!| |iicot| |signature| GF2FG |conjugate| + |paren| |removeZero| |binaryTournament| |units| + |genericLeftDiscriminant| |mix| |f02abf| |minordet| |iisec| FG2F + |queue| |bracket| |initiallyReduce| |binaryTree| + |genericLeftTraceForm| |doubleDisc| |f02adf| |determinant| |iicsc| + F2FG |nthRoot| |prod| |headReduce| |byte| |f02aef| |diagonalProduct| + |iiasin| |explogs2trigs| |fractRadix| |overlabel| |stronglyReduce| + |setLength!| |minimize| |slash| |remove| |f02aff| |diagonal| ** + |iiacos| |objects| |trigs2explogs| |wholeRadix| |overbar| + |rewriteSetWithReduction| |capacity| |module| |over| |f02agf| + |diagonalMatrix| |iiatan| |base| |byteBuffer| |swap!| |cycleRagits| + |prime| |autoReduced?| |code| |rightRegularRepresentation| |zag| + |last| |f02ajf| |scalarMatrix| |iiacot| |quote| |initiallyReduced?| + |assoc| |unknownEndian| |leftRegularRepresentation| |postfix| |f02akf| + |hermite| |iiasec| |palgLODE0| |triangular?| |supersub| |headReduced?| + |bigEndian| |rightTraceMatrix| |infix| |f02awf| |completeHermite| + |iiacsc| |chineseRemainder| |rewriteIdealWithRemainder| |isQuotient| + |presuper| |stronglyReduced?| |littleEndian| |leftTraceMatrix| + |vconcat| |f02axf| |smith| |iisinh| |divisors| + |rewriteIdealWithHeadRemainder| |initial| |presub| |reduced?| |dom| + |subtractIfCan| |rightDiscriminant| |hconcat| |plus| |iicosh| + |eulerPhi| |remainder| |zeroOf| |sub| |normalized?| |setPosition| + |leftDiscriminant| |pushdterm| |rspace| |augment| |eval| |iitanh| + |fibonacci| |headRemainder| |rarrow| |quasiComponent| |rootsOf| + |generalizedContinuumHypothesisAssumed| |represents| |vspace| + |pushucoef| |lastSubResultant| |iicoth| |cond| |harmonic| + |roughUnitIdeal?| |assign| |initials| + |generalizedContinuumHypothesisAssumed?| |continue| |mergeFactors| + |hspace| |pushuconst| |lastSubResultantElseSplit| |iisech| |jacobi| + |roughEqualIdeals?| |height| |countable?| |isMult| |superHeight| + |numberOfMonomials| |invertibleSet| |times| |iicsch| |cn| |moebiusMu| + |roughSubIdeal?| |OMputEndAttr| |nil?| |Aleph| |title| |exprToXXP| + |subHeight| |multiset| |invertible?| |iiasinh| |numberOfDivisors| + |roughBase?| |OMputEndBind| |buildSyntax| |unravel| |exprToUPS| + |doubleFloatFormat| |mergeDifference| |invertibleElseSplit?| + |previous| |iiacosh| |sumOfDivisors| |trivialIdeal?| |OMputEndBVar| + |solve| |leviCivitaSymbol| |exprToGenUPS| |messagePrint| + |squareFreePrim| |purelyAlgebraicLeadingMonomial?| |iiatanh| + |sumOfKthPowerDivisors| |collectUpper| |OMputEndError| + |triangularSystems| |kroneckerDelta| |e| |localAbs| |members| + |compdegd| |algebraicCoefficients?| |dimension| |monom| |iiacoth| + |HermiteIntegrate| |collect| |OMputEndObject| |nativeModuleExtension| + |reindex| |universe| |padecf| |univcase| |purelyTranscendental?| + |crest| |tail| |iiasech| |palgint| |collectUnder| |OMputInteger| + |hostByteOrder| |principalAncestors| |complement| |pade| |consnewpol| + |purelyAlgebraic?| |cfirst| |iiacsch| |palgextint| |mainVariable?| + |OMputFloat| |hostPlatform| |exportedOperators| |cardinality| |lcm| + |root| |nsqfree| |prepareSubResAlgo| |common| |sts2stst| |comparison| + |specialTrigs| |palglimint| |mainVariables| |OMputVariable| + |rootDirectory| |alphanumeric| |internalIntegrate0| |quotientByP| + |intChoose| |internalLastSubResultant| |clikeUniv| |equality| + |localReal?| |palgRDE| |removeSquaresIfCan| |OMputString| |bumprow| + |alphabetic| |makeCos| |append| |moduloP| |coefChoose| + |integralLastSubResultant| |weierstrass| |rischNormalize| |palgLODE| + |unprotectedRemoveRedundantFactors| |OMputSymbol| |bumptab| |hexDigit| + |makeSin| |myDegree| |modulus| |gcd| |toseLastSubResultant| |qqq| + |realElementary| |splitConstant| |removeRedundantFactors| |OMgetApp| + |bumptab1| |digit| |iiGamma| |false| |digits| |normDeriv2| + |toseInvertible?| |integralBasis| |validExponential| + |pmComplexintegrate| |certainlySubVariety?| |OMgetAtp| |untab| + |charClass| |iiabs| |continuedFraction| |plenaryPower| + |toseInvertibleSet| |localIntegralBasis| |rootNormalize| |pmintegrate| + |possiblyNewVariety?| |OMgetAttr| |bat1| |tree| |alphanumeric?| + |bringDown| |light| |c02aff| |toseSquareFreePart| |qualifier| |tanQ| + |width| |infieldint| |probablyZeroDim?| |OMgetBind| |bat| |lowerCase?| + |newReduc| |c02agf| |pastel| |quotedOperators| |zero| |mainExpression| + |callForm?| |extendedint| |selectPolynomials| |OMgetBVar| |tab1| + |upperCase?| |logical?| |c05adf| |dark| |rur| |#| |changeWeightLevel| + |getIdentifier| |limitedint| |selectOrPolynomials| |OMgetError| |tab| + |alphabetic?| |character?| |c05nbf| |getSyntaxFormsFromFile| |create| + |And| |characteristicSerie| |properties| |getConstant| |integerIfCan| + |plusInfinity| |selectAndPolynomials| |OMgetObject| |lex| |hexDigit?| + |doubleComplex?| |c05pbf| |surface| |enterInCache| |Or| + |characteristicSet| |select!| |internalIntegrate| |generator| + |minusInfinity| |quasiMonicPolynomials| |OMgetEndApp| |slex| + |translate| |escape| |complex?| |c06eaf| |coordinate| + |currentCategoryFrame| |Not| |medialSet| |delete!| |infieldIntegrate| + |univariate?| |OMgetEndAtp| |inverse| |ord| |double?| |partitions| + |c06ebf| |currentScope| |Hausdorff| |sn| |limitedIntegrate| + |univariatePolynomials| |OMgetEndAttr| |maxrow| |mkIntegral| |ffactor| + |conjugates| |c06ecf| |pushNewContour| |Frobenius| |dn| |optional| + |approximate| |extendedIntegrate| |linear?| |OMgetEndBind| |tableau| + |radPoly| |qfactor| |shuffle| |c06ekf| |findBinding| + |transcendenceDegree| |complex| |sncndn| |varselect| + |linearPolynomials| |OMgetEndBVar| |listOfLists| |rootPoly| |UP2ifCan| + |shufflein| |c06fpf| |contours| |extensionDegree| |categoryFrame| + |kmax| |bivariate?| |OMgetEndError| |tanSum| |goodPoint| |anfactor| + |sequences| |c06fqf| |structuralConstants| |inGroundField?| + |setProperties!| |ksec| |bivariatePolynomials| |OMgetEndObject| + |tanAn| |chvar| |fortranCharacter| |permutations| |c06frf| + |coordinates| |transcendent?| |type| |getProperties| |vark| + |removeRoughlyRedundantFactorsInPols| |OMgetInteger| |tanNa| + |interpret| |generate| |find| |fortranDoubleComplex| |atoms| |c06fuf| + |bounds| |algebraic?| |setProperty!| |removeConstantTerm| + |removeRoughlyRedundantFactorsInPol| |OMgetFloat| |initTable!| + |clipParametric| |fortranComplex| |makeResult| |c06gbf| |high| |sh| + |getProperty| |mkPrim| |interReduce| |OMgetVariable| |printInfo!| + |brillhartTrials| |incrementBy| |clipWithRanges| |fortranLogical| + |is?| |c06gcf| |low| |mirror| |scopes| |intPatternMatch| + |roughBasicSet| |OMgetString| |startStats!| |bezoutResultant| |expand| + |numberOfHues| SEGMENT |fortranInteger| |Is| |c06gqf| |subset?| + |monomial?| |eigenvalues| |primintegrate| |crushedSet| |OMgetSymbol| + |printStats!| |bezoutDiscriminant| |filterWhile| |yellow| + |fortranDouble| |c06gsf| |addMatchRestricted| |symmetricDifference| + |first| |rquo| |eigenvector| |expintegrate| + |rewriteSetByReducingWithParticularGenerators| |OMgetType| + |clearTable!| |filterUntil| |iifact| |fortranReal| |d01ajf| + |insertMatch| |difference| |rest| |comment| |lquo| |iibinom| + |generalizedEigenvector| |tanintegrate| + |rewriteIdealWithQuasiMonicGenerators| |OMencodingBinary| + |usingTable?| |stack| |select| |external?| ~ |substitute| |addMatch| + |d01akf| |intersect| |mindegTerm| |generalizedEigenvectors| + |primextendedint| |squareFreeFactors| |OMencodingSGML| |printingInfo?| + |removeDuplicates| |iiperm| |scalarTypeOf| |getMatch| |d01alf| |part?| + |tower| |product| |eigenvectors| |expextendedint| + |univariatePolynomialsGcds| |OMencodingXML| |makingStats?| |iipow| + |open| |fortranCarriageReturn| |failed?| |d01amf| |latex| + |LiePolyIfCan| |factorAndSplit| |primlimitedint| + |removeRoughlyRedundantFactorsInContents| |OMencodingUnknown| + |extractIfCan| |iidsum| |fortranLiteral| |optpair| |d01anf| |member?| + |trunc| |concat| |rightOne| |explimitedint| + |removeRedundantFactorsInContents| |omError| |insert!| |iidprod| + |fortranLiteralLine| |getBadValues| |d01apf| |enumerate| |degree| + |leftOne| |primextintfrac| |removeRedundantFactorsInPols| |errorInfo| + |interpretString| |ipow| |processTemplate| |resetBadValues| |d01aqf| + |setOfMinN| |quasiRegular| |rightZero| |primlimintfrac| + |irreducibleFactors| |errorKind| |stripCommentsAndBlanks| |factorial| + |operations| |makeFR| |hasTopPredicate?| |d01asf| |elements| + |complexNumeric| |quasiRegular?| |leftZero| |primintfldpoly| |output| + |lazyIrreducibleFactors| |OMReadError?| |setPrologue!| |multinomial| + |musserTrials| |topPredicate| |d01bbf| |replaceKthElement| |constant?| + |swap| |expintfldpoly| |removeIrreducibleRedundantFactors| + |OMUnknownSymbol?| |setTex!| |mr| |stopMusserTrials| |setTopPredicate| + |d01fcf| |incrementKthElement| |kernels| |mindeg| |minPoly| + |monomialIntegrate| |normalForm| |OMUnknownCD?| |setEpilogue!| |delta| + |numberOfFactors| |patternVariable| |d01gaf| |float?| |univariate| + |maxdeg| |freeOf?| |monomialIntPoly| |changeBase| |OMParseError?| + |prologue| |modularFactor| |withPredicates| |d01gbf| |integer?| + |source| |RemainderList| |operators| |inverseLaplace| F + |companionBlocks| |OMwrite| |epilogue| |useSingleFactorBound?| + |setPredicates| |d02bbf| |symbol?| |unexpand| |inputOutputBinaryFile| + |xCoord| |po| |endOfFile?| ~= |useSingleFactorBound| |inc| + |predicates| |d02bhf| |string?| |factor| |triangSolve| |reify| + |bothWays| |yCoord| |OMread| |readIfCan!| |coerce| + |useEisensteinCriterion?| |hasPredicate?| |d02cjf| |list?| |sqrt| + |univariateSolve| |separant| |bytes| |zCoord| |OMreadFile| + |readLineIfCan!| |construct| |useEisensteinCriterion| |optional?| + |d02ejf| |pair?| |real| |realSolve| |isobaric?| |super| |ip4Address| + |rCoord| |OMreadStr| |readLine!| |d02gaf| |atom?| |target| |imag| + |positiveSolve| |weights| |iprint| |thetaCoord| |OMlistCDs| + |writeLine!| |rightNorm| |lambda| |d02gbf| |null?| |directProduct| + |squareFree| |differentialVariables| |elem?| |phiCoord| + |OMlistSymbols| |sign| |leftNorm| |d02kef| |startTable!| + |linearlyDependentOverZ?| |extractBottom!| |notelem| |color| + |OMsupportsCD?| |nonQsign| |rightTrace| |makeSketch| |d02raf| + |stopTable!| |brace| |linearDependenceOverZ| |extractTop!| + |OMsupportsSymbol?| |direction| EQ |leftTrace| |inrootof| |d03edf| + |supDimElseRittWu?| |destruct| |solveLinearlyOverQ| |insertBottom!| + |minimalPolynomial| |primitiveElement| |OMunhandledSymbol| + |createThreeSpace| |someBasis| |d03eef| |algebraicSort| |insertTop!| + |position!| |nextPrime| |OMreceive| |cyclicParents| |sort!| |d03faf| + |moreAlgebraic?| |ravel| |bottom!| |eof?| |prevPrime| |OMsend| + |cyclicEqual?| |copyInto!| |top!| |reshape| |inputBinaryFile| |primes| + |OMserve| |cyclicEntries| |sorted?| |times!| |getMeasure| |monomial| + |dequeue| |increment| |selectsecond| |makeop| |cyclicCopy| |LiePoly| + |power!| |changeMeasure| |digit?| |multivariate| |node| |recolor| + |charpol| |selectfirst| |opeval| |cyclic?| |quickSort| |just| + |changeThreshhold| |variables| |drawComplex| |solve1| |makeprod| + |setelt| |heapSort| |gradient| |selectMultiDimensionalRoutines| + |drawComplexVectorField| |innerEigenvectors| |equivOperands| |imagk| + |sincos| |shellSort| |divergence| |selectNonFiniteRoutines| |category| + |setRealSteps| |update| |parseString| |equiv?| |imagj| |sinhcosh| + |copy| |outputSpacing| |laplacian| |selectSumOfSquaresRoutines| + |domain| |setImagSteps| |unparse| |impliesOperands| |imagi| + |subresultantVector| |outputGeneral| |hessian| |selectFiniteRoutines| + |package| |setClipValue| |predicate| |binary| |implies?| |octon| + |primitivePart| |outputFixed| |bandedHessian| |selectODEIVPRoutines| + |coth| |drawCurves| |option?| |packageCall| |orOperands| |ODESolve| + |pointData| |autoCoerce| |outputFloating| |jacobian| + |selectPDERoutines| |sech| |scale| |range| |innerSolve1| |or?| + |constDsolve| |parent| |exp1| |bandedJacobian| + |selectOptimizationRoutines| |csch| |connect| |match?| |colorFunction| + |position| |innerSolve| |andOperands| |showTheIFTable| + |extractProperty| |log2| |duplicates| |selectIntegrationRoutines| + |asinh| |region| |curveColor| |makeEq| |and?| |clearTheIFTable| + |extractClosed| |next| |rationalApproximation| |removeDuplicates!| + |routines| |acosh| |points| |pointColor| |modularGcdPrimitive| + |notOperand| |iFTable| |extractIndex| |relerror| |linears| + |mainSquareFreePart| |atanh| |getGraph| |clip| |modularGcd| + |variable?| |showIntensityFunctions| |extractPoint| |complexSolve| + |comp| |ddFact| |mainPrimitivePart| |acoth| |putGraph| |clipBoolean| + |reduction| |term| |expint| |traverse| |complexRoots| + |separateFactors| |mainContent| |asech| |graphs| |style| |parameters| + |signAround| |term?| |diff| |defineProperty| |realRoots| |exptMod| + |primitivePart!| |graphStates| |substring?| |toScale| |equation| + |invmod| |equiv| |algDsolve| |closeComponent| |leadingTerm| + |meshPar2Var| |nextsubResultant2| |multiple| |graphState| + |pointColorPalette| |powmod| |denomLODE| |implies| |modifyPoint| + |list| |numeric| |writable?| |meshFun2Var| |LazardQuotient2| + |applyQuote| |makeViewport2D| |suffix?| |curveColorPalette| |mulmod| + |indicialEquations| |merge!| |addPointLast| |car| |datalist| |radical| + |readable?| |meshPar1Var| |LazardQuotient| |viewport2D| |var1Steps| + |submod| |indicialEquation| |resultantEuclidean| |addPoint2| |cdr| + |exists?| |ptFunc| |subResultantChain| |getPickedPoints| |prefix?| + |var2Steps| |addmod| |setDifference| |semiResultantEuclidean2| + |denomRicDE| |addPoint| |extension| |minimumExponent| + |halfExtendedSubResultantGcd2| |ruleset| |colorDef| |setright!| + |space| |symmetricRemainder| |setIntersection| + |semiResultantEuclidean1| |leadingCoefficientRicDE| |merge| |arg1| + |shallowExpand| |maximumExponent| |halfExtendedSubResultantGcd1| + |intensity| |constantOperator| |setleft!| |tubePoints| + |positiveRemainder| |setUnion| |indiceSubResultant| + |constantCoefficientRicDE| |deepCopy| |arg2| |binarySearchTree| + |deepExpand| |rowEch| |extendedSubResultantGcd| |lighting| + |tubeRadius| |bit?| |changeVar| |indiceSubResultantEuclidean| + |shallowCopy| |apply| |nor| |char| |clearFortranOutputStack| + |rowEchLocal| |exactQuotient!| |suchThat| |clipSurface| + |constantOpIfCan| |weight| |algint| |semiIndiceSubResultantEuclidean| + |ratDsolve| |numberOfChildren| |conditions| |showFortranOutputStack| + |rowEchelonLocal| |exactQuotient| |showClipRegion| |integerBound| + |makeVariable| |algintegrate| |indicialEquationAtInfinity| + |degreeSubResultant| |children| |size| |match| |topFortranOutputStack| + |normalizedDivide| |primPartElseUnitCanonical!| |showRegion| |infix?| + |finiteBound| |palgintegrate| |degreeSubResultantEuclidean| + |reduceLODE| |child| |decrease| |setFormula!| |maxint| + |primPartElseUnitCanonical| |hitherPlane| |mask| |sortConstraints| + |palginfieldint| |semiDegreeSubResultantEuclidean| |singRicDE| |birth| + |increase| |linkToFortran| |binaryFunction| |lazyResidueClass| + |eyeDistance| |sumOfSquares| |bitLength| |lastSubResultantEuclidean| + |polyRicDE| |internal?| |setLegalFortranSourceExtensions| + |makeFloatFunction| |monicModulo| |float| |perspective| |splitLinear| + |bitCoef| |semiLastSubResultantEuclidean| |ricDsolve| |root?| + |fracPart| |unaryFunction| |lazyPseudoDivide| |zoom| |simpleBounds?| + |bitTruth| |subResultantGcdEuclidean| |triangulate| |leaf?| + |directory| |polyPart| |compiledFunction| |lazyPremWithDefault| + |rotate| |linearMatrix| |contains?| |semiSubResultantGcdEuclidean2| + |solveInField| |outputForm| |constant| |fullPartialFraction| |log| + |corrPoly| |lazyPquo| |drawStyle| |linearPart| |inf| + |semiSubResultantGcdEuclidean1| |wronskianMatrix| |argscript| + |primeFrobenius| |lifting| |lazyPrem| |outlineRender| |nonLinearPart| + |qinterval| |discriminantEuclidean| |variationOfParameters| + |superscript| |discreteLog| |lifting1| |pquo| |diagonals| |id| + |quadratic?| |lift| |interval| |semiDiscriminantEuclidean| |factors| + |subscript| |decreasePrecision| |exprex| |prem| |axes| |insert| + |changeNameToObjf| |reduce| |unit?| |chainSubResultants| |nthFactor| + |scripted?| |increasePrecision| |coerceL| |supRittWu?| |controlPanel| + |table| |optAttributes| |associates?| |schema| |nthExpon| |resetNew| + |bits| |coerceS| |RittWuCompare| GE |viewpoint| |new| |Nul| + |unitCanonical| |resultantReduit| |overlap| |symFunc| |obj| + |unitNormalize| |frobenius| |mainMonomials| GT |dimensions| + |exponents| |unitNormal| |resultantReduitEuclidean| |hcrf| + |symbolTableOf| |cache| |unit| |computePowers| |mainCoefficients| LE + |resize| |iisqrt2| |lfextendedint| |semiResultantReduitEuclidean| + |hclf| |argumentListOf| |flagFactor| |pow| |leastMonomial| LT |move| + |iisqrt3| |lflimitedint| |lexico| |divide| |retract| |returnTypeOf| + |sqfrFactor| |An| |mainMonomial| |modifyPointData| |iiexp| + |lfinfieldint| |Lazard| |OMmakeConn| |printHeader| |status| + |primeFactor| |UnVectorise| |quasiMonic?| |subspace| |iilog| + |lfintegrate| |Lazard2| |OMcloseConn| |returnType!| |nthFlag| + |Vectorise| |monic?| |makeViewport3D| |iisin| |lfextlimint| + |nextsousResultant2| |OMconnInDevice| |argumentList!| |nthExponent| + |setPoly| |deepestInitial| |viewport3D| |iicos| |subst| |BasicMethod| + |numer| |resultantnaif| |OMconnOutDevice| |endSubProgram| + |irreducibleFactor| |exponent| |iteratedInitials| |viewDeltaYDefault| + |iitan| |PollardSmallFactor| |denom| |resultantEuclideannaif| + |OMconnectTCP| |currentSubProgram| |nilFactor| |exQuo| |deepestTail| + |viewDeltaXDefault| |ptree| |showTheFTable| + |semiResultantEuclideannaif| |OMbindTCP| |newSubProgram| + |regularRepresentation| |moebius| |head| |viewZoomDefault| |dihedral| + |left| |clearTheFTable| |pi| |pdct| |OMopenFile| |clearTheSymbolTable| + |traceMatrix| |rightRecip| |mdeg| |viewPhiDefault| |cap| |right| + |fTable| |infinity| |powers| |OMopenString| |showTheSymbolTable| + |retractIfCan| |randomLC| |leftRecip| |mvar| |viewThetaDefault| |cup| + |palgint0| |partition| |OMclose| |printTypes| |leftPower| + |relativeApprox| |pointColorDefault| |wreath| |palgextint0| |complete| + |OMsetEncoding| |newTypeLists| |createZechTable| |rightPower| |rootOf| + |lineColorDefault| |SFunction| |palglimint0| |options| |kernel| + |pole?| |OMputApp| |typeLists| |createMultiplicationTable| + |derivationCoordinates| |allRootsOf| |axesColorDefault| + |skewSFunction| |draw| |keys| |palgRDE0| |listBranches| |OMputAtp| + |externalList| |createMultiplicationMatrix| |one?| + |definingPolynomial| |unitsColorDefault| |cyclotomicDecomposition| + |OMputAttr| |typeList| |createLowComplexityTable| |splitSquarefree| + |positive?| |pointSizeDefault| |cyclotomicFactorization| |leastPower| + |maxPoints| |string| |OMputBind| |parametersOf| + |createLowComplexityNormalBasis| |function| |normalDenom| |negative?| + BY |viewPosDefault| |rangeIsFinite| |idealiser| |setMinPoints| + |OMputBVar| |fortranTypeOf| |representationType| |totalfract| |zero?| + |viewSizeDefault| |functionIsContinuousAtEndPoints| |failed| + |idealiserMatrix| |minPoints| |makeObject| |OMputError| |empty| + |createPrimitiveElement| |map| |viewDefaults| |functionIsOscillatory| + |moduleSum| |parametric?| |OMputObject| |compound?| + |tableForDiscreteLogarithm| |makeTerm| |areEquivalent?| + |viewWriteDefault| |changeName| |mapUnivariate| |plotPolar| |coef| + |OMputEndApp| |getOperands| |factorsOfCyclicGroupSize| |listOfMonoms| + |isAbsolutelyIrreducible?| |currentEnv| |viewWriteAvailable| + |exprHasWeightCosWXorSinWX| |symbol| |mapUnivariateIfCan| |debug3D| + |OMputEndAtp| |getOperator| |sizeMultiplication| |symmetricSquare| + |meatAxe| |var1StepsDefault| |exprHasAlgebraicWeight| |expression| + |mapMatrixIfCan| |numFunEvals3D| |setleaves!| + |getMultiplicationMatrix| |factor1| |scanOneDimSubspaces| |printInfo| + |var2StepsDefault| |exprHasLogarithmicWeights| |integer| + |mapBivariate| |setAdaptive3D| |s21bcf| |setCondition!| NOT + |balancedBinaryTree| |getMultiplicationTable| |convert| + |symmetricProduct| |expt| |tubePointsDefault| + |combineFeatureCompatibility| |fullDisplay| |adaptive3D?| |s21bdf| + |setValue!| OR |primitive?| |symmetricPower| |showArrayValues| + |tubeRadiusDefault| |sparsityIF| |relationsIdeal| + |setScreenResolution3D| |fortranCompilerName| |empty?| AND |bfEntry| + |numberOfIrreduciblePoly| |directSum| |showScalarValues| + |stiffnessAndStabilityFactor| |saturate| |screenResolution3D| + |fortranLinkerArgs| |splitNodeOf!| |label| |bfKeys| + |numberOfPrimitivePoly| |solveLinearPolynomialEquationByFractions| + |solveRetract| |monicDivide| |stiffnessAndStabilityOfODEIF| + |groebner?| |setMaxPoints3D| |aspFilename| |remove!| |symbolTable| + |numberOfNormalPoly| |hasSolution?| |mainVariable| |divideExponents| + |systemSizeIF| |groebnerIdeal| |declare| |maxPoints3D| |dimensionsOf| + |subNodeOf?| |createIrreduciblePoly| |linSolve| |uniform01| + |unmakeSUP| |expenseOfEvaluationIF| |ideal| |setMinPoints3D| + |restorePrecision| |nodeOf?| |createPrimitivePoly| |true| + |LyndonWordsList| |normal01| |makeSUP| |accuracyIF| |leadingIdeal| + |minPoints3D| |antiCommutator| |updateStatus!| |createNormalPoly| + |LyndonWordsList1| |exponential1| |vectorise| |intermediateResultsIF| + |backOldPos| |tValues| |commutator| |extractSplittingLeaf| + |createNormalPrimitivePoly| |lyndonIfCan| |chiSquare1| |extend| + |subscriptedVariables| |generalPosition| |tRange| |associator| + |squareMatrix| |createPrimitiveNormalPoly| |lyndon| |exponential| + |truncate| |constructor| |central?| |quotient| |plot| + |complexEigenvalues| |transpose| |nextIrreduciblePoly| |lyndon?| + |chiSquare| |order| |elliptic?| |zeroDim?| |pointPlot| + |complexEigenvectors| |trim| |option| * |nextPrimitivePoly| + |numberOfComputedEntries| |factorFraction| |terms| |doubleResultant| + |inRadical?| |calcRanges| |isConnected?| |split| |operation| + |nextNormalPoly| |rst| |componentUpperBound| |squareFreePart| + |nothing| |distdfact| |in?| |fixPredicate| |connectTo| |replace| + |nextNormalPrimitivePoly| |frst| |blue| |BumInSepFFE| |rules| + |separateDegrees| |element?| |patternMatch| |normalizedAssociate| + |upperCase!| |unknown| |li| = |nextPrimitiveNormalPoly| |lazyEvaluate| + |green| |multiplyExponents| |trace2PowMod| |zeroDimPrime?| + |patternMatchTimes| |normalize| |upperCase| |leastAffineMultiple| + |lazy?| |red| |init| |laurentIfCan| |tracePowMod| |zeroDimPrimary?| + |nil| |precision| |bernoulli| |double| |outputArgs| |lowerCase!| < + |reducedQPowers| |explicitlyEmpty?| |whitePoint| |laurentRep| + |irreducible?| |rightTrim| |primaryDecomp| |chebyshevT| + |normInvertible?| |lowerCase| > |rootOfIrreduciblePoly| + |explicitEntries?| |uniform| |rationalPower| |decimal| |leftTrim| + |contract| |chebyshevU| |normFactors| |KrullNumber| <= |write!| + |matrixDimensions| |binomial| |dominantTerm| |innerint| + |leadingSupport| |cyclotomic| |npcoef| |numberOfVariables| >= |read!| + |matrixConcat3D| |poisson| |limitPlus| |exteriorDifferential| + |shrinkable| |euler| |listexp| |algebraicDecompose| |iomode| |setelt!| + |geometric| |split!| |totalDifferential| |physicalLength!| + |fixedDivisor| |characteristicPolynomial| |transcendentalDecompose| + |parents| |close!| |identityMatrix| |ridHack1| |setlast!| + |homogeneous?| |physicalLength| |laguerre| |realEigenvalues| + |internalDecompose| + |close| |reopen!| |zeroMatrix| |interpolate| + |setrest!| |leadingBasisTerm| |flexibleArray| |legendre| |declare!| + |realEigenvectors| |decompose| - |rightUnit| |mappingAst| |nullSpace| + |setfirst!| |ignore?| |elseBranch| |dmpToHdmp| + |halfExtendedResultant2| |upDateBranches| |pattern| / |display| + |leftUnit| |nullary| |nullity| |cycleSplit!| |computeInt| |thenBranch| + |hdmpToDmp| |halfExtendedResultant1| |preprocess| + |rightMinimalPolynomial| |fixedPoint| |rowEchelon| |test| |concat!| + |checkForZero| |generalizedInverse| |pToHdmp| |extendedResultant| + |internalZeroSetSplit| |leftMinimalPolynomial| |recur| |column| + |cycleTail| |logGamma| |imports| |hdmpToP| |subResultantsChain| + |internalAugment| |associatorDependence| |const| |row| |cycleLength| + |hypergeometric0F1| |sequence| |dmpToP| |eq| |lazyPseudoQuotient| + |possiblyInfinite?| |prefix| |message| |lieAlgebra?| |curry| + |maxColIndex| |cycleEntry| |rotatez| |iterationVar| |iter| |pToDmp| + |lazyPseudoRemainder| |explicitlyFinite?| |input| |jordanAlgebra?| + |diag| |minColIndex| |taylor| |invmultisect| |rotatey| |readBytes!| + |sylvesterSequence| |segment| |bernoulliB| |nextItem| |library| + |noncommutativeJordanAlgebra?| |curryRight| |maxRowIndex| |laurent| + |multisect| |rotatex| |readUInt32!| |sturmSequence| |eulerE| + |infiniteProduct| |jordanAdmissible?| |curryLeft| |minRowIndex| + |puiseux| |revert| |identity| |readInt32!| |boundOfCauchy| + |numericIfCan| |evenInfiniteProduct| |lieAdmissible?| |constantRight| + |antisymmetric?| |generalLambert| |dictionary| |readUInt16!| + |sturmVariationsOf| |complexNumericIfCan| |oddInfiniteProduct| |any| + |sylvesterMatrix| |jacobiIdentity?| |constantLeft| |symmetric?| |inv| + |evenlambert| |cons| |dioSolve| |readInt16!| |lazyVariations| + |FormatArabic| |generalInfiniteProduct| |bezoutMatrix| |set| + |powerAssociative?| |ground?| |twist| |diagonal?| |oddlambert| + |newLine| |readUInt8!| |content| |ScanArabic| |showAll?| + |alternative?| |ground| |setsubMatrix!| |square?| |lambert| |copies| + |readInt8!| |totalDegree| |exp| |FormatRoman| |showAllElements| + |flexible?| |subMatrix| |rectangularMatrix| |leadingMonomial| + |lagrange| |sayLength| |readByte!| |minimumDegree| |ScanRoman| |delay| + |rightAlternative?| |swapColumns!| |characteristic| + |leadingCoefficient| |univariatePolynomial| |setnext!| |setFieldInfo| + |monomials| |ScanFloatIgnoreSpaces| |findCycle| |leftAlternative?| + |swapRows!| |round| |primitiveMonomials| |integrate| |setprevious!| + |pol| |isPlus| |ScanFloatIgnoreSpacesIfCan| |repeating?| + |antiAssociative?| |vertConcat| |fractionPart| |reductum| + |multiplyCoefficients| |shanksDiscLogAlgorithm| |xn| + |numericalIntegration| |isTimes| |center| |repeating| |associative?| + |horizConcat| |wholePart| |erf| |quoByVar| |reflect| |dAndcExp| + |isExpt| |rk4| |recip| |antiCommutative?| |squareTop| |floor| + |coefficients| |repSq| |isPower| |rk4a| |integers| |commutative?| + |elRow1!| |ceiling| |stFunc1| |permutation| |expPot| |rroot| |rk4qc| + |oddintegers| |rightCharacteristicPolynomial| |hash| |elRow2!| |norm| + |dilog| |stFunc2| |stirling1| |qPot| |qroot| |rk4f| |int| |show| + |leftCharacteristicPolynomial| |count| |elColumn2!| |mightHaveRoots| + |sin| |stFuncN| |stirling2| |lookup| |froot| |aromberg| |mapmult| + |fractionFreeGauss!| |refine| |cos| |fixedPointExquo| |summation| |lo| + |normal?| |nthr| |asimpson| |deriv| |nthCoef| |trace| |invertIfCan| + |middle| |tan| |ode1| |factorials| |basis| |firstUncouplingMatrix| + |atrapezoidal| |gderiv| |binomThmExpt| |copy!| |roman| |cot| |ode2| + |mkcomm| |normalElement| |integral| |romberg| |compose| |pomopo!| + |plus!| |recoverAfterFail| |sec| |ode| |polarCoordinates| |simpson| + |addiag| |mapExponents| |minus!| |showTheRoutinesTable| |csc| |mpsode| + |imaginary| |genericRightNorm| |polyred| |trapezoidal| |lazyIntegrate| + |key| |linearAssociatedLog| |length| |leftScalarTimes!| + |deleteRoutine!| |asin| UP2UTS |solid| |genericRightTrace| + |padicFraction| |rombergo| |nlde| |linearAssociatedOrder| |scripts| + |rightScalarTimes!| |getExplanations| |acos| UTS2UP |solid?| + |genericRightMinimalPolynomial| |padicallyExpand| |simpsono| |powern| + |filename| |linearAssociatedExp| |droot| |systemCommand| |atan| + LODO2FUN |nary?| |denominators| |rightRankPolynomial| + |numberOfFractionalTerms| |trapezoidalo| |mapdiv| |not?| + |createNormalElement| |fill!| |prefixRagits| |name| |iroot| |acot| + RF2UTS |unary?| |numerators| |genericLeftNorm| |nthFractionalTerm| + |sup| |lazyGintegrate| |parse| |setLabelValue| |minIndex| + |fractRagits| |body| |asec| |magnitude| |convergents| + |genericLeftTrace| |makeRecord| |firstNumer| |imagE| |power| |getCode| + |maxIndex| |wholeRagits| |normal| |acsc| |cross| |approximants| + |genericLeftMinimalPolynomial| |firstDenom| |printCode| |entry?| + |radix| |dec| |sinh| |dot| |reducedForm| |incr| |leftRankPolynomial| + |compactFraction| |f02bbf| |completeSmith| |printStatement| |indices| + |randnum| |rank| |partialQuotients| |cosh| |scan| |generic| |hi| + |f02bjf| |partialFraction| |diophantineSystem| |point| |block| + |index?| |reseed| |tanh| |graphCurves| |partialDenominators| + |rightUnits| |gcdPrimitive| |f02fjf| |csubst| |returns| |entries| + |seed| |partialNumerators| |leftUnits| |symmetricGroup| |f02wef| + |particularSolution| |goto| |key?| |port| |rational| |basicSet| + |reducedContinuedFraction| |compBound| |f02xef| |alternatingGroup| + |mapSolve| |series| |repeatUntilLoop| |symbolIfCan| |rational?| + |exquo| |infRittWu?| |nullary?| |push| |error| |tablePow| + |abelianGroup| |f04adf| |quadratic| |whileLoop| |argument| + |rationalIfCan| |t| |div| |getCurve| |derivative| |bindings| |solveid| + |f04arf| |cyclicGroup| |assert| |cubic| |forLoop| |constantKernel| + |setvalue!| |quo| |listLoops| |cartesian| |testModulus| + |dihedralGroup| |f04asf| |quartic| |sin?| |constantIfCan| + |setchildren!| |lists| |closed?| |polar| |HenselLift| |f04atf| + |mathieu11| |min| |aLinear| |index| |zeroVector| |kovacic| |node?| + |rem| |open?| |cylindrical| |completeHensel| |mathieu12| |f04axf| + |aQuadratic| |zeroSquareMatrix| |laplace| |child?| |setClosed| + |spherical| |multMonom| |f04faf| |mathieu22| |rule| |aCubic| + |identitySquareMatrix| |trailingCoefficient| |distance| |tube| + |parabolic| |build| |mathieu23| |f04jgf| |aQuartic| |pair| + |lSpaceBasis| |normalizeIfCan| |nodes| |unitVector| + |parabolicCylindrical| |leadingIndex| |mathieu24| |f04maf| + |radicalSolve| |finiteBasis| |polCase| |rename| |cosSinInfo| |say| + |paraboloidal| |leadingExponent| |janko2| |f04mbf| |radicalRoots| + |principal?| |distFact| |rename!| |loopPoints| |ellipticCylindrical| + |GospersMethod| |rubiksGroup| |box| |f04mcf| |contractSolve| |divisor| + |identification| |mainValue| |generalTwoFactor| |prolateSpheroidal| + |value| |nextSubsetGray| |youngGroup| |f04qaf| |decomposeFunc| + |useNagFunctions| |LyndonCoordinates| |mainDefiningPolynomial| + |generalSqFr| |oblateSpheroidal| |firstSubsetGray| |lexGroebner| + |f07adf| |unvectorise| |rationalPoints| |LyndonBasis| |mainForm| + |twoFactor| |bipolar| |clipPointsDefault| |totalGroebner| |f07aef| + |bubbleSort!| |nonSingularModel| |zeroDimensional?| |rischDE| |result| + |setOrder| |bipolarCylindrical| |drawToScale| |expressIdealMember| + |f07fdf| |insertionSort!| |algSplitSimple| |fglmIfCan| |rischDEsys| + |getOrder| |reset| |fortran| |toroidal| |adaptive| |principalIdeal| + |f07fef| |check| |hyperelliptic| |groebner| |checkPrecision| + |monomRDE| |less?| |conical| |figureUnits| |LagrangeInterpolation| + |s01eaf| |lprop| |elliptic| |lexTriangular| |baseRDE| |userOrdered?| + |write| |modTree| |putColorInfo| |psolve| |s13aaf| |llprop| + |integralDerivationMatrix| |squareFreeLexTriangular| |polyRDE| |save| + |largest| |multiEuclideanTree| |appendPoint| |wrregime| |s13acf| + |lllp| |integralRepresents| |belong?| |monomRDEsys| |more?| + |complexZeros| |component| |rdregime| |s13adf| |lllip| + |integralCoordinates| |Ci| |baseRDEsys| |setVariableOrder| + |divisorCascade| |ranges| |bsolve| |s14aaf| |mesh?| |yCoordinates| + |Si| |weighted| |getVariableOrder| |resetAttributeButtons| |graeffe| + |pointLists| |dmp2rfi| |s14abf| |mesh| |/\\| |kind| + |inverseIntegralMatrixAtInfinity| |Ei| |rdHack1| |resetVariableOrder| + |getButtonValue| |pleskenSplit| |makeGraphImage| |se2rfi| |s14baf| + |polygon?| |\\/| |integralMatrixAtInfinity| |linGenPos| |op| + |operator| |prime?| |reciprocalPolynomial| |graphImage| |pr2dmp| + |s15adf| |polygon| |inverseIntegralMatrix| |groebgen| |midpoint| + |sample| |rootRadius| |groebSolve| |hasoln| |s15aef| |closedCurve?| + |mapDown!| |integralMatrix| |totolex| |midpoints| |rationalFunction| + |schwerpunkt| |flatten| |testDim| |ParCondList| |s17acf| |closedCurve| + |mapUp!| |setProperties| |reduceBasisAtInfinity| |entry| |minPol| + |realZeros| |taylorIfCan| |setErrorBound| |genericPosition| |redpps| + |s17adf| |curve?| |setProperty| |normalizeAtInfinity| |computeBasis| + |mainCharacterization| |removeZeroes| |script| |startPolynomial| + |null| |lfunc| |B1solve| |s17aef| |curve| |complementaryBasis| |coord| + |algebraicOf| |taylorRep| |cycleElt| |not| |inHallBasis?| |factorset| + |s17aff| |point?| |integral?| |anticoord| |ReduceOrder| |union| + |factorSquareFree| |size?| |computeCycleLength| |search| |and| + |reorder| |maxrank| |s17agf| |enterPointData| |integralAtInfinity?| + |intcompBasis| |setref| |henselFact| |eq?| |tex| |computeCycleEntry| + |or| |headAst| |minrank| |s17ahf| |composites| + |integralBasisAtInfinity| |choosemon| |deref| |hasHi| + |doublyTransitive?| |findConstructor| |xor| |heap| |minset| |s17ajf| + |components| |deleteProperty!| |ramified?| |transform| |ref| |fmecg| + |knownInfBasis| |dualSignature| |case| |gcdprim| |nextSublist| + |s17akf| |numberOfComposites| |has?| |ramifiedAtInfinity?| |pack!| + |radicalEigenvectors| |commonDenominator| |rootSplit| |coerceP| |Zero| + |gcdcofact| |overset?| |s17dcf| |numberOfComponents| |singular?| |top| + |complexLimit| |radicalEigenvector| |ratDenom| |clearDenominator| + |powerSum| |gcdcofactprim| |One| |outerProduct| |s17def| |ParCond| + |dim| |create3Space| |singularAtInfinity?| |limit| + |radicalEigenvalues| |splitDenominator| |ratPoly| |elementary| + |lintgcd| |redmat| |s17dgf| |outputAsScript| |branchPoint?| + |categories| |linearlyDependent?| |eigenMatrix| + |monicRightFactorIfCan| |rootPower| |alternating| |hex| |regime| + |s17dhf| |outputAsTex| |branchPointAtInfinity?| |linearDependence| + |normalise| |rightFactorIfCan| |rootProduct| |inspect| |cyclic| + |every?| |s17dlf| |sqfree| |matrix| |abs| |rationalPoint?| + |solveLinear| |gramschmidt| |leftFactorIfCan| |rootSimp| |extract!| + |any?| |inconsistent?| |s18acf| |Beta| |absolutelyIrreducible?| + |reducedSystem| |orthonormalBasis| |monicDecomposeIfCan| |rootKerSimp| + |setButtonValue| |elt| |host| |numFunEvals| |s18adf| |digamma| |genus| + |duplicates?| |antisymmetricTensors| |monicCompleteDecompose| + |leftRank| |setAttributeButtonStep| |trueEqual| |s18aef| |setAdaptive| + |linear| |polygamma| |getZechTable| |formula| |mapGen| + |createGenericMatrix| |divideIfCan| |rightRank| |factorList| + |adaptive?| |s18aff| |Gamma| |leaves| |mapExpon| |symmetricTensors| + |sum| |noKaratsuba| |doubleRank| |listConjugateBases| |s18dcf| + |setScreenResolution| |besselJ| |polynomial| |mainKernel| + |commutativeEquality| |tensorProduct| |karatsubaOnce| |weakBiRank| + |matrixGcd| |screenResolution| |s18def| |besselY| |distribute| + |leftMult| |permutationRepresentation| |karatsuba| |biRank| + |divideIfCan!| |setMaxPoints| |s19aaf| |besselI| + |functionIsFracPolynomial?| |rightMult| |completeEchelonBasis| + |separate| |basisOfCommutingElements| |s19abf| |second| |besselK| + |brillhartIrreducible?| |lp| |problemPoints| |makeUnit| + |createRandomElement| |pseudoDivide| |eisensteinIrreducible?| + |multiple?| |basisOfLeftAnnihilator| |s19acf| |third| |airyAi| + |zerosOf| |reverse!| |cyclicSubmodule| |pseudoQuotient| + |tryFunctionalDecomposition?| |generic?| |basisOfRightAnnihilator| + |s19adf| |airyBi| |singularitiesOf| |makeMulti| + |standardBasisOfCyclicSubmodule| |composite| + |tryFunctionalDecomposition| |quoted?| |basisOfLeftNucleus| |s20acf| + |subNode?| |polynomialZeros| |subResultantGcd| |btwFact| |inR?| + |nrows| |basisOfRightNucleus| |s20adf| |infLex?| |f2df| |logpart| + |hue| |resultant| |beauzamyBound| |isList| |ncols| + |basisOfMiddleNucleus| |s21baf| |setEmpty!| |pushFortranOutputStack| + |ef2edf| |ratpart| |bright| |shade| |discriminant| |arguments| + |bombieriNorm| |isOp| |basisOfNucleus| |s21bbf| |setStatus!| + |popFortranOutputStack| |ocf2ocdf| |mkAnswer| |nthRootIfCan| + |pseudoRemainder| |void| |rootBound| |satisfy?| |basisOfCenter| + |socf2socdf| |perfectNthPower?| |expIfCan| |shiftLeft| + |singleFactorBound| |addBadValue| |e01baf| |subTriSet?| + |basisOfLeftNucloid| |expr| |outputAsFortran| |df2fi| |perfectNthRoot| + |logIfCan| |shiftRight| |showSummary| |quadraticNorm| |badValues| + |e01bef| |subPolSet?| |basisOfRightNucloid| |edf2fi| |approxNthRoot| + |sinIfCan| |karatsubaDivide| |infinityNorm| |retractable?| |e01bff| + |internalSubPolSet?| |basisOfCentroid| |edf2df| |perfectSquare?| + |cosIfCan| |scaleRoots| |showAttributes| |ListOfTerms| |e01bgf| + |internalInfRittWu?| |radicalOfLeftTraceForm| |expenseOfEvaluation| + |perfectSqrt| |tanIfCan| |evaluateInverse| |complexNormalize| |bag| + |shiftRoots| |PDESolve| |e01bhf| |internalSubQuasiComponent?| + |showTypeInOutput| |variable| |numberOfOperations| |approxSqrt| + |cotIfCan| |evaluate| |complexElementary| |binding| |degreePartition| + |leftFactor| |e01daf| |subQuasiComponent?| |objectOf| |morphism| + |iterators| |edf2efi| |generateIrredPoly| |secIfCan| |conjug| |trigs| + |factorOfDegree| |rightFactorCandidate| |e01saf| + |removeSuperfluousQuasiComponents| |domainOf| |balancedFactorisation| + |dfRange| |complexExpand| |outputList| |cscIfCan| |adjoint| |real?| + |factorsOfDegree| |measure| |e01sbf| |subCase?| |applyRules| |dflist| + |complexIntegrate| |asinIfCan| |arity| |complexForm| |pascalTriangle| + |e01sef| |coerceImages| |removeSuperfluousCases| |qelt| |localUnquote| + |df2mf| |dimensionOfIrreducibleRepresentation| |acosIfCan| + |getDatabase| |UpTriBddDenomInv| |qsetelt| |rangePascalTriangle| + |fixedPoints| |e01sff| |prepareDecompose| |arbitrary| |ldf2vmf| + |irreducibleRepresentation| |atanIfCan| |numericalOptimization| + |LowTriBddDenomInv| |leader| |sizePascalTriangle| |max| |e02adf| + |odd?| |branchIfCan| |xRange| |setColumn!| |edf2ef| |checkRur| + |acotIfCan| |goodnessOfFit| |simplify| |fillPascalTriangle| |e02aef| + |even?| |startTableGcd!| |yRange| |setRow!| |vedf2vef| |cAcsch| + |asecIfCan| |whatInfinity| |htrigs| |safeCeiling| |e02agf| + |numberOfCycles| |stopTableGcd!| |zRange| |oneDimensionalArray| + |df2st| |cAsech| |acscIfCan| |infinite?| |simplifyExp| |safeFloor| + |map!| |cyclePartition| |e02ahf| |startTableInvSet!| + |associatedSystem| |lhs| |f2st| |cAcoth| |sinhIfCan| |finite?| + |simplifyLog| |qsetelt!| |safetyMargin| |coerceListOfPairs| |e02ajf| + |stopTableInvSet!| |uncouplingMatrices| |rhs| |ldf2lst| |cAtanh| + |delete| |coshIfCan| |pureLex| |expandPower| |sumSquares| + |coercePreimagesImages| |e02akf| |stosePrepareSubResAlgo| |sdf2lst| + |cAcosh| |tanhIfCan| |totalLex| |expandLog| |euclideanNormalForm| + |listRepresentation| |e02baf| |stoseInternalLastSubResultant| |getlo| + |cAsinh| |cothIfCan| |reverseLex| |cos2sec| |debug| + |euclideanGroebner| |permanent| |e02bbf| + |stoseIntegralLastSubResultant| |gethi| |cCsch| |sechIfCan| |leftLcm| + |cosh2sech| D |factorGroebnerBasis| |cycles| |e02bcf| + |stoseLastSubResultant| |outputMeasure| |cSech| |cschIfCan| + |rightExtendedGcd| |cot2trig| |groebnerFactorize| |e02bdf| |cycle| + |stoseInvertible?sqfreg| |acsch| |measure2Result| |cCoth| |clearCache| + |asinhIfCan| |rightGcd| |coth2trigh| |credPol| + |initializeGroupForWordProblem| |e02bef| |stoseInvertibleSetsqfreg| + |att2Result| |cTanh| |acoshIfCan| |rightExactQuotient| |csc2sin| + |redPol| |movedPoints| |e02daf| |stoseInvertible?reg| |iflist2Result| + |cCosh| |atanhIfCan| |rightRemainder| |csch2sinh| |gbasis| |e02dcf| + |wordInGenerators| |stoseInvertibleSetreg| |loadNativeModule| + |associatedEquations| |parts| |pdf2ef| |cSinh| |acothIfCan| + |rightQuotient| |sec2cos| |critT| |wordInStrongGenerators| |e02ddf| + |stoseInvertible?| |arrayStack| |pdf2df| |cAcsc| |asechIfCan| + |rightLcm| |sech2cosh| |critM| |orbits| |e02def| |stoseInvertibleSet| + |df2ef| |sort| |cAsec| |acschIfCan| |leftExtendedGcd| |sin2csc| + |noLinearFactor?| |critB| |orbit| |e02dff| |stoseSquareFreePart| + |fi2df| |cAcot| |pushdown| |leftGcd| |sinh2csch| |insertRoot!| + |critBonD| |permutationGroup| |e02gaf| |coleman| |mat| |cAtan| + |pushup| |leftExactQuotient| |tan2trig| |print| |critMTonD1| + |wordsForStrongGenerators| |e02zaf| |inverseColeman| |neglist| |log10| + |cAcos| |reducedDiscriminant| |leftRemainder| |tanh2trigh| |resolve| + |reverse| |critMonD1| |strongGenerators| |e04dgf| |listYoungTableaus| + |multiEuclidean| |cAsin| |random| |leftQuotient| |idealSimplify| + |bitand| |tan2cot| |condition| |redPo| |generators| |e04fdf| + |makeYoungTableau| |extendedEuclidean| |cCsc| |definingInequation| + |bitior| |monicLeftDivide| |tanh2coth| |level| |hMonic| + |bivariateSLPEBR| |e04gcf| |nextColeman| |euclideanSize| |cSec| + |definingEquations| |monicRightDivide| |cot2tan| |updatF| + |solveLinearPolynomialEquationByRecursion| |e04jaf| + |nextLatticePermutation| |call| |sizeLess?| |cCot| |setStatus| + |leftDivide| |coth2tanh| |sPol| |factorByRecursion| |e04mbf| + |nextPartition| |simplifyPower| |cTan| |quasiAlgebraicSet| + |rightDivide| |removeCosSq| |updatD| |factorSquareFreeByRecursion| + |e04naf| |numberOfImproperPartitions| |number?| |cCos| + |radicalSimplify| |hermiteH| |removeSinSq| |minGbasis| |e04ucf| + |randomR| |subSet| |depth| |seriesSolve| |cSin| |denominator| + |laguerreL| |removeCoshSq| |lepol| |factorSFBRlcUnit| Y |e04ycf| + |unrankImproperPartitions0| |constantToUnaryFunction| |cLog| + |numerator| |legendreP| |removeSinhSq| |prinshINFO| |charthRoot| + |f01brf| |unrankImproperPartitions1| |tubePlot| |cExp| |quadraticForm| + |writeBytes!| |expandTrigProducts| |prindINFO| |mantissa| |conditionP| + |f01bsf| |subresultantSequence| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #1=(-407 (-546))) -3943 (|has| |#1| (-350)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -3943 (|has| |#1| (-556)) (|has| |#1| (-350)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-35) |has| |#1| (-1193)) ((-95) |has| |#1| (-1193)) ((-102) . T) ((-111 #1# #1#) -3943 (|has| |#1| (-350)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -3943 (|has| |#1| (-350)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-613 #1#) -3943 (|has| |#1| (-1034 (-407 (-546)))) (|has| |#1| (-350)) (|has| |#1| (-363))) ((-613 (-546)) . T) ((-613 |#1|) . T) ((-613 $) -3943 (|has| |#1| (-556)) (|has| |#1| (-350)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-610 (-859)) . T) ((-172) . T) ((-611 (-168 (-225))) |has| |#1| (-1016)) ((-611 (-168 (-378))) |has| |#1| (-1016)) ((-611 (-535)) |has| |#1| (-611 (-535))) ((-611 (-886 (-378))) |has| |#1| (-611 (-886 (-378)))) ((-611 (-886 (-546))) |has| |#1| (-611 (-886 (-546)))) ((-611 #2=(-1163 |#1|)) . 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(|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -3943 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3943 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -3943 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-613 #1=(-407 (-546))) -12 (|has| |#2| (-1034 (-407 (-546)))) (|has| |#2| (-1094))) ((-613 (-546)) -3943 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-546))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-613 |#2|) -3943 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-610 (-859)) -3943 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-610 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-610 (-1256 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #2=(-546) |#2|) . T) ((-288 #2# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-412 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-601 #2# |#2|) . 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(|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2811 (|has| |#2| (-1093)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2811 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-613 #0=(-407 (-563))) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-613 (-563)) -2811 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-613 |#2|) -2811 (|has| |#2| (-1093)) (|has| |#2| (-172))) ((-610 (-858)) -2811 (|has| |#2| (-1093)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-610 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-610 (-1257 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-563) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1093)) ((-489 |#2|) . T) ((-601 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1093))) ((-643 |#2|) -2811 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-643 $) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-636 (-563)) -12 (|has| |#2| (-636 (-563))) (|has| |#2| (-1045))) ((-636 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2811 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2811 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2811 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2811 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2811 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1169)) -12 (|has| |#2| (-896 (-1169))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-563)))) (|has| |#2| (-1093))) ((-1034 (-563)) -12 (|has| |#2| (-1034 (-563))) (|has| |#2| (-1093))) ((-1034 |#2|) |has| |#2| (-1093)) ((-1051 |#2|) -2811 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1105) -2811 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1093) -2811 (|has| |#2| (-1093)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1208) . T) ((-1264 |#2|) |has| |#2| (-363))) +((-3409 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2532 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2751 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3409 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2532 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2751 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1208) (-1208)) (T -239)) +((-2751 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *7 (-1208)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2532 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1208)) (-4 *2 (-1208)) (-5 *1 (-239 *5 *6 *2)))) (-3409 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1208)) (-4 *5 (-1208)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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(NIL T) -8 NIL NIL NIL) (-1204 2906660 2907179 2907718 "TUBETOOL" 2908452 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1203 2905509 2905714 2905955 "TUBE" 2906453 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1202 2894176 2898268 2898365 "TSETCAT" 2903634 NIL TSETCAT (NIL T T T T) -9 NIL 2905165 NIL) (-1201 2888911 2890508 2892399 "TSETCAT-" 2892404 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2883675 2887883 2888166 "TS" 2888663 NIL TS (NIL T) -8 NIL NIL NIL) (-1199 2877938 2878784 2879726 "TRMANIP" 2882811 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1198 2877379 2877442 2877605 "TRIMAT" 2877870 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1197 2875175 2875412 2875776 "TRIGMNIP" 2877128 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1196 2874695 2874808 2874838 "TRIGCAT" 2875051 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1195 2874364 2874443 2874584 "TRIGCAT-" 2874589 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1194 2871262 2873222 2873503 "TREE" 2874118 NIL TREE (NIL T) -8 NIL NIL NIL) (-1193 2870536 2871064 2871094 "TRANFUN" 2871129 T TRANFUN (NIL) -9 NIL 2871195 NIL) (-1192 2869815 2870006 2870286 "TRANFUN-" 2870291 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1191 2869619 2869651 2869712 "TOPSP" 2869776 T TOPSP (NIL) -7 NIL NIL NIL) (-1190 2868967 2869082 2869236 "TOOLSIGN" 2869500 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1189 2867628 2868144 2868383 "TEXTFILE" 2868750 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1188 2867409 2867440 2867512 "TEX1" 2867591 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2865348 2865862 2866291 "TEX" 2867002 T TEX (NIL) -8 NIL NIL NIL) (-1186 2864996 2865059 2865149 "TEMUTL" 2865280 T TEMUTL (NIL) -7 NIL NIL NIL) (-1185 2863150 2863430 2863755 "TBCMPPK" 2864719 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1184 2855040 2861310 2861366 "TBAGG" 2861766 NIL TBAGG (NIL T T) -9 NIL 2861977 NIL) (-1183 2850110 2851598 2853352 "TBAGG-" 2853357 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1182 2849494 2849601 2849746 "TANEXP" 2849999 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1181 2848906 2849005 2849143 "TABLEAU" 2849391 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2842409 2848763 2848856 "TABLE" 2848861 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1179 2837017 2838237 2839485 "TABLBUMP" 2841195 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1178 2836239 2836386 2836567 "SYSTEM" 2836858 T SYSTEM (NIL) -8 NIL NIL NIL) (-1177 2832702 2833397 2834180 "SYSSOLP" 2835490 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1176 2831742 2832217 2832336 "SYSNNI" 2832522 NIL SYSNNI (NIL NIL) -8 NIL NIL 2832607) (-1175 2831045 2831474 2831553 "SYSINT" 2831613 NIL SYSINT (NIL NIL) -8 NIL NIL 2831658) (-1174 2827391 2828306 2829022 "SYNTAX" 2830351 T SYNTAX (NIL) -8 NIL NIL NIL) (-1173 2824549 2825151 2825783 "SYMTAB" 2826781 T SYMTAB (NIL) -8 NIL NIL NIL) (-1172 2819822 2820718 2821695 "SYMS" 2823594 T SYMS (NIL) -8 NIL NIL NIL) (-1171 2817103 2819283 2819513 "SYMPOLY" 2819630 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1170 2816620 2816695 2816818 "SYMFUNC" 2817015 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1169 2812672 2813932 2814745 "SYMBOL" 2815829 T SYMBOL (NIL) -8 NIL NIL NIL) (-1168 2806211 2807900 2809620 "SWITCH" 2810974 T SWITCH (NIL) -8 NIL NIL NIL) (-1167 2799481 2805032 2805335 "SUTS" 2805966 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2791586 2798728 2799001 "SUPXS" 2799266 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2790745 2790872 2791089 "SUPFRACF" 2791454 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2790366 2790425 2790538 "SUP2" 2790680 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2781936 2789984 2790110 "SUP" 2790275 NIL SUP (NIL T) -8 NIL NIL NIL) (-1162 2780349 2780623 2780986 "SUMRF" 2781635 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1161 2779663 2779729 2779928 "SUMFS" 2780270 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1160 2763686 2778840 2779091 "SULS" 2779470 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2763315 2763508 2763578 "SUCHTAST" 2763638 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1158 2762637 2762840 2762980 "SUCH" 2763223 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1157 2756531 2757543 2758502 "SUBSPACE" 2761725 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1156 2755961 2756051 2756215 "SUBRESP" 2756419 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1155 2750134 2751254 2752401 "STTFNC" 2754861 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2743503 2744799 2746110 "STTF" 2748870 NIL STTF (NIL T) -7 NIL NIL NIL) (-1153 2734818 2736685 2738479 "STTAYLOR" 2741744 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1152 2728064 2734682 2734765 "STRTBL" 2734770 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1151 2723455 2728019 2728050 "STRING" 2728055 T STRING (NIL) -8 NIL NIL NIL) (-1150 2718343 2722828 2722858 "STRICAT" 2722917 T STRICAT (NIL) -9 NIL 2722979 NIL) (-1149 2717853 2717930 2718074 "STREAM3" 2718260 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2716835 2717018 2717253 "STREAM2" 2717666 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2716523 2716575 2716668 "STREAM1" 2716777 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2709335 2714142 2714753 "STREAM" 2715947 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1145 2708351 2708532 2708763 "STINPROD" 2709151 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1144 2707929 2708113 2708143 "STEP" 2708223 T STEP (NIL) -9 NIL 2708301 NIL) (-1143 2701474 2707828 2707905 "STBL" 2707910 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1142 2696650 2700695 2700738 "STAGG" 2700891 NIL STAGG (NIL T) -9 NIL 2700980 NIL) (-1141 2694358 2694958 2695828 "STAGG-" 2695833 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1140 2692553 2694128 2694220 "STACK" 2694301 NIL STACK (NIL T) -8 NIL NIL NIL) (-1139 2685305 2690694 2691150 "SREGSET" 2692183 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1138 2677731 2679099 2680612 "SRDCMPK" 2683911 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2670698 2675171 2675201 "SRAGG" 2676504 T SRAGG (NIL) -9 NIL 2677112 NIL) (-1136 2669715 2669970 2670349 "SRAGG-" 2670354 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1135 2664214 2668662 2669083 "SQMATRIX" 2669341 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1134 2657964 2660932 2661659 "SPLTREE" 2663559 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1133 2653954 2654620 2655266 "SPLNODE" 2657390 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1132 2653001 2653234 2653264 "SPFCAT" 2653708 T SPFCAT (NIL) -9 NIL NIL NIL) (-1131 2651738 2651948 2652212 "SPECOUT" 2652759 T SPECOUT (NIL) -7 NIL NIL NIL) (-1130 2643390 2645134 2645164 "SPADXPT" 2649556 T SPADXPT (NIL) -9 NIL 2651590 NIL) (-1129 2643151 2643191 2643260 "SPADPRSR" 2643343 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1128 2641334 2643106 2643137 "SPADAST" 2643142 T SPADAST (NIL) -8 NIL NIL NIL) (-1127 2633305 2635052 2635095 "SPACEC" 2639468 NIL SPACEC (NIL T) -9 NIL 2641284 NIL) (-1126 2631476 2633237 2633286 "SPACE3" 2633291 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1125 2630228 2630399 2630690 "SORTPAK" 2631281 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1124 2628278 2628581 2629000 "SOLVETRA" 2629892 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1123 2627289 2627511 2627785 "SOLVESER" 2628051 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1122 2622509 2623390 2624392 "SOLVERAD" 2626341 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1121 2618324 2618933 2619662 "SOLVEFOR" 2621876 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1120 2612648 2617673 2617770 "SNTSCAT" 2617775 NIL SNTSCAT (NIL T T T T) -9 NIL 2617845 NIL) (-1119 2606791 2610971 2611362 "SMTS" 2612338 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1118 2601267 2606679 2606756 "SMP" 2606761 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1117 2599426 2599727 2600125 "SMITH" 2600964 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1116 2592319 2596471 2596574 "SMATCAT" 2597928 NIL SMATCAT (NIL NIL T T T) -9 NIL 2598478 NIL) (-1115 2589280 2590096 2591267 "SMATCAT-" 2591272 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1114 2586993 2588516 2588559 "SKAGG" 2588820 NIL SKAGG (NIL T) -9 NIL 2588955 NIL) (-1113 2583329 2586409 2586604 "SINT" 2586791 T SINT (NIL) -8 NIL NIL 2586964) (-1112 2583101 2583139 2583205 "SIMPAN" 2583285 T SIMPAN (NIL) -7 NIL NIL NIL) (-1111 2581960 2582174 2582442 "SIGNRF" 2582867 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2580786 2580930 2581214 "SIGNEF" 2581796 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2580119 2580369 2580493 "SIGAST" 2580684 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2579426 2579654 2579794 "SIG" 2580001 T SIG (NIL) -8 NIL NIL NIL) (-1107 2577116 2577570 2578076 "SHP" 2578967 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1106 2571029 2577017 2577093 "SHDP" 2577098 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1105 2570628 2570794 2570824 "SGROUP" 2570917 T SGROUP (NIL) -9 NIL 2570979 NIL) (-1104 2570486 2570512 2570585 "SGROUP-" 2570590 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1103 2567322 2568019 2568742 "SGCF" 2569785 T SGCF (NIL) -7 NIL NIL NIL) (-1102 2561744 2566769 2566866 "SFRTCAT" 2566871 NIL SFRTCAT (NIL T T T T) -9 NIL 2566910 NIL) (-1101 2555168 2556183 2557319 "SFRGCD" 2560727 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2548296 2549367 2550553 "SFQCMPK" 2554101 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2547918 2548007 2548117 "SFORT" 2548237 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1098 2547063 2547758 2547879 "SEXOF" 2547884 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1097 2542602 2543291 2543386 "SEXCAT" 2546323 NIL SEXCAT (NIL T T T T T) -9 NIL 2546901 NIL) (-1096 2541736 2542483 2542551 "SEX" 2542556 T SEX (NIL) -8 NIL NIL NIL) (-1095 2539993 2540453 2540756 "SETMN" 2541479 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2539599 2539725 2539755 "SETCAT" 2539872 T SETCAT (NIL) -9 NIL 2539957 NIL) (-1093 2539379 2539431 2539530 "SETCAT-" 2539535 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2535766 2537840 2537883 "SETAGG" 2538753 NIL SETAGG (NIL T) -9 NIL 2539093 NIL) (-1091 2535224 2535340 2535577 "SETAGG-" 2535582 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2532404 2535158 2535206 "SET" 2535211 NIL SET (NIL T) -8 NIL NIL NIL) (-1089 2531874 2532100 2532201 "SEQAST" 2532325 T SEQAST (NIL) -8 NIL NIL NIL) (-1088 2531073 2531367 2531428 "SEGXCAT" 2531714 NIL SEGXCAT (NIL T T) -9 NIL 2531834 NIL) (-1087 2530052 2530266 2530309 "SEGCAT" 2530831 NIL SEGCAT (NIL T) -9 NIL 2531052 NIL) (-1086 2529673 2529732 2529845 "SEGBIND2" 2529987 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1085 2528722 2529052 2529252 "SEGBIND" 2529508 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1084 2528323 2528523 2528600 "SEGAST" 2528667 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2527542 2527668 2527872 "SEG2" 2528167 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2526598 2527208 2527390 "SEG" 2527395 NIL SEG (NIL T) -8 NIL NIL NIL) (-1081 2526035 2526533 2526580 "SDVAR" 2526585 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1080 2518366 2525805 2525935 "SDPOL" 2525940 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1079 2516959 2517225 2517544 "SCPKG" 2518081 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1078 2516095 2516275 2516475 "SCOPE" 2516781 T SCOPE (NIL) -8 NIL NIL NIL) (-1077 2515316 2515449 2515628 "SCACHE" 2515950 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1076 2514988 2515148 2515178 "SASTCAT" 2515183 T SASTCAT (NIL) -9 NIL 2515196 NIL) (-1075 2514502 2514823 2514899 "SAOS" 2514934 T SAOS (NIL) -8 NIL NIL NIL) (-1074 2514067 2514102 2514275 "SAERFFC" 2514461 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1073 2513660 2513695 2513854 "SAEFACT" 2514026 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2507643 2513557 2513637 "SAE" 2513642 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1071 2505964 2506278 2506679 "RURPK" 2507309 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1070 2504600 2504879 2505191 "RULESET" 2505798 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1069 2504239 2504394 2504477 "RULECOLD" 2504552 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2501426 2501929 2502394 "RULE" 2503920 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1067 2500924 2501143 2501237 "RSTRCAST" 2501354 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2495773 2496567 2497487 "RSETGCD" 2500123 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2485057 2490082 2490179 "RSETCAT" 2494298 NIL RSETCAT (NIL T T T T) -9 NIL 2495395 NIL) (-1064 2482984 2483523 2484347 "RSETCAT-" 2484352 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2475371 2476746 2478266 "RSDCMPK" 2481583 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2473376 2473817 2473891 "RRCC" 2474977 NIL RRCC (NIL T T) -9 NIL 2475321 NIL) (-1061 2472727 2472901 2473180 "RRCC-" 2473185 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2472197 2472423 2472524 "RPTAST" 2472648 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2446234 2455790 2455857 "RPOLCAT" 2466521 NIL RPOLCAT (NIL T T T) -9 NIL 2469680 NIL) (-1058 2437771 2440096 2443206 "RPOLCAT-" 2443211 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2428820 2435982 2436464 "ROUTINE" 2437311 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2425655 2428446 2428586 "ROMAN" 2428702 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2423932 2424515 2424775 "ROIRC" 2425460 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2420321 2422568 2422598 "RNS" 2422902 T RNS (NIL) -9 NIL 2423175 NIL) (-1053 2418830 2419213 2419747 "RNS-" 2419822 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2418279 2418661 2418691 "RNG" 2418696 T RNG (NIL) -9 NIL 2418717 NIL) (-1051 2417671 2418033 2418076 "RMODULE" 2418138 NIL RMODULE (NIL T) -9 NIL 2418180 NIL) (-1050 2416507 2416601 2416937 "RMCAT2" 2417572 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2413384 2415853 2416150 "RMATRIX" 2416269 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2406326 2408560 2408675 "RMATCAT" 2412034 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2413016 NIL) (-1047 2405701 2405848 2406155 "RMATCAT-" 2406160 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2405268 2405343 2405471 "RINTERP" 2405620 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2404387 2404915 2404945 "RING" 2405001 T RING (NIL) -9 NIL 2405093 NIL) (-1044 2404179 2404223 2404320 "RING-" 2404325 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2403020 2403257 2403515 "RIDIST" 2403943 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2394363 2402488 2402694 "RGCHAIN" 2402868 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2393739 2394119 2394160 "RGBCSPC" 2394218 NIL RGBCSPC (NIL T) -9 NIL 2394270 NIL) (-1040 2392923 2393278 2393319 "RGBCMDL" 2393551 NIL RGBCMDL (NIL T) -9 NIL 2393665 NIL) (-1039 2392569 2392632 2392735 "RFFACTOR" 2392854 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2392294 2392329 2392426 "RFFACT" 2392528 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2390411 2390775 2391157 "RFDIST" 2391934 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2387405 2388019 2388689 "RF" 2389775 NIL RF (NIL T) -7 NIL NIL NIL) (-1035 2386858 2386950 2387113 "RETSOL" 2387307 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2386494 2386574 2386617 "RETRACT" 2386750 NIL RETRACT (NIL T) -9 NIL 2386837 NIL) (-1033 2386343 2386368 2386455 "RETRACT-" 2386460 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2385972 2386165 2386235 "RETAST" 2386295 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2378828 2385625 2385752 "RESULT" 2385867 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2377454 2378097 2378296 "RESRING" 2378731 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2377090 2377139 2377237 "RESLATC" 2377391 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2376796 2376830 2376937 "REPSQ" 2377049 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2376494 2376528 2376639 "REPDB" 2376755 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2370404 2371783 2373006 "REP2" 2375306 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2366781 2367462 2368270 "REP1" 2369631 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2364203 2364783 2365385 "REP" 2366201 T REP (NIL) -7 NIL NIL NIL) (-1023 2356956 2362344 2362800 "REGSET" 2363833 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2355769 2356104 2356354 "REF" 2356741 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2355146 2355249 2355416 "REDORDER" 2355653 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2351182 2354359 2354586 "RECLOS" 2354974 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2350234 2350415 2350630 "REALSOLV" 2350989 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2346717 2347519 2348403 "REAL0Q" 2349399 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2342318 2343306 2344367 "REAL0" 2345698 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2342164 2342205 2342235 "REAL" 2342240 T REAL (NIL) -9 NIL 2342275 NIL) (-1015 2341662 2341881 2341975 "RDUCEAST" 2342092 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2341067 2341139 2341346 "RDIV" 2341584 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2340135 2340309 2340522 "RDIST" 2340889 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2338732 2339019 2339391 "RDETRS" 2339843 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2336544 2336998 2337536 "RDETR" 2338274 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2335155 2335433 2335837 "RDEEFS" 2336260 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2333650 2333956 2334388 "RDEEF" 2334843 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2327920 2330786 2330816 "RCFIELD" 2332111 T RCFIELD (NIL) -9 NIL 2332841 NIL) (-1007 2325984 2326488 2327184 "RCFIELD-" 2327259 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2322300 2324085 2324128 "RCAGG" 2325212 NIL RCAGG (NIL T) -9 NIL 2325677 NIL) (-1005 2321928 2322022 2322185 "RCAGG-" 2322190 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2321263 2321375 2321540 "RATRET" 2321812 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2320816 2320883 2321004 "RATFACT" 2321191 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2320124 2320244 2320396 "RANDSRC" 2320686 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2319858 2319902 2319975 "RADUTIL" 2320073 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2313032 2318691 2319001 "RADIX" 2319582 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2304700 2312876 2313004 "RADFF" 2313009 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2304352 2304427 2304455 "RADCAT" 2304612 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2304137 2304185 2304282 "RADCAT-" 2304287 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2302288 2303912 2304001 "QUEUE" 2304081 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2301926 2301969 2302096 "QUATCT2" 2302239 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2295680 2298975 2299015 "QUATCAT" 2299795 NIL QUATCAT (NIL T) -9 NIL 2300561 NIL) (-993 2291845 2292875 2294255 "QUATCAT-" 2294349 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2288428 2291782 2291827 "QUAT" 2291832 NIL QUAT (NIL T) -8 NIL NIL NIL) (-991 2285948 2287512 2287553 "QUAGG" 2287928 NIL QUAGG (NIL T) -9 NIL 2288103 NIL) (-990 2285580 2285773 2285841 "QQUTAST" 2285900 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2284505 2284978 2285150 "QFORM" 2285452 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2284143 2284186 2284313 "QFCAT2" 2284456 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2275371 2280560 2280600 "QFCAT" 2281258 NIL QFCAT (NIL T) -9 NIL 2282259 NIL) (-986 2270979 2272168 2273747 "QFCAT-" 2273841 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-985 2270439 2270549 2270679 "QEQUAT" 2270869 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2263587 2264658 2265842 "QCMPACK" 2269372 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2262832 2263006 2263238 "QALGSET2" 2263407 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2260414 2260833 2261259 "QALGSET" 2262489 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-981 2259105 2259328 2259645 "PWFFINTB" 2260187 NIL PWFFINTB (NIL 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2189347 2189813 "PRIMELT" 2190460 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2188675 2188724 2188752 "PRIMCAT" 2188876 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2187682 2187860 2188088 "PRIMARR2" 2188493 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-954 2183843 2187620 2187665 "PRIMARR" 2187670 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2183486 2183542 2183653 "PREASSOC" 2183781 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2180806 2182944 2183178 "PR" 2183297 NIL PR (NIL T T) -8 NIL NIL NIL) (-951 2180281 2180414 2180442 "PPCURVE" 2180647 T PPCURVE (NIL) -9 NIL 2180783 NIL) (-950 2179903 2180076 2180159 "PORTNUM" 2180218 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2177262 2177661 2178253 "POLYROOT" 2179484 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2176645 2176703 2176937 "POLYLIFT" 2177198 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2172920 2173369 2173998 "POLYCATQ" 2176190 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2159751 2165095 2165160 "POLYCAT" 2168674 NIL POLYCAT (NIL T T 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"PLOT1" 2123104 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2116834 2118023 2119171 "PLOT" 2121084 T PLOT (NIL) -8 NIL NIL NIL) (-920 2092228 2096900 2101751 "PLEQN" 2112100 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2091921 2091968 2092071 "PINTERPA" 2092175 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2091239 2091361 2091541 "PINTERP" 2091786 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-917 2089636 2090577 2090605 "PID" 2090787 T PID (NIL) -9 NIL 2090921 NIL) (-916 2089361 2089398 2089486 "PICOERCE" 2089593 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2088609 2089130 2089217 "PI" 2089257 T PI (NIL) -8 NIL NIL 2089324) (-914 2087929 2088068 2088244 "PGROEB" 2088465 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2083516 2084330 2085235 "PGE" 2087044 T PGE (NIL) -7 NIL NIL NIL) (-912 2081640 2081886 2082252 "PGCD" 2083233 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2080978 2081081 2081242 "PFRPAC" 2081524 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2077660 2079526 2079879 "PFR" 2080657 NIL PFR (NIL 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2014379 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2013713 2013771 2013868 "PARPCURV" 2014010 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2013345 2013402 2013511 "PARPC2" 2013650 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2012865 2012951 2013070 "PAN2EXPR" 2013246 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2011671 2011986 2012214 "PALETTE" 2012657 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2010139 2010676 2011036 "PAIR" 2011357 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2004066 2009398 2009592 "PADICRC" 2009994 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 1997351 2003412 2003596 "PADICRAT" 2003914 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 1994563 1996091 1996131 "PADICCT" 1996712 NIL PADICCT (NIL NIL) -9 NIL 1996994 NIL) (-865 1992915 1994500 1994545 "PADIC" 1994550 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-864 1991872 1992072 1992340 "PADEPAC" 1992702 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 1991084 1991217 1991423 "PADE" 1991734 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 1989506 1990292 1990572 "OWP" 1990888 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 1989026 1989212 1989309 "OVERSET" 1989429 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1988099 1988631 1988803 "OVAR" 1988894 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1977006 1979208 1981408 "OUTFORM" 1985919 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1976342 1976603 1976730 "OUTBFILE" 1976899 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1975649 1975814 1975842 "OUTBCON" 1976160 T OUTBCON (NIL) -9 NIL 1976326 NIL) (-856 1975250 1975362 1975519 "OUTBCON-" 1975524 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1974514 1974635 1974796 "OUT" 1975109 T OUT (NIL) -7 NIL NIL NIL) (-854 1973922 1974243 1974332 "OSI" 1974445 T OSI (NIL) -8 NIL NIL NIL) (-853 1973478 1973790 1973818 "OSGROUP" 1973823 T OSGROUP (NIL) -9 NIL 1973845 NIL) (-852 1972223 1972450 1972735 "ORTHPOL" 1973225 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1969823 1972058 1972179 "OREUP" 1972184 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1967275 1969514 1969641 "ORESUP" 1969765 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1964803 1965303 1965864 "OREPCTO" 1966764 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1958634 1960794 1960835 "OREPCAT" 1963183 NIL OREPCAT (NIL T) -9 NIL 1964287 NIL) (-847 1955802 1956577 1957628 "OREPCAT-" 1957633 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1954979 1955251 1955279 "ORDSET" 1955588 T ORDSET (NIL) -9 NIL 1955752 NIL) (-845 1954498 1954620 1954813 "ORDSET-" 1954818 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1953132 1953889 1953917 "ORDRING" 1954119 T ORDRING (NIL) -9 NIL 1954244 NIL) (-843 1952777 1952871 1953015 "ORDRING-" 1953020 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1952183 1952620 1952648 "ORDMON" 1952653 T ORDMON (NIL) -9 NIL 1952674 NIL) (-841 1951345 1951492 1951687 "ORDFUNS" 1952032 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1950709 1951102 1951130 "ORDFIN" 1951195 T ORDFIN (NIL) -9 NIL 1951269 NIL) (-839 1949975 1950102 1950288 "ORDCOMP2" 1950569 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1946574 1948561 1948970 "ORDCOMP" 1949599 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-837 1943182 1944065 1944879 "OPTPROB" 1945780 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1939984 1940623 1941327 "OPTPACK" 1942498 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1937697 1938437 1938465 "OPTCAT" 1939284 T OPTCAT (NIL) -9 NIL 1939934 NIL) (-834 1937140 1937374 1937479 "OPSIG" 1937612 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1936908 1936947 1937013 "OPQUERY" 1937094 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1936443 1936614 1936655 "OPERCAT" 1936790 NIL OPERCAT (NIL T) -9 NIL 1936858 NIL) (-831 1936289 1936316 1936402 "OPERCAT-" 1936407 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1933457 1934600 1935104 "OP" 1935818 NIL OP (NIL T) -8 NIL NIL NIL) (-829 1932762 1932877 1933051 "ONECOMP2" 1933329 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1929614 1931559 1931928 "ONECOMP" 1932426 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-827 1929033 1929139 1929269 "OMSERVER" 1929504 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1925921 1928473 1928513 "OMSAGG" 1928574 NIL OMSAGG (NIL T) -9 NIL 1928638 NIL) (-825 1924544 1924807 1925089 "OMPKG" 1925659 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1923126 1924093 1924262 "OMLO" 1924425 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1922051 1922198 1922425 "OMEXPR" 1922952 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1921229 1921472 1921632 "OMERRK" 1921911 T OMERRK (NIL) -8 NIL NIL NIL) (-821 1920547 1920775 1920911 "OMERR" 1921113 T OMERR (NIL) -8 NIL NIL NIL) (-820 1920025 1920224 1920332 "OMENC" 1920459 T OMENC (NIL) -8 NIL NIL NIL) (-819 1913920 1915105 1916276 "OMDEV" 1918874 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1912989 1913160 1913354 "OMCONN" 1913746 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1912419 1912522 1912550 "OM" 1912849 T OM (NIL) -9 NIL NIL NIL) (-816 1911040 1911982 1912010 "OINTDOM" 1912015 T OINTDOM (NIL) -9 NIL 1912036 NIL) (-815 1906846 1908030 1908746 "OFMONOID" 1910356 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1906284 1906783 1906828 "ODVAR" 1906833 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1903744 1906029 1906184 "ODR" 1906189 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1896129 1903520 1903646 "ODPOL" 1903651 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1890012 1896001 1896106 "ODP" 1896111 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1888778 1888993 1889268 "ODETOOLS" 1889786 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1885747 1886403 1887119 "ODESYS" 1888111 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1880629 1881537 1882562 "ODERTRIC" 1884822 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1880055 1880137 1880331 "ODERED" 1880541 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1876951 1877497 1878172 "ODERAT" 1879480 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1873911 1874375 1874972 "ODEPRRIC" 1876480 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1871881 1872450 1872936 "ODEPROB" 1873445 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1868403 1868886 1869533 "ODEPRIM" 1871360 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1867652 1867754 1868014 "ODEPAL" 1868295 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1863814 1864605 1865469 "ODEPACK" 1866808 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1862847 1862954 1863183 "ODEINT" 1863703 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1856948 1858373 1859820 "ODEIFTBL" 1861420 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1852297 1853079 1854034 "ODEEF" 1856111 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1851632 1851721 1851951 "ODECONST" 1852202 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1849783 1850418 1850446 "ODECAT" 1851051 T ODECAT (NIL) -9 NIL 1851582 NIL) (-795 1849421 1849464 1849591 "OCTCT2" 1849734 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1846340 1849133 1849252 "OCT" 1849334 NIL OCT (NIL T) -8 NIL NIL NIL) (-793 1845718 1846160 1846188 "OCAMON" 1846193 T OCAMON (NIL) -9 NIL 1846214 NIL) (-792 1840499 1842892 1842932 "OC" 1844029 NIL OC (NIL T) -9 NIL 1844887 NIL) (-791 1837747 1838488 1839471 "OC-" 1839565 NIL OC- (NIL T T) -8 NIL NIL NIL) (-790 1837304 1837619 1837647 "OASGP" 1837652 T OASGP (NIL) -9 NIL 1837672 NIL) (-789 1836591 1837054 1837082 "OAMONS" 1837122 T OAMONS (NIL) -9 NIL 1837165 NIL) (-788 1836031 1836438 1836466 "OAMON" 1836471 T OAMON (NIL) -9 NIL 1836491 NIL) (-787 1835335 1835827 1835855 "OAGROUP" 1835860 T OAGROUP (NIL) -9 NIL 1835880 NIL) (-786 1835025 1835075 1835163 "NUMTUBE" 1835279 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1828598 1830116 1831652 "NUMQUAD" 1833509 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1824354 1825342 1826367 "NUMODE" 1827593 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1821735 1822589 1822617 "NUMINT" 1823540 T NUMINT (NIL) -9 NIL 1824304 NIL) (-782 1820683 1820880 1821098 "NUMFMT" 1821537 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1807042 1809987 1812519 "NUMERIC" 1818190 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1801466 1806491 1806586 "NTSCAT" 1806591 NIL NTSCAT (NIL T T T T) -9 NIL 1806630 NIL) (-779 1800660 1800825 1801018 "NTPOLFN" 1801305 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1800292 1800349 1800458 "NSUP2" 1800597 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1788177 1797117 1797929 "NSUP" 1799513 NIL NSUP (NIL T) -8 NIL NIL NIL) (-776 1778222 1787951 1788084 "NSMP" 1788089 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1776654 1776955 1777312 "NREP" 1777910 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1775245 1775497 1775855 "NPCOEF" 1776397 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1774311 1774426 1774642 "NORMRETR" 1775126 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1772352 1772642 1773051 "NORMPK" 1774019 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1772037 1772065 1772189 "NORMMA" 1772318 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1771826 1771855 1771924 "NONE1" 1772001 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1771653 1771783 1771812 "NONE" 1771817 T NONE (NIL) -8 NIL NIL NIL) (-768 1771136 1771198 1771384 "NODE1" 1771585 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1769410 1770233 1770488 "NNI" 1770835 T NNI (NIL) -8 NIL NIL 1771070) (-766 1767830 1768143 1768507 "NLINSOL" 1769078 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1764098 1765066 1765965 "NIPROB" 1766951 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1762855 1763089 1763391 "NFINTBAS" 1763860 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1762029 1762505 1762546 "NETCLT" 1762718 NIL NETCLT (NIL T) -9 NIL 1762800 NIL) (-762 1760737 1760968 1761249 "NCODIV" 1761797 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1760499 1760536 1760611 "NCNTFRAC" 1760694 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1758679 1759043 1759463 "NCEP" 1760124 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1757583 1758323 1758351 "NASRING" 1758461 T NASRING (NIL) -9 NIL 1758541 NIL) (-758 1757378 1757422 1757516 "NASRING-" 1757521 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1756531 1757030 1757058 "NARNG" 1757175 T NARNG (NIL) -9 NIL 1757266 NIL) (-756 1756223 1756290 1756424 "NARNG-" 1756429 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1755102 1755309 1755544 "NAGSP" 1756008 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1746374 1748058 1749731 "NAGS" 1753449 T NAGS (NIL) -7 NIL NIL NIL) (-753 1744922 1745230 1745561 "NAGF07" 1746063 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1739460 1740751 1742058 "NAGF04" 1743635 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1732428 1734042 1735675 "NAGF02" 1737847 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1727652 1728752 1729869 "NAGF01" 1731331 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1721280 1722846 1724431 "NAGE04" 1726087 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1712449 1714570 1716700 "NAGE02" 1719170 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1708402 1709349 1710313 "NAGE01" 1711505 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1706197 1706731 1707289 "NAGD03" 1707864 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1697947 1699875 1701829 "NAGD02" 1704263 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1691758 1693183 1694623 "NAGD01" 1696527 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1687967 1688789 1689626 "NAGC06" 1690941 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1686432 1686764 1687120 "NAGC05" 1687631 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1685808 1685927 1686071 "NAGC02" 1686308 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1684868 1685425 1685465 "NAALG" 1685544 NIL NAALG (NIL T) -9 NIL 1685605 NIL) (-739 1684703 1684732 1684822 "NAALG-" 1684827 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1678653 1679761 1680948 "MULTSQFR" 1683599 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1677972 1678047 1678231 "MULTFACT" 1678565 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1671065 1674935 1674988 "MTSCAT" 1676058 NIL MTSCAT (NIL T T) -9 NIL 1676572 NIL) (-735 1670777 1670831 1670923 "MTHING" 1671005 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1670569 1670602 1670662 "MSYSCMD" 1670737 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1667664 1670130 1670171 "MSETAGG" 1670176 NIL MSETAGG (NIL T) -9 NIL 1670210 NIL) (-732 1663776 1666419 1666739 "MSET" 1667377 NIL MSET (NIL T) -8 NIL NIL NIL) (-731 1659661 1661155 1661900 "MRING" 1663076 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1659227 1659294 1659425 "MRF2" 1659588 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1658845 1658880 1659024 "MRATFAC" 1659186 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1656457 1656752 1657183 "MPRFF" 1658550 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1650543 1656311 1656408 "MPOLY" 1656413 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1650033 1650068 1650276 "MPCPF" 1650502 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1649547 1649590 1649774 "MPC3" 1649984 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1648742 1648823 1649044 "MPC2" 1649462 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1647043 1647380 1647770 "MONOTOOL" 1648402 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1646294 1646585 1646613 "MONOID" 1646832 T MONOID (NIL) -9 NIL 1646979 NIL) (-721 1645840 1645959 1646140 "MONOID-" 1646145 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1636708 1642607 1642666 "MONOGEN" 1643340 NIL MONOGEN (NIL T T) -9 NIL 1643796 NIL) (-719 1633947 1634675 1635668 "MONOGEN-" 1635787 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1632806 1633226 1633254 "MONADWU" 1633646 T MONADWU (NIL) -9 NIL 1633884 NIL) (-717 1632178 1632337 1632585 "MONADWU-" 1632590 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1631563 1631781 1631809 "MONAD" 1632016 T MONAD (NIL) -9 NIL 1632128 NIL) (-715 1631248 1631326 1631458 "MONAD-" 1631463 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1629564 1630161 1630440 "MOEBIUS" 1631001 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1628956 1629334 1629374 "MODULE" 1629379 NIL MODULE (NIL T) -9 NIL 1629405 NIL) (-712 1628524 1628620 1628810 "MODULE-" 1628815 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1626283 1626932 1627259 "MODRING" 1628348 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1623271 1624388 1624909 "MODOP" 1625812 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1621886 1622338 1622615 "MODMONOM" 1623134 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1611733 1620177 1620591 "MODMON" 1621523 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1608950 1610601 1610877 "MODFIELD" 1611608 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1607954 1608231 1608421 "MMLFORM" 1608780 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1607480 1607523 1607702 "MMAP" 1607905 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1605697 1606430 1606471 "MLO" 1606894 NIL MLO (NIL T) -9 NIL 1607136 NIL) (-703 1603064 1603579 1604181 "MLIFT" 1605178 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1602455 1602539 1602693 "MKUCFUNC" 1602975 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1602054 1602124 1602247 "MKRECORD" 1602378 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1601102 1601263 1601491 "MKFUNC" 1601865 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1600490 1600594 1600750 "MKFLCFN" 1600985 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1600033 1600400 1600459 "MKCHSET" 1600464 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-697 1599310 1599412 1599597 "MKBCFUNC" 1599926 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-696 1596054 1598864 1599000 "MINT" 1599194 T MINT (NIL) -8 NIL NIL NIL) (-695 1594866 1595109 1595386 "MHROWRED" 1595809 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-694 1590301 1593401 1593806 "MFLOAT" 1594481 T MFLOAT (NIL) -8 NIL NIL NIL) (-693 1589658 1589734 1589905 "MFINFACT" 1590213 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-692 1585993 1586836 1587715 "MESH" 1588799 T MESH (NIL) -7 NIL NIL NIL) (-691 1584383 1584695 1585048 "MDDFACT" 1585680 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-690 1581225 1583542 1583583 "MDAGG" 1583838 NIL MDAGG (NIL T) -9 NIL 1583981 NIL) (-689 1571021 1580518 1580725 "MCMPLX" 1581038 T MCMPLX (NIL) -8 NIL NIL NIL) (-688 1570162 1570308 1570508 "MCDEN" 1570870 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-687 1568052 1568322 1568702 "MCALCFN" 1569892 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-686 1566977 1567217 1567450 "MAYBE" 1567858 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-685 1564589 1565112 1565674 "MATSTOR" 1566448 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-684 1560594 1563961 1564209 "MATRIX" 1564374 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-683 1556363 1557067 1557803 "MATLIN" 1559951 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-682 1554957 1555110 1555443 "MATCAT2" 1556198 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-681 1545105 1548246 1548323 "MATCAT" 1553206 NIL MATCAT (NIL T T T) -9 NIL 1554623 NIL) (-680 1541469 1542482 1543838 "MATCAT-" 1543843 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-679 1539581 1539905 1540289 "MAPPKG3" 1541144 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-678 1538562 1538735 1538957 "MAPPKG2" 1539405 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-677 1537061 1537345 1537672 "MAPPKG1" 1538268 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-676 1536167 1536467 1536644 "MAPPAST" 1536904 T MAPPAST (NIL) -8 NIL NIL NIL) (-675 1535778 1535836 1535959 "MAPHACK3" 1536103 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-674 1535370 1535431 1535545 "MAPHACK2" 1535710 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-673 1534808 1534911 1535053 "MAPHACK1" 1535261 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-672 1532914 1533508 1533812 "MAGMA" 1534536 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-671 1532420 1532638 1532729 "MACROAST" 1532843 T MACROAST (NIL) -8 NIL NIL NIL) (-670 1528887 1530659 1531120 "M3D" 1531992 NIL M3D (NIL T) -8 NIL NIL NIL) (-669 1523043 1527256 1527297 "LZSTAGG" 1528079 NIL LZSTAGG (NIL T) -9 NIL 1528374 NIL) (-668 1519017 1520174 1521631 "LZSTAGG-" 1521636 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-667 1516131 1516908 1517395 "LWORD" 1518562 NIL LWORD (NIL T) -8 NIL NIL NIL) (-666 1515734 1515935 1516010 "LSTAST" 1516076 T LSTAST (NIL) -8 NIL NIL NIL) (-665 1508966 1515505 1515639 "LSQM" 1515644 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-664 1508190 1508329 1508557 "LSPP" 1508821 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-663 1505032 1505689 1506402 "LSMP1" 1507509 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1502867 1503161 1503610 "LSMP" 1504728 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-661 1496794 1502034 1502075 "LSAGG" 1502137 NIL LSAGG (NIL T) -9 NIL 1502215 NIL) (-660 1493489 1494413 1495626 "LSAGG-" 1495631 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-659 1491115 1492633 1492882 "LPOLY" 1493284 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-658 1490697 1490782 1490905 "LPEFRAC" 1491024 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-657 1490349 1490461 1490489 "LOGIC" 1490600 T LOGIC (NIL) -9 NIL 1490681 NIL) (-656 1490211 1490234 1490305 "LOGIC-" 1490310 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1489404 1489544 1489737 "LODOOPS" 1490067 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1487942 1488177 1488530 "LODOF" 1489151 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-653 1484312 1486695 1486736 "LODOCAT" 1487174 NIL LODOCAT (NIL T) -9 NIL 1487385 NIL) (-652 1484045 1484103 1484230 "LODOCAT-" 1484235 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-651 1481414 1483886 1484004 "LODO2" 1484009 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-650 1478898 1481351 1481396 "LODO1" 1481401 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-649 1476370 1478814 1478880 "LODO" 1478885 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-648 1475230 1475395 1475707 "LODEEF" 1476193 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1473577 1474324 1474577 "LO" 1475062 NIL LO (NIL T T T) -8 NIL NIL NIL) (-646 1468863 1471707 1471748 "LNAGG" 1472695 NIL LNAGG (NIL T) -9 NIL 1473139 NIL) (-645 1468010 1468224 1468566 "LNAGG-" 1468571 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-644 1464173 1464935 1465574 "LMOPS" 1467425 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-643 1463568 1463930 1463971 "LMODULE" 1464032 NIL LMODULE (NIL T) -9 NIL 1464074 NIL) (-642 1460814 1463213 1463336 "LMDICT" 1463478 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-641 1460540 1460722 1460782 "LITERAL" 1460787 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-640 1460065 1460139 1460278 "LIST3" 1460460 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1458199 1458511 1458910 "LIST2MAP" 1459712 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-638 1457206 1457384 1457612 "LIST2" 1458017 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-637 1450435 1456152 1456450 "LIST" 1456941 NIL LIST (NIL T) -8 NIL NIL NIL) (-636 1449165 1449801 1449842 "LINEXP" 1450097 NIL LINEXP (NIL T) -9 NIL 1450246 NIL) (-635 1447812 1448072 1448369 "LINDEP" 1448917 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-634 1444650 1445350 1446108 "LIMITRF" 1447086 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-633 1442949 1443237 1443646 "LIMITPS" 1444352 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-632 1441998 1442441 1442481 "LIECAT" 1442621 NIL LIECAT (NIL T) -9 NIL 1442772 NIL) (-631 1441839 1441866 1441954 "LIECAT-" 1441959 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1436326 1441350 1441578 "LIE" 1441660 NIL LIE (NIL T T) -8 NIL NIL NIL) (-629 1428940 1435775 1435940 "LIB" 1436181 T LIB (NIL) -8 NIL NIL NIL) (-628 1424577 1425458 1426393 "LGROBP" 1428057 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-627 1423417 1424109 1424137 "LFCAT" 1424344 T LFCAT (NIL) -9 NIL 1424483 NIL) (-626 1421283 1421557 1421919 "LF" 1423138 NIL LF (NIL T T) -7 NIL NIL NIL) (-625 1418187 1418815 1419503 "LEXTRIPK" 1420647 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-624 1414958 1415757 1416260 "LEXP" 1417767 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-623 1414461 1414679 1414771 "LETAST" 1414886 T LETAST (NIL) -8 NIL NIL NIL) (-622 1412859 1413172 1413573 "LEADCDET" 1414143 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-621 1412049 1412123 1412352 "LAZM3PK" 1412780 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-620 1407017 1410126 1410664 "LAUPOL" 1411561 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-619 1406582 1406626 1406794 "LAPLACE" 1406967 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-618 1405663 1406213 1406254 "LALG" 1406316 NIL LALG (NIL T) -9 NIL 1406375 NIL) (-617 1405377 1405436 1405572 "LALG-" 1405577 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1403351 1404478 1404729 "LA" 1405210 NIL LA (NIL T T T) -8 NIL NIL NIL) (-615 1403186 1403210 1403251 "KVTFROM" 1403313 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-614 1401989 1402403 1402632 "KTVLOGIC" 1402977 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-613 1401824 1401848 1401889 "KRCFROM" 1401951 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-612 1400728 1400915 1401214 "KOVACIC" 1401624 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-611 1400563 1400587 1400628 "KONVERT" 1400690 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-610 1400398 1400422 1400463 "KOERCE" 1400525 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-609 1399900 1399981 1400111 "KERNEL2" 1400312 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1397634 1398394 1398787 "KERNEL" 1399539 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-607 1391485 1396173 1396227 "KDAGG" 1396604 NIL KDAGG (NIL T T) -9 NIL 1396810 NIL) (-606 1391014 1391138 1391343 "KDAGG-" 1391348 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-605 1384191 1390675 1390830 "KAFILE" 1390892 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-604 1378678 1383702 1383930 "JORDAN" 1384012 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-603 1378084 1378327 1378448 "JOINAST" 1378577 T JOINAST (NIL) -8 NIL NIL NIL) (-602 1377930 1377989 1378044 "JAVACODE" 1378049 T JAVACODE (NIL) -8 NIL NIL NIL) (-601 1374229 1376135 1376189 "IXAGG" 1377118 NIL IXAGG (NIL T T) -9 NIL 1377577 NIL) (-600 1373148 1373454 1373873 "IXAGG-" 1373878 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-599 1368728 1373070 1373129 "IVECTOR" 1373134 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-598 1367494 1367731 1367997 "ITUPLE" 1368495 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-597 1365930 1366107 1366413 "ITRIGMNP" 1367316 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-596 1364675 1364879 1365162 "ITFUN3" 1365706 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-595 1364307 1364364 1364473 "ITFUN2" 1364612 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-594 1362144 1363169 1363468 "ITAYLOR" 1364041 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-593 1351127 1356281 1357444 "ISUPS" 1361014 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-592 1350231 1350371 1350607 "ISUMP" 1350974 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-591 1345495 1350032 1350111 "ISTRING" 1350184 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-590 1344998 1345216 1345308 "ISAST" 1345423 T ISAST (NIL) -8 NIL NIL NIL) (-589 1344208 1344289 1344505 "IRURPK" 1344912 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-588 1343144 1343345 1343585 "IRSN" 1343988 T IRSN (NIL) -7 NIL NIL NIL) (-587 1341173 1341528 1341964 "IRRF2F" 1342782 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-586 1340920 1340958 1341034 "IRREDFFX" 1341129 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-585 1339535 1339794 1340093 "IROOT" 1340653 NIL IROOT (NIL T) -7 NIL NIL NIL) (-584 1338607 1338720 1338941 "IR2F" 1339418 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-583 1336220 1336715 1337281 "IR2" 1338085 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-582 1332852 1333904 1334596 "IR" 1335560 NIL IR (NIL T) -8 NIL NIL NIL) (-581 1332643 1332677 1332737 "IPRNTPK" 1332812 T IPRNTPK (NIL) -7 NIL NIL NIL) (-580 1329264 1332532 1332601 "IPF" 1332606 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-579 1327629 1329189 1329246 "IPADIC" 1329251 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-578 1326969 1327189 1327319 "IP4ADDR" 1327519 T IP4ADDR (NIL) -8 NIL NIL NIL) (-577 1326469 1326673 1326783 "IOMODE" 1326879 T IOMODE (NIL) -8 NIL NIL NIL) (-576 1325542 1326066 1326193 "IOBFILE" 1326362 T IOBFILE (NIL) -8 NIL NIL NIL) (-575 1325030 1325446 1325474 "IOBCON" 1325479 T IOBCON (NIL) -9 NIL 1325500 NIL) (-574 1324527 1324585 1324775 "INVLAPLA" 1324966 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-573 1314224 1316565 1318939 "INTTR" 1322203 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-572 1310568 1311310 1312174 "INTTOOLS" 1313409 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-571 1310154 1310245 1310362 "INTSLPE" 1310471 T INTSLPE (NIL) -7 NIL NIL NIL) (-570 1308149 1310077 1310136 "INTRVL" 1310141 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-569 1305751 1306263 1306838 "INTRF" 1307634 NIL INTRF (NIL T) -7 NIL NIL NIL) (-568 1305162 1305259 1305401 "INTRET" 1305649 NIL INTRET (NIL T) -7 NIL NIL NIL) (-567 1303159 1303548 1304018 "INTRAT" 1304770 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-566 1300387 1300970 1301596 "INTPM" 1302644 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-565 1297113 1297705 1298443 "INTPAF" 1299780 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-564 1292292 1293254 1294305 "INTPACK" 1296082 T INTPACK (NIL) -7 NIL NIL NIL) (-563 1291544 1291696 1291904 "INTHERTR" 1292134 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1290983 1291063 1291251 "INTHERAL" 1291458 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1288829 1289272 1289729 "INTHEORY" 1290546 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1280195 1281798 1283559 "INTG0" 1287199 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1266468 1269833 1273218 "INTFTBL" 1276830 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1265717 1265855 1266028 "INTFACT" 1266327 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1263108 1263552 1264114 "INTEF" 1265273 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1261575 1262280 1262308 "INTDOM" 1262609 T INTDOM (NIL) -9 NIL 1262816 NIL) (-555 1260944 1261118 1261360 "INTDOM-" 1261365 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1257439 1259328 1259382 "INTCAT" 1260181 NIL INTCAT (NIL T) -9 NIL 1260501 NIL) (-553 1256912 1257014 1257142 "INTBIT" 1257331 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1255583 1255737 1256051 "INTALG" 1256757 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1255040 1255130 1255300 "INTAF" 1255487 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1248496 1254850 1254990 "INTABL" 1254995 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1247959 1248372 1248400 "INT8" 1248405 T INT8 (NIL) -8 NIL NIL 1248413) (-548 1247421 1247834 1247862 "INT32" 1247867 T INT32 (NIL) -8 NIL NIL 1247875) (-547 1246883 1247296 1247324 "INT16" 1247329 T INT16 (NIL) -8 NIL NIL 1247337) (-546 1243796 1246612 1246739 "INT" 1246776 T INT (NIL) -8 NIL NIL NIL) (-545 1238813 1241485 1241513 "INS" 1242447 T INS (NIL) -9 NIL 1243112 NIL) (-544 1236053 1236824 1237798 "INS-" 1237871 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1234901 1235106 1235382 "INPSIGN" 1235828 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1234019 1234136 1234333 "INPRODPF" 1234781 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1232913 1233030 1233267 "INPRODFF" 1233899 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1231913 1232065 1232325 "INNMFACT" 1232749 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1231110 1231207 1231395 "INMODGCD" 1231812 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1229619 1229863 1230187 "INFSP" 1230855 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1228803 1228920 1229103 "INFPROD0" 1229499 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228413 1228473 1228571 "INFORM1" 1228738 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-535 1225295 1226478 1226993 "INFORM" 1227906 T INFORM (NIL) -8 NIL NIL NIL) (-534 1224818 1224907 1225021 "INFINITY" 1225201 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1223994 1224538 1224639 "INETCLTS" 1224737 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1222611 1222860 1223181 "INEP" 1223742 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1221887 1222508 1222573 "INDE" 1222578 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1221451 1221519 1221636 "INCRMAPS" 1221814 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1220269 1220720 1220926 "INBFILE" 1221265 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1215580 1216505 1217449 "INBFF" 1219357 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1214488 1214757 1214785 "INBCON" 1215298 T INBCON (NIL) -9 NIL 1215564 NIL) (-526 1213740 1213963 1214239 "INBCON-" 1214244 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1213242 1213461 1213553 "INAST" 1213668 T INAST (NIL) -8 NIL NIL NIL) (-524 1212696 1212921 1213027 "IMPTAST" 1213156 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1209189 1212540 1212644 "IMATRIX" 1212649 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1207901 1208024 1208339 "IMATQF" 1209045 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1206121 1206348 1206685 "IMATLIN" 1207657 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1200749 1206045 1206103 "ILIST" 1206108 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1198702 1200609 1200722 "IIARRAY2" 1200727 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1194137 1198613 1198677 "IFF" 1198682 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1193511 1193754 1193870 "IFAST" 1194041 T IFAST (NIL) -8 NIL NIL NIL) (-516 1188554 1192803 1192991 "IFARRAY" 1193368 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1187761 1188458 1188531 "IFAMON" 1188536 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1187345 1187410 1187464 "IEVALAB" 1187671 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1187020 1187088 1187248 "IEVALAB-" 1187253 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1186297 1186909 1186984 "IDPOAMS" 1186989 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-511 1185631 1186186 1186261 "IDPOAM" 1186266 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-510 1185289 1185545 1185608 "IDPO" 1185613 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1184374 1184624 1184677 "IDPC" 1185090 NIL IDPC (NIL T T) -9 NIL 1185239 NIL) (-508 1183870 1184266 1184339 "IDPAM" 1184344 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1183273 1183762 1183835 "IDPAG" 1183840 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1183041 1183188 1183238 "IDENT" 1183243 T IDENT (NIL) -8 NIL NIL NIL) (-505 1179296 1180144 1181039 "IDECOMP" 1182198 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1172170 1173219 1174266 "IDEAL" 1178332 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1171334 1171446 1171645 "ICDEN" 1172054 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1170433 1170814 1170961 "ICARD" 1171207 T ICARD (NIL) -8 NIL NIL NIL) (-501 1168493 1168806 1169211 "IBPTOOLS" 1170110 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1164127 1168113 1168226 "IBITS" 1168412 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1160850 1161426 1162121 "IBATOOL" 1163544 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1158630 1159091 1159624 "IBACHIN" 1160385 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1156507 1158476 1158579 "IARRAY2" 1158584 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1152660 1156433 1156490 "IARRAY1" 1156495 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1146663 1151072 1151553 "IAN" 1152199 T IAN (NIL) -8 NIL NIL NIL) (-494 1146174 1146231 1146404 "IALGFACT" 1146600 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1145702 1145815 1145843 "HYPCAT" 1146050 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1145240 1145357 1145543 "HYPCAT-" 1145548 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1144862 1145035 1145118 "HOSTNAME" 1145177 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1144707 1144744 1144785 "HOMOTOP" 1144790 NIL HOMOTOP (NIL T) -9 NIL 1144823 NIL) (-489 1141386 1142717 1142758 "HOAGG" 1143739 NIL HOAGG (NIL T) -9 NIL 1144418 NIL) (-488 1139980 1140379 1140905 "HOAGG-" 1140910 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1134040 1139575 1139724 "HEXADEC" 1139851 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1132788 1133010 1133273 "HEUGCD" 1133817 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1131891 1132625 1132755 "HELLFDIV" 1132760 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1130119 1131668 1131756 "HEAP" 1131835 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1129410 1129671 1129805 "HEADAST" 1130005 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1123337 1129325 1129387 "HDP" 1129392 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1117119 1122972 1123124 "HDMP" 1123238 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1116444 1116583 1116747 "HB" 1116975 T HB (NIL) -7 NIL NIL NIL) (-479 1109943 1116290 1116394 "HASHTBL" 1116399 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1109446 1109664 1109756 "HASAST" 1109871 T HASAST (NIL) -8 NIL NIL NIL) (-477 1107263 1109068 1109250 "HACKPI" 1109284 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1102985 1107116 1107229 "GTSET" 1107234 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1096513 1102863 1102961 "GSTBL" 1102966 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1088828 1095544 1095809 "GSERIES" 1096304 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1087995 1088386 1088414 "GROUP" 1088617 T GROUP (NIL) -9 NIL 1088751 NIL) (-472 1087361 1087520 1087771 "GROUP-" 1087776 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1085730 1086049 1086436 "GROEBSOL" 1087038 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1084670 1084932 1084983 "GRMOD" 1085512 NIL GRMOD (NIL T T) -9 NIL 1085680 NIL) (-469 1084438 1084474 1084602 "GRMOD-" 1084607 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1079764 1080792 1081792 "GRIMAGE" 1083458 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1078231 1078491 1078815 "GRDEF" 1079460 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1077675 1077791 1077932 "GRAY" 1078110 T GRAY (NIL) -7 NIL NIL NIL) (-465 1076888 1077268 1077319 "GRALG" 1077472 NIL GRALG (NIL T T) -9 NIL 1077565 NIL) (-464 1076549 1076622 1076785 "GRALG-" 1076790 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1073353 1076134 1076312 "GPOLSET" 1076456 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1072707 1072764 1073022 "GOSPER" 1073290 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1068466 1069145 1069671 "GMODPOL" 1072406 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1067471 1067655 1067893 "GHENSEL" 1068278 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1061522 1062365 1063392 "GENUPS" 1066555 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1061219 1061270 1061359 "GENUFACT" 1061465 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1060631 1060708 1060873 "GENPGCD" 1061137 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1060105 1060140 1060353 "GENMFACT" 1060590 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1058673 1058928 1059235 "GENEEZ" 1059848 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1052617 1058284 1058446 "GDMP" 1058596 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1042016 1046388 1047494 "GCNAALG" 1051600 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1040443 1041271 1041299 "GCDDOM" 1041554 T GCDDOM (NIL) -9 NIL 1041711 NIL) (-451 1039913 1040040 1040255 "GCDDOM-" 1040260 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1028533 1030859 1033251 "GBINTERN" 1037604 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-449 1026370 1026662 1027083 "GBF" 1028208 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-448 1025151 1025316 1025583 "GBEUCLID" 1026186 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-447 1023823 1024008 1024312 "GB" 1024930 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-446 1023172 1023297 1023446 "GAUSSFAC" 1023694 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1021539 1021841 1022155 "GALUTIL" 1022891 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1019847 1020121 1020445 "GALPOLYU" 1021266 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1017212 1017502 1017909 "GALFACTU" 1019544 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1009018 1010517 1012125 "GALFACT" 1015644 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1006406 1007064 1007092 "FVFUN" 1008248 T FVFUN (NIL) -9 NIL 1008968 NIL) (-440 1005672 1005854 1005882 "FVC" 1006173 T FVC (NIL) -9 NIL 1006356 NIL) (-439 1005342 1005497 1005565 "FUNDESC" 1005624 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1004984 1005139 1005220 "FUNCTION" 1005294 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1003802 1004285 1004488 "FTEM" 1004801 T FTEM (NIL) -8 NIL NIL NIL) (-436 1001585 1002133 1002596 "FT" 1003359 T FT (NIL) -8 NIL NIL NIL) (-435 999841 1000130 1000534 "FSUPFACT" 1001276 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 998238 998527 998859 "FST" 999529 T FST (NIL) -8 NIL NIL NIL) (-433 997409 997515 997710 "FSRED" 998120 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 996088 996343 996697 "FSPRMELT" 997124 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 993173 993611 994110 "FSPECF" 995651 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 992687 992741 992918 "FSINT" 993114 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 991014 991680 991983 "FSERIES" 992466 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 990028 990144 990375 "FSCINT" 990894 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 989070 989213 989440 "FSAGG2" 989881 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-426 985304 988014 988055 "FSAGG" 988425 NIL FSAGG (NIL T) -9 NIL 988684 NIL) (-425 983066 983667 984463 "FSAGG-" 984558 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-424 980721 981000 981554 "FS2UPS" 982784 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 979578 979749 980058 "FS2EXPXP" 980546 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-422 979160 979203 979358 "FS2" 979529 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-421 961249 969663 969703 "FS" 973551 NIL FS (NIL T) -9 NIL 975840 NIL) (-420 949980 952943 956972 "FS-" 957269 NIL FS- (NIL T T) -8 NIL NIL NIL) (-419 949406 949521 949673 "FRUTIL" 949860 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944513 947124 947164 "FRNAALG" 948560 NIL FRNAALG (NIL T) -9 NIL 949167 NIL) (-417 940242 941296 942554 "FRNAALG-" 943304 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-416 939880 939923 940050 "FRNAAF2" 940193 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-415 938287 938734 939029 "FRMOD" 939692 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-414 937482 937569 937858 "FRIDEAL2" 938194 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935261 935865 936182 "FRIDEAL" 937273 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 934401 934808 934849 "FRETRCT" 934854 NIL FRETRCT (NIL T) -9 NIL 935030 NIL) (-411 933534 933758 934102 "FRETRCT-" 934107 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-410 930746 931922 931981 "FRAMALG" 932863 NIL FRAMALG (NIL T T) -9 NIL 933155 NIL) (-409 928880 929335 929965 "FRAMALG-" 930188 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-408 928516 928573 928680 "FRAC2" 928817 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 922494 927991 928267 "FRAC" 928272 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 922130 922187 922294 "FR2" 922431 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-405 913699 917706 919037 "FR" 920831 NIL FR (NIL T) -8 NIL NIL NIL) (-404 908376 911224 911252 "FPS" 912371 T FPS (NIL) -9 NIL 912928 NIL) (-403 907825 907934 908098 "FPS-" 908244 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 905281 906914 906942 "FPC" 907167 T FPC (NIL) -9 NIL 907309 NIL) (-401 905074 905114 905211 "FPC-" 905216 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 903952 904562 904603 "FPATMAB" 904608 NIL FPATMAB (NIL T) -9 NIL 904760 NIL) (-399 901652 902128 902554 "FPARFRAC" 903589 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 897085 897583 898265 "FORTRAN" 901084 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 894761 895323 895351 "FORTFN" 896411 T FORTFN (NIL) -9 NIL 897035 NIL) (-396 894525 894575 894603 "FORTCAT" 894662 T FORTCAT (NIL) -9 NIL 894724 NIL) (-395 892241 892741 893280 "FORT" 894006 T FORT (NIL) -7 NIL NIL NIL) (-394 892029 892059 892128 "FORMULA1" 892205 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-393 890162 890645 891035 "FORMULA" 891659 T FORMULA (NIL) -8 NIL NIL NIL) (-392 889685 889737 889910 "FORDER" 890104 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 888781 888945 889138 "FOP" 889512 T FOP (NIL) -7 NIL NIL NIL) (-390 887389 888061 888235 "FNLA" 888663 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 886144 886533 886561 "FNCAT" 887021 T FNCAT (NIL) -9 NIL 887281 NIL) (-388 885710 886103 886131 "FNAME" 886136 T FNAME (NIL) -8 NIL NIL NIL) (-387 884373 885302 885330 "FMTC" 885335 T FMTC (NIL) -9 NIL 885371 NIL) (-386 880734 881896 882525 "FMONOID" 883777 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 878158 878804 878832 "FMFUN" 879976 T FMFUN (NIL) -9 NIL 880684 NIL) (-384 875352 876186 876240 "FMCAT" 877435 NIL FMCAT (NIL T T) -9 NIL 877930 NIL) (-383 874621 874802 874830 "FMC" 875120 T FMC (NIL) -9 NIL 875302 NIL) (-382 873514 874387 874487 "FM1" 874566 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-381 872733 873256 873405 "FM" 873410 NIL FM (NIL T T) -8 NIL NIL NIL) (-380 870507 870923 871417 "FLOATRP" 872284 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867945 868445 869023 "FLOATCP" 869974 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-378 861573 865674 866295 "FLOAT" 867344 T FLOAT (NIL) -8 NIL NIL NIL) (-377 860382 861186 861227 "FLINEXP" 861232 NIL FLINEXP (NIL T) -9 NIL 861325 NIL) (-376 859536 859771 860099 "FLINEXP-" 860104 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 858612 858756 858980 "FLASORT" 859388 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 855829 856671 856723 "FLALG" 857950 NIL FLALG (NIL T T) -9 NIL 858417 NIL) (-373 854871 855014 855241 "FLAGG2" 855682 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 848655 852357 852398 "FLAGG" 853660 NIL FLAGG (NIL T) -9 NIL 854312 NIL) (-371 847381 847720 848210 "FLAGG-" 848215 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 844356 845330 845389 "FINRALG" 846517 NIL FINRALG (NIL T T) -9 NIL 847025 NIL) (-369 843516 843745 844084 "FINRALG-" 844089 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 842922 843135 843163 "FINITE" 843359 T FINITE (NIL) -9 NIL 843466 NIL) (-367 835380 837541 837581 "FINAALG" 841248 NIL FINAALG (NIL T) -9 NIL 842701 NIL) (-366 830721 831762 832906 "FINAALG-" 834285 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 829405 829717 829771 "FILECAT" 830455 NIL FILECAT (NIL T T) -9 NIL 830671 NIL) (-364 828800 829160 829263 "FILE" 829335 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 826670 828162 828190 "FIELD" 828230 T FIELD (NIL) -9 NIL 828310 NIL) (-362 825290 825675 826186 "FIELD-" 826191 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 823168 823925 824272 "FGROUP" 824976 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 822258 822422 822642 "FGLMICPK" 823000 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 818127 822183 822240 "FFX" 822245 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 817728 817789 817924 "FFSLPE" 818060 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 817232 817268 817477 "FFPOLY2" 817686 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-356 813225 814004 814800 "FFPOLY" 816468 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 809113 813144 813207 "FFP" 813212 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 804276 808456 808646 "FFNBX" 808967 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-353 799252 803411 803669 "FFNBP" 804130 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-352 793922 798536 798747 "FFNB" 799085 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-351 792754 792952 793267 "FFINTBAS" 793719 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-350 788984 791161 791189 "FFIELDC" 791809 T FFIELDC (NIL) -9 NIL 792185 NIL) (-349 787647 788017 788514 "FFIELDC-" 788519 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-348 787217 787262 787386 "FFHOM" 787589 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-347 784915 785399 785916 "FFF" 786732 NIL FFF (NIL T) -7 NIL NIL NIL) (-346 780570 784657 784758 "FFCGX" 784858 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-345 776240 780302 780409 "FFCGP" 780513 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-344 771460 775967 776075 "FFCG" 776176 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-343 770871 770914 771149 "FFCAT2" 771411 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-342 752713 761742 761828 "FFCAT" 766993 NIL FFCAT (NIL T T T) -9 NIL 768444 NIL) (-341 747911 748958 750272 "FFCAT-" 751502 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 743346 747822 747886 "FF" 747891 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-339 732559 736318 737538 "FEXPR" 742198 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 731559 731994 732035 "FEVALAB" 732119 NIL FEVALAB (NIL T) -9 NIL 732380 NIL) (-337 730718 730928 731266 "FEVALAB-" 731271 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 727784 728499 728614 "FDIVCAT" 730182 NIL FDIVCAT (NIL T T T T) -9 NIL 730619 NIL) (-335 727546 727573 727743 "FDIVCAT-" 727748 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-334 726766 726853 727130 "FDIV2" 727453 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-333 725359 726149 726352 "FDIV" 726665 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-332 724045 724304 724593 "FCPAK1" 725090 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 723173 723545 723686 "FCOMP" 723936 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 706910 710323 713861 "FC" 719655 T FC (NIL) -8 NIL NIL NIL) (-329 699491 703474 703514 "FAXF" 705316 NIL FAXF (NIL T) -9 NIL 706008 NIL) (-328 696770 697425 698250 "FAXF-" 698715 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 691870 696146 696322 "FARRAY" 696627 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 687130 689155 689208 "FAMR" 690231 NIL FAMR (NIL T T) -9 NIL 690691 NIL) (-325 686020 686322 686757 "FAMR-" 686762 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 685216 685942 685995 "FAMONOID" 686000 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 683028 683712 683765 "FAMONC" 684706 NIL FAMONC (NIL T T) -9 NIL 685092 NIL) (-322 681720 682782 682919 "FAGROUP" 682924 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 679515 679834 680237 "FACUTIL" 681401 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 678614 678799 679021 "FACTFUNC" 679325 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 671021 677865 678077 "EXPUPXS" 678470 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 668504 669044 669630 "EXPRTUBE" 670455 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 664698 665290 666027 "EXPRODE" 667843 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 659105 659692 660505 "EXPR2UPS" 663996 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 658741 658798 658905 "EXPR2" 659042 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 644176 657396 657824 "EXPR" 658345 NIL EXPR (NIL T) -8 NIL NIL NIL) (-313 635607 643308 643605 "EXPEXPAN" 644013 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 635114 635331 635422 "EXITAST" 635536 T EXITAST (NIL) -8 NIL NIL NIL) (-311 634941 635071 635100 "EXIT" 635105 T EXIT (NIL) -8 NIL NIL NIL) (-310 634568 634630 634743 "EVALCYC" 634873 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 634109 634227 634268 "EVALAB" 634438 NIL EVALAB (NIL T) -9 NIL 634542 NIL) (-308 633590 633712 633933 "EVALAB-" 633938 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 631058 632326 632354 "EUCDOM" 632909 T EUCDOM (NIL) -9 NIL 633259 NIL) (-306 629463 629905 630495 "EUCDOM-" 630500 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 629095 629152 629261 "ESTOOLS2" 629400 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 628846 628888 628968 "ESTOOLS1" 629047 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 616386 619144 621894 "ESTOOLS" 626116 T ESTOOLS (NIL) -7 NIL NIL NIL) (-302 616131 616163 616245 "ESCONT1" 616348 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-301 612506 613266 614046 "ESCONT" 615371 T ESCONT (NIL) -7 NIL NIL NIL) (-300 612181 612231 612331 "ES2" 612450 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-299 611811 611869 611978 "ES1" 612117 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-298 605716 607444 607472 "ES" 610240 T ES (NIL) -9 NIL 611649 NIL) (-297 600664 601950 603767 "ES-" 603931 NIL ES- (NIL T) -8 NIL NIL NIL) (-296 599880 600009 600185 "ERROR" 600508 T ERROR (NIL) -7 NIL NIL NIL) (-295 593385 599739 599830 "EQTBL" 599835 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 593017 593074 593183 "EQ2" 593322 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 585574 588331 589780 "EQ" 591601 NIL -3942 (NIL T) -8 NIL NIL NIL) (-292 580866 581912 583005 "EP" 584513 NIL EP (NIL T) -7 NIL NIL NIL) (-291 579448 579749 580066 "ENV" 580569 T ENV (NIL) -8 NIL NIL NIL) (-290 578627 579147 579175 "ENTIRER" 579180 T ENTIRER (NIL) -9 NIL 579226 NIL) (-289 575185 576636 577006 "EMR" 578426 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 574329 574514 574568 "ELTAGG" 574948 NIL ELTAGG (NIL T T) -9 NIL 575159 NIL) (-287 574048 574110 574251 "ELTAGG-" 574256 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 573837 573866 573920 "ELTAB" 574004 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 572963 573109 573308 "ELFUTS" 573688 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 572705 572761 572789 "ELEMFUN" 572894 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 572575 572596 572664 "ELEMFUN-" 572669 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 567466 570675 570716 "ELAGG" 571656 NIL ELAGG (NIL T) -9 NIL 572119 NIL) (-281 565751 566185 566848 "ELAGG-" 566853 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 564408 564688 564983 "ELABEXPR" 565476 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 557401 559075 559902 "EFUPXS" 563684 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 550978 552652 553462 "EFULS" 556677 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 548400 548758 549237 "EFSTRUC" 550610 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 537472 539037 540597 "EF" 546915 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 536573 536957 537106 "EAB" 537343 T EAB (NIL) -8 NIL NIL NIL) (-274 535782 536532 536560 "E04UCFA" 536565 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 534991 535741 535769 "E04NAFA" 535774 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 534200 534950 534978 "E04MBFA" 534983 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 533409 534159 534187 "E04JAFA" 534192 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 532620 533368 533396 "E04GCFA" 533401 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 531831 532579 532607 "E04FDFA" 532612 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 531040 531790 531818 "E04DGFA" 531823 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 525218 526565 527929 "E04AGNT" 529696 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 523924 524404 524444 "DVARCAT" 524919 NIL DVARCAT (NIL T) -9 NIL 525118 NIL) (-265 523128 523340 523654 "DVARCAT-" 523659 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 516069 522927 523056 "DSMP" 523061 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 515734 515793 515891 "DROPT1" 516004 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 510849 511975 513112 "DROPT0" 514617 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 505659 506794 507862 "DROPT" 509801 T DROPT (NIL) -8 NIL NIL NIL) (-260 504004 504329 504715 "DRAWPT" 505293 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 503637 503690 503808 "DRAWHACK" 503945 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502368 502637 502928 "DRAWCX" 503366 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 501884 501952 502103 "DRAWCURV" 502294 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492355 494314 496429 "DRAWCFUN" 499789 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 486942 487865 488944 "DRAW" 491329 NIL DRAW (NIL T) -7 NIL NIL NIL) (-254 483755 485637 485678 "DQAGG" 486307 NIL DQAGG (NIL T) -9 NIL 486580 NIL) (-253 472070 478733 478816 "DPOLCAT" 480668 NIL DPOLCAT (NIL T T T T) -9 NIL 481213 NIL) (-252 466960 468289 470230 "DPOLCAT-" 470235 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 460122 466821 466919 "DPMO" 466924 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 453187 459902 460069 "DPMM" 460074 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 452819 453106 453154 "DOMCTOR" 453159 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 452114 452341 452478 "DOMAIN" 452702 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 445896 451749 451901 "DMP" 452015 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 445496 445552 445696 "DLP" 445834 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 439368 444823 445013 "DLIST" 445338 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 436213 438221 438262 "DLAGG" 438812 NIL DLAGG (NIL T) -9 NIL 439042 NIL) (-243 435026 435656 435684 "DIVRING" 435776 T DIVRING (NIL) -9 NIL 435859 NIL) (-242 434263 434453 434753 "DIVRING-" 434758 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 432365 432722 433128 "DISPLAY" 433877 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 431213 431416 431681 "DIRPROD2" 432158 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-239 425162 431127 431190 "DIRPROD" 431195 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 414432 420377 420430 "DIRPCAT" 420840 NIL DIRPCAT (NIL NIL T) -9 NIL 421680 NIL) (-237 411758 412400 413281 "DIRPCAT-" 413618 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 411045 411205 411391 "DIOSP" 411592 T DIOSP (NIL) -7 NIL NIL NIL) (-235 407747 409957 409998 "DIOPS" 410432 NIL DIOPS (NIL T) -9 NIL 410661 NIL) (-234 407296 407410 407601 "DIOPS-" 407606 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 406188 406782 406810 "DIFRING" 406997 T DIFRING (NIL) -9 NIL 407107 NIL) (-232 405834 405911 406063 "DIFRING-" 406068 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 403639 404877 404918 "DIFEXT" 405281 NIL DIFEXT (NIL T) -9 NIL 405575 NIL) (-230 401924 402352 403018 "DIFEXT-" 403023 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 399246 401456 401497 "DIAGG" 401502 NIL DIAGG (NIL T) -9 NIL 401522 NIL) (-228 398630 398787 399039 "DIAGG-" 399044 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 394094 397589 397866 "DHMATRIX" 398399 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 389706 390615 391625 "DFSFUN" 393104 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 384826 388637 388949 "DFLOAT" 389414 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 383054 383335 383731 "DFINTTLS" 384534 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 380118 381075 381475 "DERHAM" 382720 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 377967 379893 379982 "DEQUEUE" 380062 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 377182 377315 377511 "DEGRED" 377829 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 373757 374457 375265 "DEFINTRF" 376455 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 371396 371837 372408 "DEFINTEF" 373304 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 370773 371016 371131 "DEFAST" 371301 T DEFAST (NIL) -8 NIL NIL NIL) (-217 364833 370368 370517 "DECIMAL" 370644 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 362345 362803 363309 "DDFACT" 364377 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 361941 361984 362135 "DBLRESP" 362296 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 359840 360174 360534 "DBASE" 361708 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359109 359320 359466 "DATAARY" 359739 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 358242 359068 359096 "D03FAFA" 359101 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 357376 358201 358229 "D03EEFA" 358234 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 355326 355792 356281 "D03AGNT" 356907 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 354642 355285 355313 "D02EJFA" 355318 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 353958 354601 354629 "D02CJFA" 354634 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 353274 353917 353945 "D02BHFA" 353950 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 352590 353233 353261 "D02BBFA" 353266 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 345788 347376 348982 "D02AGNT" 351004 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 343557 344079 344625 "D01WGTS" 345262 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 342652 343516 343544 "D01TRNS" 343549 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 341747 342611 342639 "D01GBFA" 342644 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 340842 341706 341734 "D01FCFA" 341739 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 339937 340801 340829 "D01ASFA" 340834 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339032 339896 339924 "D01AQFA" 339929 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338127 338991 339019 "D01APFA" 339024 T D01APFA (NIL) -8 NIL NIL NIL) (-197 337222 338086 338114 "D01ANFA" 338119 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 336317 337181 337209 "D01AMFA" 337214 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 335412 336276 336304 "D01ALFA" 336309 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 334507 335371 335399 "D01AKFA" 335404 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 333602 334466 334494 "D01AJFA" 334499 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 326899 328450 330011 "D01AGNT" 332061 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 326236 326364 326516 "CYCLOTOM" 326767 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 322971 323684 324411 "CYCLES" 325529 T CYCLES (NIL) -7 NIL NIL NIL) (-189 322283 322417 322588 "CVMP" 322832 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320054 320312 320688 "CTRIGMNP" 322011 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 319590 319785 319886 "CTORKIND" 319973 T CTORKIND (NIL) -8 NIL NIL NIL) (-186 318938 319197 319225 "CTORCAT" 319407 T CTORCAT (NIL) -9 NIL 319520 NIL) (-185 318536 318647 318806 "CTORCAT-" 318811 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-184 318052 318239 318337 "CTORCALL" 318458 T CTORCALL (NIL) -8 NIL NIL NIL) (-183 317543 317843 317917 "CTOR" 317998 T CTOR (NIL) -8 NIL NIL NIL) (-182 316917 317016 317169 "CSTTOOLS" 317440 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 312716 313373 314131 "CRFP" 316229 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 312218 312437 312529 "CRCEAST" 312644 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 311265 311450 311678 "CRAPACK" 312022 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 310649 310750 310954 "CPMATCH" 311141 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 310374 310402 310508 "CPIMA" 310615 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 306738 307410 308128 "COORDSYS" 309709 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 306122 306251 306401 "CONTOUR" 306608 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302050 304125 304617 "CONTFRAC" 305662 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 301930 301951 301979 "CONDUIT" 302016 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301103 301623 301651 "COMRING" 301656 T COMRING (NIL) -9 NIL 301708 NIL) (-171 300184 300461 300645 "COMPPROP" 300939 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 299845 299880 300008 "COMPLPAT" 300143 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 299481 299538 299645 "COMPLEX2" 299782 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-168 289556 299290 299399 "COMPLEX" 299404 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289274 289309 289407 "COMPFACT" 289515 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 273445 283656 283696 "COMPCAT" 284700 NIL COMPCAT (NIL T) -9 NIL 286096 NIL) (-165 262982 265898 269518 "COMPCAT-" 269874 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 262711 262739 262842 "COMMUPC" 262948 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 262506 262539 262598 "COMMONOP" 262672 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262110 262310 262385 "COMMAAST" 262451 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 261693 261861 261948 "COMM" 262043 T COMM (NIL) -8 NIL NIL NIL) (-160 260942 261136 261164 "COMBOPC" 261502 T COMBOPC (NIL) -9 NIL 261677 NIL) (-159 259838 260048 260290 "COMBINAT" 260732 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256036 256609 257249 "COMBF" 259260 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 254822 255152 255387 "COLOR" 255821 T COLOR (NIL) -8 NIL NIL NIL) (-156 254325 254543 254635 "COLONAST" 254750 T COLONAST (NIL) -8 NIL NIL NIL) (-155 253965 254012 254137 "CMPLXRT" 254272 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 253440 253665 253764 "CLLCTAST" 253886 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 248942 249970 251050 "CLIP" 252380 T CLIP (NIL) -7 NIL NIL NIL) (-152 247324 248048 248287 "CLIF" 248769 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 243546 245470 245511 "CLAGG" 246440 NIL CLAGG (NIL T) -9 NIL 246976 NIL) (-150 241968 242425 243008 "CLAGG-" 243013 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 241512 241597 241737 "CINTSLPE" 241877 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239013 239484 240032 "CHVAR" 241040 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 238256 238776 238804 "CHARZ" 238809 T CHARZ (NIL) -9 NIL 238824 NIL) (-146 238010 238050 238128 "CHARPOL" 238210 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237137 237690 237718 "CHARNZ" 237765 T CHARNZ (NIL) -9 NIL 237821 NIL) (-144 235126 235827 236162 "CHAR" 236822 T CHAR (NIL) -8 NIL NIL NIL) (-143 234852 234913 234941 "CFCAT" 235052 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234097 234208 234390 "CDEN" 234736 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230089 233250 233530 "CCLASS" 233837 T CCLASS (NIL) -8 NIL NIL NIL) (-140 229396 229539 229702 "CATEGORY" 229946 T -10 (NIL) -8 NIL NIL NIL) (-139 229028 229315 229363 "CATCTOR" 229368 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 228502 228728 228827 "CATAST" 228949 T CATAST (NIL) -8 NIL NIL NIL) (-137 228005 228223 228315 "CASEAST" 228430 T CASEAST (NIL) -8 NIL NIL NIL) (-136 227113 227261 227482 "CARTEN2" 227852 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222165 223142 223895 "CARTEN" 226416 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 220507 221315 221572 "CARD" 221928 T CARD (NIL) -8 NIL NIL NIL) (-133 220110 220311 220386 "CAPSLAST" 220452 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 219482 219810 219838 "CACHSET" 219970 T CACHSET (NIL) -9 NIL 220047 NIL) (-131 218978 219274 219302 "CABMON" 219352 T CABMON (NIL) -9 NIL 219408 NIL) (-130 218478 218682 218792 "BYTEORD" 218888 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 213879 217983 218155 "BYTEBUF" 218326 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212883 213413 213555 "BYTE" 213718 T BYTE (NIL) -8 NIL NIL 213840) (-127 210442 212575 212682 "BTREE" 212809 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 207942 210090 210212 "BTOURN" 210352 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205361 207412 207453 "BTCAT" 207521 NIL BTCAT (NIL T) -9 NIL 207598 NIL) (-124 205028 205108 205257 "BTCAT-" 205262 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200320 204171 204199 "BTAGG" 204421 T BTAGG (NIL) -9 NIL 204582 NIL) (-122 199810 199935 200141 "BTAGG-" 200146 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 196856 199088 199303 "BSTREE" 199627 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 195994 196120 196304 "BRILL" 196712 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 192694 194720 194761 "BRAGG" 195410 NIL BRAGG (NIL T) -9 NIL 195668 NIL) (-118 191226 191631 192185 "BRAGG-" 192190 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 184511 190572 190756 "BPADICRT" 191074 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 182863 184448 184493 "BPADIC" 184498 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 182561 182591 182705 "BOUNDZRO" 182827 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 180182 180626 181146 "BOP1" 182074 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 175697 176788 177655 "BOP" 179335 T BOP (NIL) -8 NIL NIL NIL) (-112 174399 175121 175314 "BOOLEAN" 175524 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 173761 174139 174193 "BMODULE" 174198 NIL BMODULE (NIL T T) -9 NIL 174263 NIL) (-110 169591 173559 173632 "BITS" 173708 T BITS (NIL) -8 NIL NIL NIL) (-109 169003 169125 169267 "BINDING" 169469 T BINDING (NIL) -8 NIL NIL NIL) (-108 163066 168600 168748 "BINARY" 168875 T BINARY (NIL) -8 NIL NIL NIL) (-107 160893 162321 162362 "BGAGG" 162622 NIL BGAGG (NIL T) -9 NIL 162759 NIL) (-106 160724 160756 160847 "BGAGG-" 160852 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 159822 160108 160313 "BFUNCT" 160539 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 158506 158687 158975 "BEZOUT" 159646 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155025 157358 157688 "BBTREE" 158209 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 154759 154812 154840 "BASTYPE" 154959 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 154612 154640 154713 "BASTYPE-" 154718 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154046 154122 154274 "BALFACT" 154523 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 152929 153461 153647 "AUTOMOR" 153891 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 152655 152660 152686 "ATTREG" 152691 T ATTREG (NIL) -9 NIL NIL NIL) (-97 150934 151352 151704 "ATTRBUT" 152321 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 150569 150762 150828 "ATTRAST" 150886 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150105 150218 150244 "ATRIG" 150445 T ATRIG (NIL) -9 NIL NIL NIL) (-94 149914 149955 150042 "ATRIG-" 150047 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 149585 149745 149771 "ASTCAT" 149776 T ASTCAT (NIL) -9 NIL 149806 NIL) (-92 149312 149371 149490 "ASTCAT-" 149495 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 147509 149088 149176 "ASTACK" 149255 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146014 146311 146676 "ASSOCEQ" 147191 NIL ASSOCEQ (NIL 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(NIL T T) -7 NIL NIL NIL) (-1160 2775563 2790746 2790997 "SULS" 2791376 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2775192 2775385 2775455 "SUCHTAST" 2775515 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1158 2774514 2774717 2774857 "SUCH" 2775100 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1157 2768408 2769420 2770379 "SUBSPACE" 2773602 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1156 2767838 2767928 2768092 "SUBRESP" 2768296 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1155 2761203 2762503 2763814 "STTF" 2766574 NIL STTF (NIL T) -7 NIL NIL NIL) (-1154 2755376 2756496 2757643 "STTFNC" 2760103 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1153 2746687 2748558 2750352 "STTAYLOR" 2753617 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1152 2739931 2746551 2746634 "STRTBL" 2746639 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1151 2735322 2739886 2739917 "STRING" 2739922 T STRING (NIL) -8 NIL NIL NIL) (-1150 2730210 2734695 2734725 "STRICAT" 2734784 T STRICAT (NIL) -9 NIL 2734846 NIL) (-1149 2723013 2727829 2728440 "STREAM" 2729634 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1148 2722523 2722600 2722744 "STREAM3" 2722930 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1147 2721505 2721688 2721923 "STREAM2" 2722336 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1146 2721193 2721245 2721338 "STREAM1" 2721447 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1145 2720209 2720390 2720621 "STINPROD" 2721009 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1144 2719787 2719971 2720001 "STEP" 2720081 T STEP (NIL) -9 NIL 2720159 NIL) (-1143 2713330 2719686 2719763 "STBL" 2719768 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1142 2708504 2712551 2712594 "STAGG" 2712747 NIL STAGG (NIL T) -9 NIL 2712836 NIL) (-1141 2706206 2706808 2707680 "STAGG-" 2707685 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1140 2704401 2705976 2706068 "STACK" 2706149 NIL STACK (NIL T) -8 NIL NIL NIL) (-1139 2697124 2702542 2702998 "SREGSET" 2704031 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1138 2689549 2690918 2692431 "SRDCMPK" 2695730 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2682516 2686989 2687019 "SRAGG" 2688322 T SRAGG (NIL) -9 NIL 2688930 NIL) (-1136 2681533 2681788 2682167 "SRAGG-" 2682172 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1135 2676020 2680480 2680901 "SQMATRIX" 2681159 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1134 2669767 2672738 2673465 "SPLTREE" 2675365 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1133 2665757 2666423 2667069 "SPLNODE" 2669193 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1132 2664804 2665037 2665067 "SPFCAT" 2665511 T SPFCAT (NIL) -9 NIL NIL NIL) (-1131 2663541 2663751 2664015 "SPECOUT" 2664562 T SPECOUT (NIL) -7 NIL NIL NIL) (-1130 2655193 2656937 2656967 "SPADXPT" 2661359 T SPADXPT (NIL) -9 NIL 2663393 NIL) (-1129 2654954 2654994 2655063 "SPADPRSR" 2655146 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1128 2653136 2654909 2654940 "SPADAST" 2654945 T SPADAST (NIL) -8 NIL NIL NIL) (-1127 2645107 2646854 2646897 "SPACEC" 2651270 NIL SPACEC (NIL T) -9 NIL 2653086 NIL) (-1126 2643264 2645039 2645088 "SPACE3" 2645093 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1125 2642016 2642187 2642478 "SORTPAK" 2643069 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1124 2640066 2640369 2640788 "SOLVETRA" 2641680 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1123 2639077 2639299 2639573 "SOLVESER" 2639839 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1122 2634288 2635178 2636180 "SOLVERAD" 2638129 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1121 2630103 2630712 2631441 "SOLVEFOR" 2633655 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1120 2624400 2629452 2629549 "SNTSCAT" 2629554 NIL SNTSCAT (NIL T T T T) -9 NIL 2629624 NIL) (-1119 2618533 2622723 2623114 "SMTS" 2624090 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1118 2612973 2618421 2618498 "SMP" 2618503 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1117 2611132 2611433 2611831 "SMITH" 2612670 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1116 2604019 2608183 2608286 "SMATCAT" 2609637 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610187 NIL) (-1115 2600959 2601782 2602960 "SMATCAT-" 2602965 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1114 2598672 2600195 2600238 "SKAGG" 2600499 NIL SKAGG (NIL T) -9 NIL 2600634 NIL) (-1113 2595007 2598088 2598283 "SINT" 2598470 T SINT (NIL) -8 NIL NIL 2598643) (-1112 2594779 2594817 2594883 "SIMPAN" 2594963 T SIMPAN (NIL) -7 NIL NIL NIL) (-1111 2594085 2594314 2594454 "SIG" 2594661 T SIG (NIL) -8 NIL NIL NIL) (-1110 2592923 2593144 2593419 "SIGNRF" 2593844 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1109 2591728 2591879 2592170 "SIGNEF" 2592752 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1108 2591061 2591311 2591435 "SIGAST" 2591626 T SIGAST (NIL) -8 NIL NIL NIL) (-1107 2588751 2589205 2589711 "SHP" 2590602 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1106 2582651 2588652 2588728 "SHDP" 2588733 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1105 2582250 2582416 2582446 "SGROUP" 2582539 T SGROUP (NIL) -9 NIL 2582601 NIL) (-1104 2582108 2582134 2582207 "SGROUP-" 2582212 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1103 2578943 2579641 2580364 "SGCF" 2581407 T SGCF (NIL) -7 NIL NIL NIL) (-1102 2573338 2578390 2578487 "SFRTCAT" 2578492 NIL SFRTCAT (NIL T T T T) -9 NIL 2578531 NIL) (-1101 2566759 2567777 2568913 "SFRGCD" 2572321 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559886 2560958 2562144 "SFQCMPK" 2565692 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2559508 2559597 2559707 "SFORT" 2559827 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1098 2558653 2559348 2559469 "SEXOF" 2559474 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1097 2557787 2558534 2558602 "SEX" 2558607 T SEX (NIL) -8 NIL NIL NIL) (-1096 2553326 2554015 2554110 "SEXCAT" 2557047 NIL SEXCAT (NIL T T T T T) -9 NIL 2557625 NIL) (-1095 2550506 2553260 2553308 "SET" 2553313 NIL SET (NIL T) -8 NIL NIL NIL) (-1094 2548757 2549219 2549524 "SETMN" 2550247 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1093 2548363 2548489 2548519 "SETCAT" 2548636 T SETCAT (NIL) -9 NIL 2548721 NIL) (-1092 2548143 2548195 2548294 "SETCAT-" 2548299 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1091 2544530 2546604 2546647 "SETAGG" 2547517 NIL SETAGG (NIL T) -9 NIL 2547857 NIL) (-1090 2543988 2544104 2544341 "SETAGG-" 2544346 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1089 2543458 2543684 2543785 "SEQAST" 2543909 T SEQAST (NIL) -8 NIL NIL NIL) (-1088 2542657 2542951 2543012 "SEGXCAT" 2543298 NIL SEGXCAT (NIL T T) -9 NIL 2543418 NIL) (-1087 2541711 2542323 2542505 "SEG" 2542510 NIL SEG (NIL T) -8 NIL NIL NIL) (-1086 2540690 2540904 2540947 "SEGCAT" 2541469 NIL SEGCAT (NIL T) -9 NIL 2541690 NIL) (-1085 2539739 2540069 2540269 "SEGBIND" 2540525 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1084 2539360 2539419 2539532 "SEGBIND2" 2539674 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1083 2538960 2539161 2539238 "SEGAST" 2539305 T SEGAST (NIL) -8 NIL NIL NIL) (-1082 2538179 2538305 2538509 "SEG2" 2538804 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1081 2537616 2538114 2538161 "SDVAR" 2538166 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1080 2529898 2537386 2537516 "SDPOL" 2537521 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1079 2528491 2528757 2529076 "SCPKG" 2529613 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1078 2527627 2527807 2528007 "SCOPE" 2528313 T SCOPE (NIL) -8 NIL NIL NIL) (-1077 2526847 2526981 2527160 "SCACHE" 2527482 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1076 2526519 2526679 2526709 "SASTCAT" 2526714 T SASTCAT (NIL) -9 NIL 2526727 NIL) (-1075 2526033 2526354 2526430 "SAOS" 2526465 T SAOS (NIL) -8 NIL NIL NIL) (-1074 2525598 2525633 2525806 "SAERFFC" 2525992 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1073 2519564 2525495 2525575 "SAE" 2525580 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1072 2519157 2519192 2519351 "SAEFACT" 2519523 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1071 2517478 2517792 2518193 "RURPK" 2518823 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1070 2516114 2516393 2516705 "RULESET" 2517312 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1069 2513301 2513804 2514269 "RULE" 2515795 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1068 2512940 2513095 2513178 "RULECOLD" 2513253 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1067 2512438 2512657 2512751 "RSTRCAST" 2512868 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2507286 2508081 2509001 "RSETGCD" 2511637 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496543 2501595 2501692 "RSETCAT" 2505811 NIL RSETCAT (NIL T T T T) -9 NIL 2506908 NIL) (-1064 2494470 2495009 2495833 "RSETCAT-" 2495838 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486855 2488232 2489752 "RSDCMPK" 2493069 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484860 2485301 2485375 "RRCC" 2486461 NIL RRCC (NIL T T) -9 NIL 2486805 NIL) (-1061 2484211 2484385 2484664 "RRCC-" 2484669 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483681 2483907 2484008 "RPTAST" 2484132 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457679 2467274 2467341 "RPOLCAT" 2478005 NIL RPOLCAT (NIL T T T) -9 NIL 2481164 NIL) (-1058 2449177 2451517 2454639 "RPOLCAT-" 2454644 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2440224 2447388 2447870 "ROUTINE" 2448717 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2437049 2439850 2439990 "ROMAN" 2440106 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2435320 2435909 2436169 "ROIRC" 2436854 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431705 2433956 2433986 "RNS" 2434290 T RNS (NIL) -9 NIL 2434563 NIL) (-1053 2430214 2430597 2431131 "RNS-" 2431206 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429663 2430045 2430075 "RNG" 2430080 T RNG (NIL) -9 NIL 2430101 NIL) (-1051 2429055 2429417 2429460 "RMODULE" 2429522 NIL RMODULE (NIL T) -9 NIL 2429564 NIL) (-1050 2427891 2427985 2428321 "RMCAT2" 2428956 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424768 2427237 2427534 "RMATRIX" 2427653 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417710 2419944 2420059 "RMATCAT" 2423418 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2424400 NIL) (-1047 2417085 2417232 2417539 "RMATCAT-" 2417544 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416652 2416727 2416855 "RINTERP" 2417004 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415771 2416299 2416329 "RING" 2416385 T RING (NIL) -9 NIL 2416477 NIL) (-1044 2415563 2415607 2415704 "RING-" 2415709 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2414404 2414641 2414899 "RIDIST" 2415327 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405720 2413872 2414078 "RGCHAIN" 2414252 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2405096 2405476 2405517 "RGBCSPC" 2405575 NIL RGBCSPC (NIL T) -9 NIL 2405627 NIL) (-1040 2404280 2404635 2404676 "RGBCMDL" 2404908 NIL RGBCMDL (NIL T) -9 NIL 2405022 NIL) (-1039 2401274 2401888 2402558 "RF" 2403644 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400920 2400983 2401086 "RFFACTOR" 2401205 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400645 2400680 2400777 "RFFACT" 2400879 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398762 2399126 2399508 "RFDIST" 2400285 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2398215 2398307 2398470 "RETSOL" 2398664 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397851 2397931 2397974 "RETRACT" 2398107 NIL RETRACT (NIL T) -9 NIL 2398194 NIL) (-1033 2397700 2397725 2397812 "RETRACT-" 2397817 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2397329 2397522 2397592 "RETAST" 2397652 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2390183 2396982 2397109 "RESULT" 2397224 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388801 2389452 2389651 "RESRING" 2390086 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2388437 2388486 2388584 "RESLATC" 2388738 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2388142 2388177 2388284 "REPSQ" 2388396 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385564 2386144 2386746 "REP" 2387562 T REP (NIL) -7 NIL NIL NIL) (-1026 2385261 2385296 2385407 "REPDB" 2385523 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2379161 2380550 2381773 "REP2" 2384073 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375538 2376219 2377027 "REP1" 2378388 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2368261 2373679 2374135 "REGSET" 2375168 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2367074 2367409 2367659 "REF" 2368046 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2366451 2366554 2366721 "REDORDER" 2366958 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2362446 2365664 2365891 "RECLOS" 2366279 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361498 2361679 2361894 "REALSOLV" 2362253 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2361344 2361385 2361415 "REAL" 2361420 T REAL (NIL) -9 NIL 2361455 NIL) (-1017 2357827 2358629 2359513 "REAL0Q" 2360509 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2353428 2354416 2355477 "REAL0" 2356808 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352926 2353145 2353239 "RDUCEAST" 2353356 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2352331 2352403 2352610 "RDIV" 2352848 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2351399 2351573 2351786 "RDIST" 2352153 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349996 2350283 2350655 "RDETRS" 2351107 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347808 2348262 2348800 "RDETR" 2349538 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2346419 2346697 2347101 "RDEEFS" 2347524 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344914 2345220 2345652 "RDEEF" 2346107 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2339167 2342050 2342080 "RCFIELD" 2343375 T RCFIELD (NIL) -9 NIL 2344105 NIL) (-1007 2337231 2337735 2338431 "RCFIELD-" 2338506 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333547 2335332 2335375 "RCAGG" 2336459 NIL RCAGG (NIL T) -9 NIL 2336924 NIL) (-1005 2333175 2333269 2333432 "RCAGG-" 2333437 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332510 2332622 2332787 "RATRET" 2333059 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2332063 2332130 2332251 "RATFACT" 2332438 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2331371 2331491 2331643 "RANDSRC" 2331933 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2331105 2331149 2331222 "RADUTIL" 2331320 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2324248 2329938 2330248 "RADIX" 2330829 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315896 2324092 2324220 "RADFF" 2324225 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315548 2315623 2315651 "RADCAT" 2315808 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2315333 2315381 2315478 "RADCAT-" 2315483 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313484 2315108 2315197 "QUEUE" 2315277 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2310052 2313421 2313466 "QUAT" 2313471 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309690 2309733 2309860 "QUATCT2" 2310003 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2303429 2306739 2306779 "QUATCAT" 2307559 NIL QUATCAT (NIL T) -9 NIL 2308325 NIL) (-992 2299573 2300610 2301997 "QUATCAT-" 2302091 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2297093 2298657 2298698 "QUAGG" 2299073 NIL QUAGG (NIL T) -9 NIL 2299248 NIL) (-990 2296725 2296918 2296986 "QQUTAST" 2297045 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295650 2296123 2296295 "QFORM" 2296597 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286854 2292067 2292107 "QFCAT" 2292765 NIL QFCAT (NIL T) -9 NIL 2293766 NIL) (-987 2282426 2283627 2285218 "QFCAT-" 2285312 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2282064 2282107 2282234 "QFCAT2" 2282377 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281524 2281634 2281764 "QEQUAT" 2281954 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274671 2275743 2276927 "QCMPACK" 2280457 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2272247 2272668 2273096 "QALGSET" 2274326 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271492 2271666 2271898 "QALGSET2" 2272067 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2270182 2270406 2270723 "PWFFINTB" 2271265 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2268364 2268532 2268886 "PUSHVAR" 2269996 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2264282 2265336 2265377 "PTRANFN" 2267261 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262684 2262975 2263297 "PTPACK" 2263993 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2262316 2262373 2262482 "PTFUNC2" 2262621 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256843 2261188 2261229 "PTCAT" 2261525 NIL PTCAT (NIL T) -9 NIL 2261678 NIL) (-975 2256501 2256536 2256660 "PSQFR" 2256802 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2255096 2255394 2255728 "PSEUDLIN" 2256199 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241859 2244230 2246554 "PSETPK" 2252856 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234903 2237617 2237713 "PSETCAT" 2240734 NIL PSETCAT (NIL T T T T) -9 NIL 2241548 NIL) (-971 2232739 2233373 2234194 "PSETCAT-" 2234199 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2232088 2232253 2232281 "PSCURVE" 2232549 T PSCURVE (NIL) -9 NIL 2232716 NIL) (-969 2228436 2229926 2229991 "PSCAT" 2230835 NIL PSCAT (NIL T T T) -9 NIL 2231075 NIL) (-968 2227499 2227715 2228115 "PSCAT-" 2228120 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2226231 2226864 2227069 "PRTITION" 2227314 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225733 2225952 2226044 "PRTDAST" 2226159 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214823 2217037 2219225 "PRS" 2223595 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212681 2214173 2214213 "PRQAGG" 2214396 NIL PRQAGG (NIL T) -9 NIL 2214498 NIL) (-963 2212067 2212296 2212324 "PROPLOG" 2212509 T PROPLOG (NIL) -9 NIL 2212631 NIL) (-962 2209237 2209881 2210345 "PROPFRML" 2211635 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2208697 2208807 2208937 "PROPERTY" 2209127 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2202782 2206863 2207683 "PRODUCT" 2207923 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2200087 2202240 2202474 "PR" 2202593 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2199883 2199915 2199974 "PRINT" 2200048 T PRINT (NIL) -7 NIL NIL NIL) (-957 2199223 2199340 2199492 "PRIMES" 2199763 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2197288 2197689 2198155 "PRIMELT" 2198802 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2197017 2197066 2197094 "PRIMCAT" 2197218 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2193178 2196955 2197000 "PRIMARR" 2197005 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2192185 2192363 2192591 "PRIMARR2" 2192996 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2191828 2191884 2191995 "PREASSOC" 2192123 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2191303 2191436 2191464 "PPCURVE" 2191669 T PPCURVE (NIL) -9 NIL 2191805 NIL) (-950 2190925 2191098 2191181 "PORTNUM" 2191240 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2188284 2188683 2189275 "POLYROOT" 2190506 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2182221 2187888 2188048 "POLY" 2188157 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2181604 2181662 2181896 "POLYLIFT" 2182157 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2177879 2178328 2178957 "POLYCATQ" 2181149 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2164688 2170054 2170119 "POLYCAT" 2173633 NIL POLYCAT (NIL T T T) -9 NIL 2175561 NIL) (-944 2158137 2159999 2162383 "POLYCAT-" 2162388 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2157724 2157792 2157912 "POLY2UP" 2158063 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2157356 2157413 2157522 "POLY2" 2157661 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2156041 2156280 2156556 "POLUTIL" 2157130 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2154396 2154673 2155004 "POLTOPOL" 2155763 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2149913 2154332 2154378 "POINT" 2154383 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2148100 2148457 2148832 "PNTHEORY" 2149558 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2146519 2146816 2147228 "PMTOOLS" 2147798 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2146112 2146190 2146307 "PMSYM" 2146435 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2145622 2145691 2145865 "PMQFCAT" 2146037 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2144977 2145087 2145243 "PMPRED" 2145499 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2144373 2144459 2144620 "PMPREDFS" 2144878 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2143016 2143224 2143609 "PMPLCAT" 2144135 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2142548 2142627 2142779 "PMLSAGG" 2142931 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2142023 2142099 2142280 "PMKERNEL" 2142466 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2141640 2141715 2141828 "PMINS" 2141942 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2141068 2141137 2141353 "PMFS" 2141565 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2140296 2140414 2140619 "PMDOWN" 2140945 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2139459 2139618 2139800 "PMASS" 2140134 T PMASS (NIL) -7 NIL NIL NIL) (-925 2138733 2138844 2139007 "PMASSFS" 2139345 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2138388 2138456 2138550 "PLOTTOOL" 2138659 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2132995 2134199 2135347 "PLOT" 2137260 T PLOT (NIL) -8 NIL NIL NIL) (-922 2128799 2129843 2130764 "PLOT3D" 2132094 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2127711 2127888 2128123 "PLOT1" 2128603 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2103100 2107777 2112628 "PLEQN" 2122977 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2102418 2102540 2102720 "PINTERP" 2102965 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2102111 2102158 2102261 "PINTERPA" 2102365 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2101359 2101880 2101967 "PI" 2102007 T PI (NIL) -8 NIL NIL 2102074) (-916 2099748 2100697 2100725 "PID" 2100907 T PID (NIL) -9 NIL 2101041 NIL) (-915 2099473 2099510 2099598 "PICOERCE" 2099705 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2098793 2098932 2099108 "PGROEB" 2099329 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2094380 2095194 2096099 "PGE" 2097908 T PGE (NIL) -7 NIL NIL NIL) (-912 2092503 2092750 2093116 "PGCD" 2094097 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2091841 2091944 2092105 "PFRPAC" 2092387 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2088509 2090389 2090742 "PFR" 2091520 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2086898 2087142 2087467 "PFOTOOLS" 2088256 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2085431 2085670 2086021 "PFOQ" 2086655 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2083904 2084116 2084479 "PFO" 2085215 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2080484 2083793 2083862 "PF" 2083867 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2077910 2079155 2079183 "PFECAT" 2079768 T PFECAT (NIL) -9 NIL 2080152 NIL) (-904 2077355 2077509 2077723 "PFECAT-" 2077728 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2075958 2076210 2076511 "PFBRU" 2077104 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2073823 2074176 2074608 "PFBR" 2075609 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2069732 2071199 2071875 "PERM" 2073180 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2064993 2065939 2066809 "PERMGRP" 2068895 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2063125 2064056 2064097 "PERMCAT" 2064543 NIL PERMCAT (NIL T) -9 NIL 2064848 NIL) (-898 2062778 2062819 2062943 "PERMAN" 2063078 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2060314 2062443 2062565 "PENDTREE" 2062689 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2058399 2059141 2059182 "PDRING" 2059839 NIL PDRING (NIL T) -9 NIL 2060125 NIL) (-895 2057502 2057720 2058082 "PDRING-" 2058087 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2054744 2055495 2056163 "PDEPROB" 2056854 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2052289 2052793 2053348 "PDEPACK" 2054209 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2051201 2051391 2051642 "PDECOMP" 2052088 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2048806 2049623 2049651 "PDECAT" 2050438 T PDECAT (NIL) -9 NIL 2051151 NIL) (-890 2048557 2048590 2048680 "PCOMP" 2048767 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2046762 2047358 2047655 "PBWLB" 2048286 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2039262 2040835 2042173 "PATTERN" 2045445 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2038894 2038951 2039060 "PATTERN2" 2039199 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2036651 2037039 2037496 "PATTERN1" 2038483 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2034046 2034600 2035081 "PATRES" 2036216 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2033610 2033677 2033809 "PATRES2" 2033973 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2031493 2031898 2032305 "PATMATCH" 2033277 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2031029 2031212 2031253 "PATMAB" 2031360 NIL PATMAB (NIL T) -9 NIL 2031443 NIL) (-881 2029574 2029883 2030141 "PATLRES" 2030834 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2029120 2029243 2029284 "PATAB" 2029289 NIL PATAB (NIL T) -9 NIL 2029461 NIL) (-879 2026601 2027133 2027706 "PARTPERM" 2028567 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2026222 2026285 2026387 "PARSURF" 2026532 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2025854 2025911 2026020 "PARSU2" 2026159 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2025618 2025658 2025725 "PARSER" 2025807 T PARSER (NIL) -7 NIL NIL NIL) (-875 2025239 2025302 2025404 "PARSCURV" 2025549 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2024871 2024928 2025037 "PARSC2" 2025176 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2024510 2024568 2024665 "PARPCURV" 2024807 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2024142 2024199 2024308 "PARPC2" 2024447 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2023662 2023748 2023867 "PAN2EXPR" 2024043 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2022466 2022783 2023011 "PALETTE" 2023454 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2020934 2021471 2021831 "PAIR" 2022152 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2014831 2020193 2020387 "PADICRC" 2020789 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2008087 2014177 2014361 "PADICRAT" 2014679 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2006429 2008024 2008069 "PADIC" 2008074 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2003631 2005169 2005209 "PADICCT" 2005790 NIL PADICCT (NIL NIL) -9 NIL 2006072 NIL) (-864 2002588 2002788 2003056 "PADEPAC" 2003418 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2001800 2001933 2002139 "PADE" 2002450 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2000214 2001008 2001288 "OWP" 2001604 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 1999734 1999920 2000017 "OVERSET" 2000137 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1998807 1999339 1999511 "OVAR" 1999602 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1998071 1998192 1998353 "OUT" 1998666 T OUT (NIL) -7 NIL NIL NIL) (-858 1986969 1989180 1991380 "OUTFORM" 1995891 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1986305 1986566 1986693 "OUTBFILE" 1986862 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1985612 1985777 1985805 "OUTBCON" 1986123 T OUTBCON (NIL) -9 NIL 1986289 NIL) (-855 1985213 1985325 1985482 "OUTBCON-" 1985487 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1984620 1984942 1985031 "OSI" 1985144 T OSI (NIL) -8 NIL NIL NIL) (-853 1984176 1984488 1984516 "OSGROUP" 1984521 T OSGROUP (NIL) -9 NIL 1984543 NIL) (-852 1982921 1983148 1983433 "ORTHPOL" 1983923 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1980499 1982756 1982877 "OREUP" 1982882 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1977929 1980190 1980317 "ORESUP" 1980441 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1975457 1975957 1976518 "OREPCTO" 1977418 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1969273 1971448 1971489 "OREPCAT" 1973837 NIL OREPCAT (NIL T) -9 NIL 1974941 NIL) (-847 1966420 1967202 1968260 "OREPCAT-" 1968265 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1965597 1965869 1965897 "ORDSET" 1966206 T ORDSET (NIL) -9 NIL 1966370 NIL) (-845 1965116 1965238 1965431 "ORDSET-" 1965436 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1963742 1964507 1964535 "ORDRING" 1964737 T ORDRING (NIL) -9 NIL 1964862 NIL) (-843 1963387 1963481 1963625 "ORDRING-" 1963630 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1962793 1963230 1963258 "ORDMON" 1963263 T ORDMON (NIL) -9 NIL 1963284 NIL) (-841 1961955 1962102 1962297 "ORDFUNS" 1962642 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1961319 1961712 1961740 "ORDFIN" 1961805 T ORDFIN (NIL) -9 NIL 1961879 NIL) (-839 1957905 1959905 1960314 "ORDCOMP" 1960943 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1957171 1957298 1957484 "ORDCOMP2" 1957765 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1953779 1954662 1955476 "OPTPROB" 1956377 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1950581 1951220 1951924 "OPTPACK" 1953095 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1948294 1949034 1949062 "OPTCAT" 1949881 T OPTCAT (NIL) -9 NIL 1950531 NIL) (-834 1947737 1947971 1948076 "OPSIG" 1948209 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1947505 1947544 1947610 "OPQUERY" 1947691 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1944663 1945816 1946320 "OP" 1947034 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1944198 1944369 1944410 "OPERCAT" 1944545 NIL OPERCAT (NIL T) -9 NIL 1944613 NIL) (-830 1944044 1944071 1944157 "OPERCAT-" 1944162 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1940883 1942841 1943210 "ONECOMP" 1943708 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1940188 1940303 1940477 "ONECOMP2" 1940755 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1939607 1939713 1939843 "OMSERVER" 1940078 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1936495 1939047 1939087 "OMSAGG" 1939148 NIL OMSAGG (NIL T) -9 NIL 1939212 NIL) (-825 1935118 1935381 1935663 "OMPKG" 1936233 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1934548 1934651 1934679 "OM" 1934978 T OM (NIL) -9 NIL NIL NIL) (-823 1933122 1934097 1934266 "OMLO" 1934429 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1932047 1932194 1932421 "OMEXPR" 1932948 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1931365 1931593 1931729 "OMERR" 1931931 T OMERR (NIL) -8 NIL NIL NIL) (-820 1930543 1930786 1930946 "OMERRK" 1931225 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1930021 1930220 1930328 "OMENC" 1930455 T OMENC (NIL) -8 NIL NIL NIL) (-818 1923916 1925101 1926272 "OMDEV" 1928870 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1922985 1923156 1923350 "OMCONN" 1923742 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1921598 1922548 1922576 "OINTDOM" 1922581 T OINTDOM (NIL) -9 NIL 1922602 NIL) (-815 1917404 1918588 1919304 "OFMONOID" 1920914 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1916842 1917341 1917386 "ODVAR" 1917391 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1914292 1916587 1916742 "ODR" 1916747 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1906628 1914068 1914194 "ODPOL" 1914199 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1900498 1906500 1906605 "ODP" 1906610 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1899264 1899479 1899754 "ODETOOLS" 1900272 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1896231 1896889 1897605 "ODESYS" 1898597 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1891113 1892021 1893046 "ODERTRIC" 1895306 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1890539 1890621 1890815 "ODERED" 1891025 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1887427 1887975 1888652 "ODERAT" 1889962 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1884384 1884851 1885448 "ODEPRRIC" 1886956 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1882354 1882923 1883409 "ODEPROB" 1883918 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1878874 1879359 1880006 "ODEPRIM" 1881833 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1878123 1878225 1878485 "ODEPAL" 1878766 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1874285 1875076 1875940 "ODEPACK" 1877279 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1873318 1873425 1873654 "ODEINT" 1874174 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1867419 1868844 1870291 "ODEIFTBL" 1871891 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1862754 1863540 1864499 "ODEEF" 1866578 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1862089 1862178 1862408 "ODECONST" 1862659 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1860240 1860875 1860903 "ODECAT" 1861508 T ODECAT (NIL) -9 NIL 1862039 NIL) (-795 1857139 1859952 1860071 "OCT" 1860153 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1856777 1856820 1856947 "OCTCT2" 1857090 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1851543 1853951 1853991 "OC" 1855088 NIL OC (NIL T) -9 NIL 1855946 NIL) (-792 1848770 1849518 1850508 "OC-" 1850602 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1848148 1848590 1848618 "OCAMON" 1848623 T OCAMON (NIL) -9 NIL 1848644 NIL) (-790 1847705 1848020 1848048 "OASGP" 1848053 T OASGP (NIL) -9 NIL 1848073 NIL) (-789 1846992 1847455 1847483 "OAMONS" 1847523 T OAMONS (NIL) -9 NIL 1847566 NIL) (-788 1846432 1846839 1846867 "OAMON" 1846872 T OAMON (NIL) -9 NIL 1846892 NIL) (-787 1845736 1846228 1846256 "OAGROUP" 1846261 T OAGROUP (NIL) -9 NIL 1846281 NIL) (-786 1845426 1845476 1845564 "NUMTUBE" 1845680 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1838999 1840517 1842053 "NUMQUAD" 1843910 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1834755 1835743 1836768 "NUMODE" 1837994 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1832136 1832990 1833018 "NUMINT" 1833941 T NUMINT (NIL) -9 NIL 1834705 NIL) (-782 1831084 1831281 1831499 "NUMFMT" 1831938 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1817443 1820388 1822920 "NUMERIC" 1828591 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1811840 1816892 1816987 "NTSCAT" 1816992 NIL NTSCAT (NIL T T T T) -9 NIL 1817031 NIL) (-779 1811034 1811199 1811392 "NTPOLFN" 1811679 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1798866 1807859 1808671 "NSUP" 1810255 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1798498 1798555 1798664 "NSUP2" 1798803 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1788481 1798272 1798405 "NSMP" 1798410 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1786913 1787214 1787571 "NREP" 1788169 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1785504 1785756 1786114 "NPCOEF" 1786656 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1784570 1784685 1784901 "NORMRETR" 1785385 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1782611 1782901 1783310 "NORMPK" 1784278 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1782296 1782324 1782448 "NORMMA" 1782577 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1782123 1782253 1782282 "NONE" 1782287 T NONE (NIL) -8 NIL NIL NIL) (-769 1781912 1781941 1782010 "NONE1" 1782087 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1781395 1781457 1781643 "NODE1" 1781844 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1779665 1780489 1780744 "NNI" 1781091 T NNI (NIL) -8 NIL NIL 1781326) (-766 1778085 1778398 1778762 "NLINSOL" 1779333 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1774353 1775321 1776220 "NIPROB" 1777206 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1773110 1773344 1773646 "NFINTBAS" 1774115 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1772284 1772760 1772801 "NETCLT" 1772973 NIL NETCLT (NIL T) -9 NIL 1773055 NIL) (-762 1770992 1771223 1771504 "NCODIV" 1772052 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1770754 1770791 1770866 "NCNTFRAC" 1770949 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1768934 1769298 1769718 "NCEP" 1770379 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1767831 1768578 1768606 "NASRING" 1768716 T NASRING (NIL) -9 NIL 1768796 NIL) (-758 1767626 1767670 1767764 "NASRING-" 1767769 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1766779 1767278 1767306 "NARNG" 1767423 T NARNG (NIL) -9 NIL 1767514 NIL) (-756 1766471 1766538 1766672 "NARNG-" 1766677 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1765350 1765557 1765792 "NAGSP" 1766256 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1756622 1758306 1759979 "NAGS" 1763697 T NAGS (NIL) -7 NIL NIL NIL) (-753 1755170 1755478 1755809 "NAGF07" 1756311 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1749708 1750999 1752306 "NAGF04" 1753883 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1742676 1744290 1745923 "NAGF02" 1748095 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1737900 1739000 1740117 "NAGF01" 1741579 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1731528 1733094 1734679 "NAGE04" 1736335 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1722697 1724818 1726948 "NAGE02" 1729418 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1718650 1719597 1720561 "NAGE01" 1721753 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1716445 1716979 1717537 "NAGD03" 1718112 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1708195 1710123 1712077 "NAGD02" 1714511 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1702006 1703431 1704871 "NAGD01" 1706775 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1698215 1699037 1699874 "NAGC06" 1701189 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1696680 1697012 1697368 "NAGC05" 1697879 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1696056 1696175 1696319 "NAGC02" 1696556 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1695116 1695673 1695713 "NAALG" 1695792 NIL NAALG (NIL T) -9 NIL 1695853 NIL) (-739 1694951 1694980 1695070 "NAALG-" 1695075 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1688901 1690009 1691196 "MULTSQFR" 1693847 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1688220 1688295 1688479 "MULTFACT" 1688813 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1681305 1685183 1685236 "MTSCAT" 1686306 NIL MTSCAT (NIL T T) -9 NIL 1686820 NIL) (-735 1681017 1681071 1681163 "MTHING" 1681245 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1680809 1680842 1680902 "MSYSCMD" 1680977 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1676918 1679564 1679884 "MSET" 1680522 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1674013 1676479 1676520 "MSETAGG" 1676525 NIL MSETAGG (NIL T) -9 NIL 1676559 NIL) (-731 1669881 1671392 1672137 "MRING" 1673313 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1669447 1669514 1669645 "MRF2" 1669808 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1669065 1669100 1669244 "MRATFAC" 1669406 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1666677 1666972 1667403 "MPRFF" 1668770 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1660729 1666531 1666628 "MPOLY" 1666633 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1660219 1660254 1660462 "MPCPF" 1660688 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1659733 1659776 1659960 "MPC3" 1660170 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1658928 1659009 1659230 "MPC2" 1659648 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1657229 1657566 1657956 "MONOTOOL" 1658588 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1656480 1656771 1656799 "MONOID" 1657018 T MONOID (NIL) -9 NIL 1657165 NIL) (-721 1656026 1656145 1656326 "MONOID-" 1656331 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1646877 1652793 1652852 "MONOGEN" 1653526 NIL MONOGEN (NIL T T) -9 NIL 1653982 NIL) (-719 1644095 1644830 1645830 "MONOGEN-" 1645949 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1642954 1643374 1643402 "MONADWU" 1643794 T MONADWU (NIL) -9 NIL 1644032 NIL) (-717 1642326 1642485 1642733 "MONADWU-" 1642738 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1641711 1641929 1641957 "MONAD" 1642164 T MONAD (NIL) -9 NIL 1642276 NIL) (-715 1641396 1641474 1641606 "MONAD-" 1641611 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1639712 1640309 1640588 "MOEBIUS" 1641149 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1639104 1639482 1639522 "MODULE" 1639527 NIL MODULE (NIL T) -9 NIL 1639553 NIL) (-712 1638672 1638768 1638958 "MODULE-" 1638963 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1636379 1637036 1637363 "MODRING" 1638496 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1633350 1634484 1635005 "MODOP" 1635908 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1631965 1632417 1632694 "MODMONOM" 1633213 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1621762 1630256 1630670 "MODMON" 1631602 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1618945 1620606 1620882 "MODFIELD" 1621637 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1617949 1618226 1618416 "MMLFORM" 1618775 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1617475 1617518 1617697 "MMAP" 1617900 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1615684 1616425 1616466 "MLO" 1616889 NIL MLO (NIL T) -9 NIL 1617131 NIL) (-703 1613050 1613566 1614168 "MLIFT" 1615165 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1612441 1612525 1612679 "MKUCFUNC" 1612961 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1612040 1612110 1612233 "MKRECORD" 1612364 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1611087 1611249 1611477 "MKFUNC" 1611851 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1610475 1610579 1610735 "MKFLCFN" 1610970 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610018 1610385 1610444 "MKCHSET" 1610449 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-697 1609295 1609397 1609582 "MKBCFUNC" 1609911 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-696 1606029 1608849 1608985 "MINT" 1609179 T MINT (NIL) -8 NIL NIL NIL) (-695 1604841 1605084 1605361 "MHROWRED" 1605784 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-694 1600248 1603376 1603781 "MFLOAT" 1604456 T MFLOAT (NIL) -8 NIL NIL NIL) (-693 1599605 1599681 1599852 "MFINFACT" 1600160 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-692 1595920 1596768 1597652 "MESH" 1598741 T MESH (NIL) -7 NIL NIL NIL) (-691 1594310 1594622 1594975 "MDDFACT" 1595607 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-690 1591152 1593469 1593510 "MDAGG" 1593765 NIL MDAGG (NIL T) -9 NIL 1593908 NIL) (-689 1580922 1590445 1590652 "MCMPLX" 1590965 T MCMPLX (NIL) -8 NIL NIL NIL) (-688 1580063 1580209 1580409 "MCDEN" 1580771 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-687 1577953 1578223 1578603 "MCALCFN" 1579793 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-686 1576878 1577118 1577351 "MAYBE" 1577759 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-685 1574490 1575013 1575575 "MATSTOR" 1576349 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-684 1570495 1573862 1574110 "MATRIX" 1574275 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-683 1566259 1566968 1567704 "MATLIN" 1569852 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-682 1556413 1559551 1559628 "MATCAT" 1564508 NIL MATCAT (NIL T T T) -9 NIL 1565925 NIL) (-681 1552769 1553790 1555146 "MATCAT-" 1555151 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-680 1551363 1551516 1551849 "MATCAT2" 1552604 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-679 1549475 1549799 1550183 "MAPPKG3" 1551038 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-678 1548456 1548629 1548851 "MAPPKG2" 1549299 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-677 1546955 1547239 1547566 "MAPPKG1" 1548162 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-676 1546061 1546361 1546538 "MAPPAST" 1546798 T MAPPAST (NIL) -8 NIL NIL NIL) (-675 1545672 1545730 1545853 "MAPHACK3" 1545997 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-674 1545264 1545325 1545439 "MAPHACK2" 1545604 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-673 1544701 1544805 1544947 "MAPHACK1" 1545155 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-672 1542807 1543401 1543705 "MAGMA" 1544429 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-671 1542313 1542531 1542622 "MACROAST" 1542736 T MACROAST (NIL) -8 NIL NIL NIL) (-670 1538779 1540552 1541013 "M3D" 1541885 NIL M3D (NIL T) -8 NIL NIL NIL) (-669 1532933 1537148 1537189 "LZSTAGG" 1537971 NIL LZSTAGG (NIL T) -9 NIL 1538266 NIL) (-668 1528890 1530064 1531521 "LZSTAGG-" 1531526 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-667 1526004 1526781 1527268 "LWORD" 1528435 NIL LWORD (NIL T) -8 NIL NIL NIL) (-666 1525607 1525808 1525883 "LSTAST" 1525949 T LSTAST (NIL) -8 NIL NIL NIL) (-665 1518800 1525378 1525512 "LSQM" 1525517 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-664 1518024 1518163 1518391 "LSPP" 1518655 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-663 1515836 1516137 1516593 "LSMP" 1517713 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-662 1512615 1513289 1514019 "LSMP1" 1515138 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-661 1506540 1511782 1511823 "LSAGG" 1511885 NIL LSAGG (NIL T) -9 NIL 1511963 NIL) (-660 1503235 1504159 1505372 "LSAGG-" 1505377 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-659 1500861 1502379 1502628 "LPOLY" 1503030 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-658 1500443 1500528 1500651 "LPEFRAC" 1500770 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-657 1498790 1499537 1499790 "LO" 1500275 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1498442 1498554 1498582 "LOGIC" 1498693 T LOGIC (NIL) -9 NIL 1498774 NIL) (-655 1498304 1498327 1498398 "LOGIC-" 1498403 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-654 1497497 1497637 1497830 "LODOOPS" 1498160 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-653 1494947 1497413 1497479 "LODO" 1497484 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-652 1493485 1493720 1494073 "LODOF" 1494694 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-651 1489833 1492238 1492279 "LODOCAT" 1492717 NIL LODOCAT (NIL T) -9 NIL 1492928 NIL) (-650 1489566 1489624 1489751 "LODOCAT-" 1489756 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-649 1486913 1489407 1489525 "LODO2" 1489530 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-648 1484375 1486850 1486895 "LODO1" 1486900 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-647 1483235 1483400 1483712 "LODEEF" 1484198 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-646 1478521 1481365 1481406 "LNAGG" 1482353 NIL LNAGG (NIL T) -9 NIL 1482797 NIL) (-645 1477668 1477882 1478224 "LNAGG-" 1478229 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-644 1473831 1474593 1475232 "LMOPS" 1477083 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-643 1473226 1473588 1473629 "LMODULE" 1473690 NIL LMODULE (NIL T) -9 NIL 1473732 NIL) (-642 1470472 1472871 1472994 "LMDICT" 1473136 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-641 1470198 1470380 1470440 "LITERAL" 1470445 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-640 1463429 1469144 1469442 "LIST" 1469933 NIL LIST (NIL T) -8 NIL NIL NIL) (-639 1462954 1463028 1463167 "LIST3" 1463349 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-638 1461961 1462139 1462367 "LIST2" 1462772 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-637 1460095 1460407 1460806 "LIST2MAP" 1461608 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-636 1458817 1459461 1459502 "LINEXP" 1459757 NIL LINEXP (NIL T) -9 NIL 1459906 NIL) (-635 1457464 1457724 1458021 "LINDEP" 1458569 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-634 1454231 1454950 1455727 "LIMITRF" 1456719 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-633 1452506 1452802 1453218 "LIMITPS" 1453926 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-632 1446961 1452017 1452245 "LIE" 1452327 NIL LIE (NIL T T) -8 NIL NIL NIL) (-631 1446010 1446453 1446493 "LIECAT" 1446633 NIL LIECAT (NIL T) -9 NIL 1446784 NIL) (-630 1445851 1445878 1445966 "LIECAT-" 1445971 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-629 1438463 1445300 1445465 "LIB" 1445706 T LIB (NIL) -8 NIL NIL NIL) (-628 1434098 1434981 1435916 "LGROBP" 1437580 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-627 1431964 1432238 1432600 "LF" 1433819 NIL LF (NIL T T) -7 NIL NIL NIL) (-626 1430804 1431496 1431524 "LFCAT" 1431731 T LFCAT (NIL) -9 NIL 1431870 NIL) (-625 1427706 1428336 1429024 "LEXTRIPK" 1430168 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-624 1424477 1425276 1425779 "LEXP" 1427286 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-623 1423980 1424198 1424290 "LETAST" 1424405 T LETAST (NIL) -8 NIL NIL NIL) (-622 1422378 1422691 1423092 "LEADCDET" 1423662 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-621 1421568 1421642 1421871 "LAZM3PK" 1422299 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-620 1416512 1419645 1420183 "LAUPOL" 1421080 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-619 1416077 1416121 1416289 "LAPLACE" 1416462 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-618 1414043 1415178 1415429 "LA" 1415910 NIL LA (NIL T T T) -8 NIL NIL NIL) (-617 1413116 1413674 1413715 "LALG" 1413777 NIL LALG (NIL T) -9 NIL 1413836 NIL) (-616 1412830 1412889 1413025 "LALG-" 1413030 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-615 1412665 1412689 1412730 "KVTFROM" 1412792 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-614 1411466 1411882 1412111 "KTVLOGIC" 1412456 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-613 1411301 1411325 1411366 "KRCFROM" 1411428 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-612 1410205 1410392 1410691 "KOVACIC" 1411101 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-611 1410040 1410064 1410105 "KONVERT" 1410167 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-610 1409875 1409899 1409940 "KOERCE" 1410002 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-609 1407609 1408369 1408762 "KERNEL" 1409514 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-608 1407111 1407192 1407322 "KERNEL2" 1407523 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-607 1400962 1405650 1405704 "KDAGG" 1406081 NIL KDAGG (NIL T T) -9 NIL 1406287 NIL) (-606 1400491 1400615 1400820 "KDAGG-" 1400825 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-605 1393666 1400152 1400307 "KAFILE" 1400369 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-604 1388121 1393177 1393405 "JORDAN" 1393487 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-603 1387527 1387770 1387891 "JOINAST" 1388020 T JOINAST (NIL) -8 NIL NIL NIL) (-602 1387373 1387432 1387487 "JAVACODE" 1387492 T JAVACODE (NIL) -8 NIL NIL NIL) (-601 1383672 1385578 1385632 "IXAGG" 1386561 NIL IXAGG (NIL T T) -9 NIL 1387020 NIL) (-600 1382591 1382897 1383316 "IXAGG-" 1383321 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-599 1378171 1382513 1382572 "IVECTOR" 1382577 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-598 1376937 1377174 1377440 "ITUPLE" 1377938 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-597 1375373 1375550 1375856 "ITRIGMNP" 1376759 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-596 1374118 1374322 1374605 "ITFUN3" 1375149 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-595 1373750 1373807 1373916 "ITFUN2" 1374055 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-594 1371579 1372612 1372911 "ITAYLOR" 1373484 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-593 1360551 1365716 1366879 "ISUPS" 1370449 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-592 1359655 1359795 1360031 "ISUMP" 1360398 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-591 1354919 1359456 1359535 "ISTRING" 1359608 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-590 1354422 1354640 1354732 "ISAST" 1354847 T ISAST (NIL) -8 NIL NIL NIL) (-589 1353632 1353713 1353929 "IRURPK" 1354336 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-588 1352568 1352769 1353009 "IRSN" 1353412 T IRSN (NIL) -7 NIL NIL NIL) (-587 1350597 1350952 1351388 "IRRF2F" 1352206 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-586 1350344 1350382 1350458 "IRREDFFX" 1350553 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-585 1348959 1349218 1349517 "IROOT" 1350077 NIL IROOT (NIL T) -7 NIL NIL NIL) (-584 1345590 1346643 1347335 "IR" 1348299 NIL IR (NIL T) -8 NIL NIL NIL) (-583 1343203 1343698 1344264 "IR2" 1345068 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-582 1342275 1342388 1342609 "IR2F" 1343086 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-581 1342066 1342100 1342160 "IPRNTPK" 1342235 T IPRNTPK (NIL) -7 NIL NIL NIL) (-580 1338673 1341955 1342024 "IPF" 1342029 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-579 1337027 1338598 1338655 "IPADIC" 1338660 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-578 1336366 1336587 1336717 "IP4ADDR" 1336917 T IP4ADDR (NIL) -8 NIL NIL NIL) (-577 1335866 1336070 1336180 "IOMODE" 1336276 T IOMODE (NIL) -8 NIL NIL NIL) (-576 1334939 1335463 1335590 "IOBFILE" 1335759 T IOBFILE (NIL) -8 NIL NIL NIL) (-575 1334427 1334843 1334871 "IOBCON" 1334876 T IOBCON (NIL) -9 NIL 1334897 NIL) (-574 1333924 1333982 1334172 "INVLAPLA" 1334363 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-573 1323572 1325926 1328312 "INTTR" 1331588 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-572 1319916 1320658 1321522 "INTTOOLS" 1322757 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-571 1319502 1319593 1319710 "INTSLPE" 1319819 T INTSLPE (NIL) -7 NIL NIL NIL) (-570 1317483 1319425 1319484 "INTRVL" 1319489 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-569 1315085 1315597 1316172 "INTRF" 1316968 NIL INTRF (NIL T) -7 NIL NIL NIL) (-568 1314496 1314593 1314735 "INTRET" 1314983 NIL INTRET (NIL T) -7 NIL NIL NIL) (-567 1312493 1312882 1313352 "INTRAT" 1314104 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-566 1309721 1310304 1310930 "INTPM" 1311978 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-565 1306423 1307023 1307768 "INTPAF" 1309107 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-564 1301602 1302564 1303615 "INTPACK" 1305392 T INTPACK (NIL) -7 NIL NIL NIL) (-563 1298506 1301331 1301458 "INT" 1301495 T INT (NIL) -8 NIL NIL NIL) (-562 1297758 1297910 1298118 "INTHERTR" 1298348 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-561 1297197 1297277 1297465 "INTHERAL" 1297672 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-560 1295043 1295486 1295943 "INTHEORY" 1296760 T INTHEORY (NIL) -7 NIL NIL NIL) (-559 1286351 1287972 1289751 "INTG0" 1293395 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-558 1266924 1271714 1276524 "INTFTBL" 1281561 T INTFTBL (NIL) -8 NIL NIL NIL) (-557 1266173 1266311 1266484 "INTFACT" 1266783 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-556 1263558 1264004 1264568 "INTEF" 1265727 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-555 1262017 1262730 1262758 "INTDOM" 1263059 T INTDOM (NIL) -9 NIL 1263266 NIL) (-554 1261386 1261560 1261802 "INTDOM-" 1261807 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-553 1257873 1259770 1259824 "INTCAT" 1260623 NIL INTCAT (NIL T) -9 NIL 1260943 NIL) (-552 1257345 1257448 1257576 "INTBIT" 1257765 T INTBIT (NIL) -7 NIL NIL NIL) (-551 1256016 1256170 1256484 "INTALG" 1257190 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-550 1255473 1255563 1255733 "INTAF" 1255920 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-549 1248927 1255283 1255423 "INTABL" 1255428 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-548 1248258 1248697 1248762 "INT8" 1248796 T INT8 (NIL) -8 NIL NIL 1248841) (-547 1247588 1248027 1248092 "INT32" 1248126 T INT32 (NIL) -8 NIL NIL 1248171) (-546 1246918 1247357 1247422 "INT16" 1247456 T INT16 (NIL) -8 NIL NIL 1247501) (-545 1241925 1244607 1244635 "INS" 1245569 T INS (NIL) -9 NIL 1246234 NIL) (-544 1239165 1239936 1240910 "INS-" 1240983 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237940 1238167 1238465 "INPSIGN" 1238918 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237058 1237175 1237372 "INPRODPF" 1237820 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235952 1236069 1236306 "INPRODFF" 1236938 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234952 1235104 1235364 "INNMFACT" 1235788 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234149 1234246 1234434 "INMODGCD" 1234851 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232657 1232902 1233226 "INFSP" 1233894 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231841 1231958 1232141 "INFPROD0" 1232537 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228722 1229906 1230421 "INFORM" 1231334 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228332 1228392 1228490 "INFORM1" 1228657 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227855 1227944 1228058 "INFINITY" 1228238 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227031 1227575 1227676 "INETCLTS" 1227774 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225647 1225897 1226218 "INEP" 1226779 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224923 1225544 1225609 "INDE" 1225614 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224487 1224555 1224672 "INCRMAPS" 1224850 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223305 1223756 1223962 "INBFILE" 1224301 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218605 1219541 1220485 "INBFF" 1222393 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217513 1217782 1217810 "INBCON" 1218323 T INBCON (NIL) -9 NIL 1218589 NIL) (-526 1216765 1216988 1217264 "INBCON-" 1217269 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216267 1216486 1216578 "INAST" 1216693 T INAST (NIL) -8 NIL NIL NIL) (-524 1215721 1215946 1216052 "IMPTAST" 1216181 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212215 1215565 1215669 "IMATRIX" 1215674 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210927 1211050 1211365 "IMATQF" 1212071 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209147 1209374 1209711 "IMATLIN" 1210683 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203773 1209071 1209129 "ILIST" 1209134 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201726 1203633 1203746 "IIARRAY2" 1203751 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197151 1201637 1201701 "IFF" 1201706 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196525 1196768 1196884 "IFAST" 1197055 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191568 1195817 1196005 "IFARRAY" 1196382 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190775 1191472 1191545 "IFAMON" 1191550 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190359 1190424 1190478 "IEVALAB" 1190685 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190034 1190102 1190262 "IEVALAB-" 1190267 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189692 1189948 1190011 "IDPO" 1190016 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188969 1189581 1189656 "IDPOAMS" 1189661 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188303 1188858 1188933 "IDPOAM" 1188938 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187388 1187638 1187691 "IDPC" 1188104 NIL IDPC (NIL T T) -9 NIL 1188253 NIL) (-508 1186884 1187280 1187353 "IDPAM" 1187358 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186287 1186776 1186849 "IDPAG" 1186854 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186055 1186202 1186252 "IDENT" 1186257 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182310 1183158 1184053 "IDECOMP" 1185212 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175174 1176233 1177280 "IDEAL" 1181346 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174338 1174450 1174649 "ICDEN" 1175058 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173436 1173818 1173965 "ICARD" 1174211 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171496 1171809 1172214 "IBPTOOLS" 1173113 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167130 1171116 1171229 "IBITS" 1171415 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163853 1164429 1165124 "IBATOOL" 1166547 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161632 1162094 1162627 "IBACHIN" 1163388 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159509 1161478 1161581 "IARRAY2" 1161586 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155662 1159435 1159492 "IARRAY1" 1159497 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149646 1154074 1154555 "IAN" 1155201 T IAN (NIL) -8 NIL NIL NIL) (-494 1149157 1149214 1149387 "IALGFACT" 1149583 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148685 1148798 1148826 "HYPCAT" 1149033 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148223 1148340 1148526 "HYPCAT-" 1148531 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147845 1148018 1148101 "HOSTNAME" 1148160 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147690 1147727 1147768 "HOMOTOP" 1147773 NIL HOMOTOP (NIL T) -9 NIL 1147806 NIL) (-489 1144369 1145700 1145741 "HOAGG" 1146722 NIL HOAGG (NIL T) -9 NIL 1147401 NIL) (-488 1142963 1143362 1143888 "HOAGG-" 1143893 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136994 1142558 1142707 "HEXADEC" 1142834 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135742 1135964 1136227 "HEUGCD" 1136771 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134845 1135579 1135709 "HELLFDIV" 1135714 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133072 1134622 1134710 "HEAP" 1134789 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132362 1132624 1132758 "HEADAST" 1132958 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126276 1132277 1132339 "HDP" 1132344 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120019 1125911 1126063 "HDMP" 1126177 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119343 1119483 1119647 "HB" 1119875 T HB (NIL) -7 NIL NIL NIL) (-479 1112840 1119189 1119293 "HASHTBL" 1119298 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112343 1112561 1112653 "HASAST" 1112768 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110148 1111965 1112147 "HACKPI" 1112181 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105843 1110001 1110114 "GTSET" 1110119 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099369 1105721 1105819 "GSTBL" 1105824 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091674 1098400 1098665 "GSERIES" 1099160 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090841 1091232 1091260 "GROUP" 1091463 T GROUP (NIL) -9 NIL 1091597 NIL) (-472 1090207 1090366 1090617 "GROUP-" 1090622 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088574 1088895 1089282 "GROEBSOL" 1089884 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087514 1087776 1087827 "GRMOD" 1088356 NIL GRMOD (NIL T T) -9 NIL 1088524 NIL) (-469 1087282 1087318 1087446 "GRMOD-" 1087451 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082599 1083636 1084636 "GRIMAGE" 1086302 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081065 1081326 1081650 "GRDEF" 1082295 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080509 1080625 1080766 "GRAY" 1080944 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079722 1080102 1080153 "GRALG" 1080306 NIL GRALG (NIL T T) -9 NIL 1080399 NIL) (-464 1079383 1079456 1079619 "GRALG-" 1079624 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076187 1078968 1079146 "GPOLSET" 1079290 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075541 1075598 1075856 "GOSPER" 1076124 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071300 1071979 1072505 "GMODPOL" 1075240 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070305 1070489 1070727 "GHENSEL" 1071112 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064356 1065199 1066226 "GENUPS" 1069389 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064053 1064104 1064193 "GENUFACT" 1064299 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063465 1063542 1063707 "GENPGCD" 1063971 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062939 1062974 1063187 "GENMFACT" 1063424 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061505 1061762 1062069 "GENEEZ" 1062682 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055406 1061116 1061278 "GDMP" 1061428 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044775 1049177 1050283 "GCNAALG" 1054389 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043194 1044030 1044058 "GCDDOM" 1044313 T GCDDOM (NIL) -9 NIL 1044470 NIL) (-451 1042664 1042791 1043006 "GCDDOM-" 1043011 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041336 1041521 1041825 "GB" 1042443 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029952 1032282 1034674 "GBINTERN" 1039027 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027789 1028081 1028502 "GBF" 1029627 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026570 1026735 1027002 "GBEUCLID" 1027605 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025919 1026044 1026193 "GAUSSFAC" 1026441 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024286 1024588 1024902 "GALUTIL" 1025638 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022594 1022868 1023192 "GALPOLYU" 1024013 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019959 1020249 1020656 "GALFACTU" 1022291 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011765 1013264 1014872 "GALFACT" 1018391 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009153 1009811 1009839 "FVFUN" 1010995 T FVFUN (NIL) -9 NIL 1011715 NIL) (-440 1008419 1008601 1008629 "FVC" 1008920 T FVC (NIL) -9 NIL 1009103 NIL) (-439 1008089 1008244 1008312 "FUNDESC" 1008371 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007731 1007886 1007967 "FUNCTION" 1008041 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005502 1006053 1006519 "FT" 1007285 T FT (NIL) -8 NIL NIL NIL) (-436 1004320 1004803 1005006 "FTEM" 1005319 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002576 1002865 1003269 "FSUPFACT" 1004011 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000973 1001262 1001594 "FST" 1002264 T FST (NIL) -8 NIL NIL NIL) (-433 1000144 1000250 1000445 "FSRED" 1000855 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998822 999078 999432 "FSPRMELT" 999859 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995907 996345 996844 "FSPECF" 998385 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977961 986410 986450 "FS" 990298 NIL FS (NIL T) -9 NIL 992587 NIL) (-429 966608 969601 973657 "FS-" 973954 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966122 966176 966353 "FSINT" 966549 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964441 965115 965418 "FSERIES" 965901 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963455 963571 963802 "FSCINT" 964321 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959689 962399 962440 "FSAGG" 962810 NIL FSAGG (NIL T) -9 NIL 963069 NIL) (-424 957451 958052 958848 "FSAGG-" 958943 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956493 956636 956863 "FSAGG2" 957304 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954147 954427 954981 "FS2UPS" 956211 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953729 953772 953927 "FS2" 954098 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952586 952757 953066 "FS2EXPXP" 953554 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952012 952127 952279 "FRUTIL" 952466 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943452 947507 948865 "FR" 950686 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938527 941170 941210 "FRNAALG" 942606 NIL FRNAALG (NIL T) -9 NIL 943213 NIL) (-416 934200 935276 936551 "FRNAALG-" 937301 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933838 933881 934008 "FRNAAF2" 934151 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932245 932692 932987 "FRMOD" 933650 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930023 930628 930945 "FRIDEAL" 932036 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929218 929305 929594 "FRIDEAL2" 929930 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928351 928765 928806 "FRETRCT" 928811 NIL FRETRCT (NIL T) -9 NIL 928987 NIL) (-410 927463 927694 928045 "FRETRCT-" 928050 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924667 925851 925910 "FRAMALG" 926792 NIL FRAMALG (NIL T T) -9 NIL 927084 NIL) (-408 922801 923256 923886 "FRAMALG-" 924109 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916749 922276 922552 "FRAC" 922557 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916385 916442 916549 "FRAC2" 916686 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916021 916078 916185 "FR2" 916322 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910686 913546 913574 "FPS" 914693 T FPS (NIL) -9 NIL 915250 NIL) (-403 910135 910244 910408 "FPS-" 910554 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907581 909224 909252 "FPC" 909477 T FPC (NIL) -9 NIL 909619 NIL) (-401 907374 907414 907511 "FPC-" 907516 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906252 906862 906903 "FPATMAB" 906908 NIL FPATMAB (NIL T) -9 NIL 907060 NIL) (-399 903952 904428 904854 "FPARFRAC" 905889 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899345 899844 900526 "FORTRAN" 903384 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897061 897561 898100 "FORT" 898826 T FORT (NIL) -7 NIL NIL NIL) (-396 894737 895299 895327 "FORTFN" 896387 T FORTFN (NIL) -9 NIL 897011 NIL) (-395 894501 894551 894579 "FORTCAT" 894638 T FORTCAT (NIL) -9 NIL 894700 NIL) (-394 892634 893117 893507 "FORMULA" 894131 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892422 892452 892521 "FORMULA1" 892598 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891945 891997 892170 "FORDER" 892364 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891041 891205 891398 "FOP" 891772 T FOP (NIL) -7 NIL NIL NIL) (-390 889649 890321 890495 "FNLA" 890923 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888404 888793 888821 "FNCAT" 889281 T FNCAT (NIL) -9 NIL 889541 NIL) (-388 887970 888363 888391 "FNAME" 888396 T FNAME (NIL) -8 NIL NIL NIL) (-387 886625 887562 887590 "FMTC" 887595 T FMTC (NIL) -9 NIL 887631 NIL) (-386 882985 884148 884777 "FMONOID" 886029 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882204 882727 882876 "FM" 882881 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879628 880274 880302 "FMFUN" 881446 T FMFUN (NIL) -9 NIL 882154 NIL) (-383 878897 879078 879106 "FMC" 879396 T FMC (NIL) -9 NIL 879578 NIL) (-382 876091 876925 876979 "FMCAT" 878174 NIL FMCAT (NIL T T) -9 NIL 878669 NIL) (-381 874984 875857 875957 "FM1" 876036 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872758 873174 873668 "FLOATRP" 874535 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866359 870487 871108 "FLOAT" 872157 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863797 864297 864875 "FLOATCP" 865826 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862598 863410 863451 "FLINEXP" 863456 NIL FLINEXP (NIL T) -9 NIL 863549 NIL) (-376 861752 861987 862315 "FLINEXP-" 862320 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860828 860972 861196 "FLASORT" 861604 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858045 858887 858939 "FLALG" 860166 NIL FLALG (NIL T T) -9 NIL 860633 NIL) (-373 851829 855531 855572 "FLAGG" 856834 NIL FLAGG (NIL T) -9 NIL 857486 NIL) (-372 850555 850894 851384 "FLAGG-" 851389 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849597 849740 849967 "FLAGG2" 850408 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846564 847546 847605 "FINRALG" 848733 NIL FINRALG (NIL T T) -9 NIL 849241 NIL) (-369 845724 845953 846292 "FINRALG-" 846297 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845130 845343 845371 "FINITE" 845567 T FINITE (NIL) -9 NIL 845674 NIL) (-367 837588 839749 839789 "FINAALG" 843456 NIL FINAALG (NIL T) -9 NIL 844909 NIL) (-366 832920 833970 835114 "FINAALG-" 836493 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832315 832675 832778 "FILE" 832850 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830999 831311 831365 "FILECAT" 832049 NIL FILECAT (NIL T T) -9 NIL 832265 NIL) (-363 828859 830361 830389 "FIELD" 830429 T FIELD (NIL) -9 NIL 830509 NIL) (-362 827479 827864 828375 "FIELD-" 828380 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825356 826114 826461 "FGROUP" 827165 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824446 824610 824830 "FGLMICPK" 825188 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820305 824371 824428 "FFX" 824433 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819906 819967 820102 "FFSLPE" 820238 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815895 816678 817474 "FFPOLY" 819142 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815399 815435 815644 "FFPOLY2" 815853 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811269 815318 815381 "FFP" 815386 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806694 811180 811244 "FF" 811249 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801847 806037 806227 "FFNBX" 806548 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796803 800982 801240 "FFNBP" 801701 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791463 796087 796298 "FFNB" 796636 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790295 790493 790808 "FFINTBAS" 791260 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786515 788702 788730 "FFIELDC" 789350 T FFIELDC (NIL) -9 NIL 789726 NIL) (-348 785177 785548 786045 "FFIELDC-" 786050 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784746 784792 784916 "FFHOM" 785119 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782441 782928 783445 "FFF" 784261 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778086 782183 782284 "FFCGX" 782384 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773734 777818 777925 "FFCGP" 778029 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768944 773461 773569 "FFCG" 773670 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750769 759815 759901 "FFCAT" 765066 NIL FFCAT (NIL T T T) -9 NIL 766517 NIL) (-341 745967 747014 748328 "FFCAT-" 749558 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745378 745421 745656 "FFCAT2" 745918 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734575 738350 739570 "FEXPR" 744230 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733575 734010 734051 "FEVALAB" 734135 NIL FEVALAB (NIL T) -9 NIL 734396 NIL) (-337 732734 732944 733282 "FEVALAB-" 733287 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731327 732117 732320 "FDIV" 732633 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728393 729108 729223 "FDIVCAT" 730791 NIL FDIVCAT (NIL T T T T) -9 NIL 731228 NIL) (-334 728155 728182 728352 "FDIVCAT-" 728357 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727375 727462 727739 "FDIV2" 728062 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726061 726320 726609 "FCPAK1" 727106 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725187 725561 725702 "FCOMP" 725952 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708916 712337 715875 "FC" 721669 T FC (NIL) -8 NIL NIL NIL) (-329 701487 705480 705520 "FAXF" 707322 NIL FAXF (NIL T) -9 NIL 708014 NIL) (-328 698763 699421 700246 "FAXF-" 700711 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693863 698139 698315 "FARRAY" 698620 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689108 691148 691201 "FAMR" 692224 NIL FAMR (NIL T T) -9 NIL 692684 NIL) (-325 687998 688300 688735 "FAMR-" 688740 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687194 687920 687973 "FAMONOID" 687978 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685006 685690 685743 "FAMONC" 686684 NIL FAMONC (NIL T T) -9 NIL 687070 NIL) (-322 683698 684760 684897 "FAGROUP" 684902 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681493 681812 682215 "FACUTIL" 683379 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680592 680777 680999 "FACTFUNC" 681303 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672989 679843 680055 "EXPUPXS" 680448 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670472 671012 671598 "EXPRTUBE" 672423 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666666 667258 667995 "EXPRODE" 669811 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652032 665321 665749 "EXPR" 666270 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646439 647026 647839 "EXPR2UPS" 651330 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646075 646132 646239 "EXPR2" 646376 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637472 645207 645504 "EXPEXPAN" 645912 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637299 637429 637458 "EXIT" 637463 T EXIT (NIL) -8 NIL NIL NIL) (-311 636806 637023 637114 "EXITAST" 637228 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636433 636495 636608 "EVALCYC" 636738 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635974 636092 636133 "EVALAB" 636303 NIL EVALAB (NIL T) -9 NIL 636407 NIL) (-308 635455 635577 635798 "EVALAB-" 635803 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632915 634191 634219 "EUCDOM" 634774 T EUCDOM (NIL) -9 NIL 635124 NIL) (-306 631320 631762 632352 "EUCDOM-" 632357 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618858 621618 624368 "ESTOOLS" 628590 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618490 618547 618656 "ESTOOLS2" 618795 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618241 618283 618363 "ESTOOLS1" 618442 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612146 613874 613902 "ES" 616670 T ES (NIL) -9 NIL 618079 NIL) (-301 607093 608380 610197 "ES-" 610361 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603467 604228 605008 "ESCONT" 606333 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603212 603244 603326 "ESCONT1" 603429 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602887 602937 603037 "ES2" 603156 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602517 602575 602684 "ES1" 602823 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601733 601862 602038 "ERROR" 602361 T ERROR (NIL) -7 NIL NIL NIL) (-295 595236 601592 601683 "EQTBL" 601688 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587787 590550 591999 "EQ" 593820 NIL -2126 (NIL T) -8 NIL NIL NIL) (-293 587419 587476 587585 "EQ2" 587724 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582708 583757 584850 "EP" 586358 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581290 581591 581908 "ENV" 582411 T ENV (NIL) -8 NIL NIL NIL) (-290 580461 580989 581017 "ENTIRER" 581022 T ENTIRER (NIL) -9 NIL 581068 NIL) (-289 576955 578416 578786 "EMR" 580260 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576099 576284 576338 "ELTAGG" 576718 NIL ELTAGG (NIL T T) -9 NIL 576929 NIL) (-287 575818 575880 576021 "ELTAGG-" 576026 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575607 575636 575690 "ELTAB" 575774 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574733 574879 575078 "ELFUTS" 575458 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574475 574531 574559 "ELEMFUN" 574664 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574345 574366 574434 "ELEMFUN-" 574439 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569236 572445 572486 "ELAGG" 573426 NIL ELAGG (NIL T) -9 NIL 573889 NIL) (-281 567521 567955 568618 "ELAGG-" 568623 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566178 566458 566753 "ELABEXPR" 567246 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559042 560845 561672 "EFUPXS" 565454 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552492 554293 555103 "EFULS" 558318 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549914 550272 550751 "EFSTRUC" 552124 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538985 540551 542111 "EF" 548429 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538086 538470 538619 "EAB" 538856 T EAB (NIL) -8 NIL NIL NIL) (-274 537295 538045 538073 "E04UCFA" 538078 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536504 537254 537282 "E04NAFA" 537287 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535713 536463 536491 "E04MBFA" 536496 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534922 535672 535700 "E04JAFA" 535705 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534133 534881 534909 "E04GCFA" 534914 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533344 534092 534120 "E04FDFA" 534125 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532553 533303 533331 "E04DGFA" 533336 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526726 528078 529442 "E04AGNT" 531209 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525432 525912 525952 "DVARCAT" 526427 NIL DVARCAT (NIL T) -9 NIL 526626 NIL) (-265 524636 524848 525162 "DVARCAT-" 525167 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517528 524435 524564 "DSMP" 524569 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512337 513473 514541 "DROPT" 516480 T DROPT (NIL) -8 NIL NIL NIL) (-262 512002 512061 512159 "DROPT1" 512272 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507117 508243 509380 "DROPT0" 510885 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505462 505787 506173 "DRAWPT" 506751 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500049 500972 502051 "DRAW" 504436 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499682 499735 499853 "DRAWHACK" 499990 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498413 498682 498973 "DRAWCX" 499411 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497928 497997 498148 "DRAWCURV" 498339 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488396 490358 492473 "DRAWCFUN" 495833 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485209 487091 487132 "DQAGG" 487761 NIL DQAGG (NIL T) -9 NIL 488034 NIL) (-253 473480 480187 480270 "DPOLCAT" 482122 NIL DPOLCAT (NIL T T T T) -9 NIL 482667 NIL) (-252 468316 469665 471623 "DPOLCAT-" 471628 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461465 468177 468275 "DPMO" 468280 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454517 461245 461412 "DPMM" 461417 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454149 454436 454484 "DOMCTOR" 454489 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453444 453671 453808 "DOMAIN" 454032 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447187 453079 453231 "DMP" 453345 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446787 446843 446987 "DLP" 447125 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440657 446114 446304 "DLIST" 446629 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437501 439510 439551 "DLAGG" 440101 NIL DLAGG (NIL T) -9 NIL 440331 NIL) (-243 436306 436944 436972 "DIVRING" 437064 T DIVRING (NIL) -9 NIL 437147 NIL) (-242 435543 435733 436033 "DIVRING-" 436038 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433645 434002 434408 "DISPLAY" 435157 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427581 433559 433622 "DIRPROD" 433627 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426429 426632 426897 "DIRPROD2" 427374 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415686 421644 421697 "DIRPCAT" 422107 NIL DIRPCAT (NIL NIL T) -9 NIL 422947 NIL) (-237 413012 413654 414535 "DIRPCAT-" 414872 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412299 412459 412645 "DIOSP" 412846 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409001 411211 411252 "DIOPS" 411686 NIL DIOPS (NIL T) -9 NIL 411915 NIL) (-234 408550 408664 408855 "DIOPS-" 408860 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407434 408036 408064 "DIFRING" 408251 T DIFRING (NIL) -9 NIL 408361 NIL) (-232 407080 407157 407309 "DIFRING-" 407314 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404877 406123 406164 "DIFEXT" 406527 NIL DIFEXT (NIL T) -9 NIL 406821 NIL) (-230 403162 403590 404256 "DIFEXT-" 404261 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400484 402694 402735 "DIAGG" 402740 NIL DIAGG (NIL T) -9 NIL 402760 NIL) (-228 399868 400025 400277 "DIAGG-" 400282 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395333 398827 399104 "DHMATRIX" 399637 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390945 391854 392864 "DFSFUN" 394343 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386050 389876 390188 "DFLOAT" 390653 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384278 384559 384955 "DFINTTLS" 385758 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381334 382299 382699 "DERHAM" 383944 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379183 381109 381198 "DEQUEUE" 381278 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378398 378531 378727 "DEGRED" 379045 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374793 375538 376391 "DEFINTRF" 377626 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372320 372789 373388 "DEFINTEF" 374312 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371697 371940 372055 "DEFAST" 372225 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365728 371292 371441 "DECIMAL" 371568 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363238 363698 364204 "DDFACT" 365272 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362834 362877 363028 "DBLRESP" 363189 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360733 361067 361427 "DBASE" 362601 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360002 360213 360359 "DATAARY" 360632 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359135 359961 359989 "D03FAFA" 359994 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358269 359094 359122 "D03EEFA" 359127 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356219 356685 357174 "D03AGNT" 357800 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355535 356178 356206 "D02EJFA" 356211 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354851 355494 355522 "D02CJFA" 355527 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354167 354810 354838 "D02BHFA" 354843 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353483 354126 354154 "D02BBFA" 354159 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346680 348269 349875 "D02AGNT" 351897 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344448 344971 345517 "D01WGTS" 346154 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343542 344407 344435 "D01TRNS" 344440 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342637 343501 343529 "D01GBFA" 343534 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341732 342596 342624 "D01FCFA" 342629 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340827 341691 341719 "D01ASFA" 341724 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339922 340786 340814 "D01AQFA" 340819 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339017 339881 339909 "D01APFA" 339914 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338112 338976 339004 "D01ANFA" 339009 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337207 338071 338099 "D01AMFA" 338104 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336302 337166 337194 "D01ALFA" 337199 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335397 336261 336289 "D01AKFA" 336294 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334492 335356 335384 "D01AJFA" 335389 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327787 329340 330901 "D01AGNT" 332951 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327124 327252 327404 "CYCLOTOM" 327655 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323859 324572 325299 "CYCLES" 326417 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323171 323305 323476 "CVMP" 323720 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320942 321200 321576 "CTRIGMNP" 322899 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320433 320733 320807 "CTOR" 320888 T CTOR (NIL) -8 NIL NIL NIL) (-186 319969 320164 320265 "CTORKIND" 320352 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319317 319576 319604 "CTORCAT" 319786 T CTORCAT (NIL) -9 NIL 319899 NIL) (-184 318915 319026 319185 "CTORCAT-" 319190 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318431 318618 318716 "CTORCALL" 318837 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317805 317904 318057 "CSTTOOLS" 318328 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313604 314261 315019 "CRFP" 317117 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313106 313325 313417 "CRCEAST" 313532 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312153 312338 312566 "CRAPACK" 312910 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311537 311638 311842 "CPMATCH" 312029 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311262 311290 311396 "CPIMA" 311503 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307626 308298 309016 "COORDSYS" 310597 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307010 307139 307289 "CONTOUR" 307496 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302928 305013 305505 "CONTFRAC" 306550 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302808 302829 302857 "CONDUIT" 302894 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301973 302501 302529 "COMRING" 302534 T COMRING (NIL) -9 NIL 302586 NIL) (-171 301054 301331 301515 "COMPPROP" 301809 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300715 300750 300878 "COMPLPAT" 301013 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290764 300524 300633 "COMPLEX" 300638 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290400 290457 290564 "COMPLEX2" 290701 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290118 290153 290251 "COMPFACT" 290359 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274272 284500 284540 "COMPCAT" 285544 NIL COMPCAT (NIL T) -9 NIL 286940 NIL) (-165 263783 266711 270338 "COMPCAT-" 270694 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263512 263540 263643 "COMMUPC" 263749 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263307 263340 263399 "COMMONOP" 263473 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262890 263058 263145 "COMM" 263240 T COMM (NIL) -8 NIL NIL NIL) (-161 262493 262694 262769 "COMMAAST" 262835 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261742 261936 261964 "COMBOPC" 262302 T COMBOPC (NIL) -9 NIL 262477 NIL) (-159 260638 260848 261090 "COMBINAT" 261532 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256835 257409 258049 "COMBF" 260060 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255620 255951 256186 "COLOR" 256620 T COLOR (NIL) -8 NIL NIL NIL) (-156 255123 255341 255433 "COLONAST" 255548 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254763 254810 254935 "CMPLXRT" 255070 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254238 254463 254562 "CLLCTAST" 254684 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249738 250768 251848 "CLIP" 253178 T CLIP (NIL) -7 NIL NIL NIL) (-152 248111 248844 249083 "CLIF" 249565 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244333 246257 246298 "CLAGG" 247227 NIL CLAGG (NIL T) -9 NIL 247763 NIL) (-150 242755 243212 243795 "CLAGG-" 243800 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242299 242384 242524 "CINTSLPE" 242664 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239800 240271 240819 "CHVAR" 241827 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239035 239563 239591 "CHARZ" 239596 T CHARZ (NIL) -9 NIL 239611 NIL) (-146 238789 238829 238907 "CHARPOL" 238989 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237908 238469 238497 "CHARNZ" 238544 T CHARNZ (NIL) -9 NIL 238600 NIL) (-144 235897 236598 236933 "CHAR" 237593 T CHAR (NIL) -8 NIL NIL NIL) (-143 235623 235684 235712 "CFCAT" 235823 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234868 234979 235161 "CDEN" 235507 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230860 234021 234301 "CCLASS" 234608 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230167 230310 230473 "CATEGORY" 230717 T -10 (NIL) -8 NIL NIL NIL) (-139 229799 230086 230134 "CATCTOR" 230139 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229273 229499 229598 "CATAST" 229720 T CATAST (NIL) -8 NIL NIL NIL) (-137 228776 228994 229086 "CASEAST" 229201 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223812 224805 225558 "CARTEN" 228079 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222920 223068 223289 "CARTEN2" 223659 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221262 222070 222327 "CARD" 222683 T CARD (NIL) -8 NIL NIL NIL) (-133 220865 221066 221141 "CAPSLAST" 221207 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220237 220565 220593 "CACHSET" 220725 T CACHSET (NIL) -9 NIL 220802 NIL) (-131 219733 220029 220057 "CABMON" 220107 T CABMON (NIL) -9 NIL 220163 NIL) (-130 219233 219437 219547 "BYTEORD" 219643 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218236 218767 218909 "BYTE" 219072 T BYTE (NIL) -8 NIL NIL 219194) (-128 213636 217741 217913 "BYTEBUF" 218084 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211193 213328 213435 "BTREE" 213562 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208690 210841 210963 "BTOURN" 211103 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206107 208160 208201 "BTCAT" 208269 NIL BTCAT (NIL T) -9 NIL 208346 NIL) (-124 205774 205854 206003 "BTCAT-" 206008 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201066 204917 204945 "BTAGG" 205167 T BTAGG (NIL) -9 NIL 205328 NIL) (-122 200556 200681 200887 "BTAGG-" 200892 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197599 199834 200049 "BSTREE" 200373 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196737 196863 197047 "BRILL" 197455 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193436 195463 195504 "BRAGG" 196153 NIL BRAGG (NIL T) -9 NIL 196411 NIL) (-118 191965 192371 192926 "BRAGG-" 192931 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185221 191311 191495 "BPADICRT" 191813 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183563 185158 185203 "BPADIC" 185208 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183261 183291 183405 "BOUNDZRO" 183527 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178776 179867 180734 "BOP" 182414 T BOP (NIL) -8 NIL NIL NIL) (-113 176397 176841 177361 "BOP1" 178289 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175099 175821 176014 "BOOLEAN" 176224 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174461 174839 174893 "BMODULE" 174898 NIL BMODULE (NIL T T) -9 NIL 174963 NIL) (-110 170289 174259 174332 "BITS" 174408 T BITS (NIL) -8 NIL NIL NIL) (-109 169701 169823 169965 "BINDING" 170167 T BINDING (NIL) -8 NIL NIL NIL) (-108 163735 169298 169446 "BINARY" 169573 T BINARY (NIL) -8 NIL NIL NIL) (-107 161562 162990 163031 "BGAGG" 163291 NIL BGAGG (NIL T) -9 NIL 163428 NIL) (-106 161393 161425 161516 "BGAGG-" 161521 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160491 160777 160982 "BFUNCT" 161208 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159181 159359 159647 "BEZOUT" 160315 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155698 158033 158363 "BBTREE" 158884 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155432 155485 155513 "BASTYPE" 155632 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155285 155313 155386 "BASTYPE-" 155391 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154719 154795 154947 "BALFACT" 155196 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153602 154134 154320 "AUTOMOR" 154564 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153328 153333 153359 "ATTREG" 153364 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151607 152025 152377 "ATTRBUT" 152994 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151242 151435 151501 "ATTRAST" 151559 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150778 150891 150917 "ATRIG" 151118 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150587 150628 150715 "ATRIG-" 150720 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150258 150418 150444 "ASTCAT" 150449 T ASTCAT (NIL) -9 NIL 150479 NIL) (-92 149985 150044 150163 "ASTCAT-" 150168 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148182 149761 149849 "ASTACK" 149928 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146687 146984 147349 "ASSOCEQ" 147864 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145719 146346 146470 "ASP9" 146594 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145482 145667 145706 "ASP8" 145711 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144350 145087 145229 "ASP80" 145371 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143248 143985 144117 "ASP7" 144249 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142202 142925 143043 "ASP78" 143161 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141171 141882 141999 "ASP77" 142116 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140083 140809 140940 "ASP74" 141071 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138983 139718 139850 "ASP73" 139982 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138087 138809 138909 "ASP6" 138914 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137031 137764 137882 "ASP55" 138000 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135980 136705 136824 "ASP50" 136943 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135068 135681 135791 "ASP4" 135901 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134156 134769 134879 "ASP49" 134989 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132940 133695 133863 "ASP42" 134045 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131716 132473 132643 "ASP41" 132827 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130666 131393 131511 "ASP35" 131629 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130431 130614 130653 "ASP34" 130658 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130168 130235 130311 "ASP33" 130386 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129061 129803 129935 "ASP31" 130067 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128826 129009 129048 "ASP30" 129053 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128561 128630 128706 "ASP29" 128781 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128326 128509 128548 "ASP28" 128553 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128091 128274 128313 "ASP27" 128318 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127175 127789 127900 "ASP24" 128011 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126251 126977 127089 "ASP20" 127094 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125339 125952 126062 "ASP1" 126172 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124281 125013 125132 "ASP19" 125251 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124018 124085 124161 "ASP12" 124236 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122870 123617 123761 "ASP10" 123905 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120769 122714 122805 "ARRAY2" 122810 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116583 120417 120531 "ARRAY1" 120686 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115615 115788 116009 "ARRAY12" 116406 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109974 111845 111920 "ARR2CAT" 114550 NIL ARR2CAT (NIL T T T) -9 NIL 115308 NIL) (-56 107408 108152 109106 "ARR2CAT-" 109111 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107000 107235 107314 "ARITY" 107347 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106206 "APPRULE" 106836 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104373 104664 104859 "ANY" 105222 T ANY (NIL) -8 NIL NIL NIL) (-51 103651 103774 103931 "ANY1" 104247 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101208 102088 102415 "ANTISYM" 103375 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100912 101009 "ANON" 101129 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index efc90bfc..9a594e45 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,6854 +1,10399 @@ -(727719 . 3444026016) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1256 *4)) (-4 *4 (-636 (-546))) - (-5 *2 (-1256 (-407 (-546)))) (-5 *1 (-1284 *4))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-1256 *4)) (-4 *4 (-636 (-546))) - (-5 *2 (-1256 (-546))) (-5 *1 (-1284 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1256 *4)) (-4 *4 (-636 (-546))) (-5 *2 (-112)) - (-5 *1 (-1284 *4))))) +(735849 . 3444870411) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-816)) (-14 *5 (-1169)) (-5 *2 (-640 (-1230 *5 *4))) + (-5 *1 (-1107 *4 *5)) (-5 *3 (-1230 *5 *4))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *5 *6 *5 *4 *7 *3) + (-12 (-5 *4 (-684 (-563))) (-5 *5 (-112)) (-5 *7 (-684 (-225))) + (-5 *3 (-563)) (-5 *6 (-225)) (-5 *2 (-1031)) (-5 *1 (-750))))) (((*1 *2 *3) - (-12 (-4 *5 (-13 (-611 *2) 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