diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 12 | ||||
| -rw-r--r-- | src/algebra/data.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/integer.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/si.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/strap/CHAR.lsp | 222 | ||||
| -rw-r--r-- | src/algebra/strap/DFLOAT.lsp | 826 | ||||
| -rw-r--r-- | src/algebra/strap/INT.lsp | 359 | ||||
| -rw-r--r-- | src/algebra/strap/SINT.lsp | 388 | ||||
| -rw-r--r-- | src/algebra/string.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/interp/compiler.boot | 6 | ||||
| -rw-r--r-- | src/interp/parse.boot | 6 | ||||
| -rw-r--r-- | src/interp/postpar.boot | 2 | ||||
| -rw-r--r-- | src/interp/sys-macros.lisp | 3 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1396 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1317 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8912 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30632 |
19 files changed, 22428 insertions, 22304 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 5d6974e8..3bb9fdb9 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,15 @@ +2009-06-01 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * interp/compiler.boot (compGreaterThan): New. Compile + greater-than expressions. + * interp/parse.boot (parseGreaterThan): Remove. + * algebra/data.spad.pamphlet (Byte): Implement all comparison + functions. + * algebra/integer.spad.pamphlet (Integer): Likewise. + * algebra/sf.spad.pamphlet (DoubleFloat): Likewise. + * algebra/si.spad.pamphlet (SingleInteger): Likewise. + * algebra/string.spad.pamphlet (Character): Likewise. + 2009-05-31 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/term.spad.pamphlet (is?$OperatorCategory): New. diff --git a/src/algebra/data.spad.pamphlet b/src/algebra/data.spad.pamphlet index 2760df04..6bc803dd 100644 --- a/src/algebra/data.spad.pamphlet +++ b/src/algebra/data.spad.pamphlet @@ -42,6 +42,9 @@ Byte(): Public == Private where coerce(x: %): Character == char rep x x = y == byteEqual(x,y)$Lisp x < y == byteLessThan(x,y)$Lisp + x > y == byteGreaterThan(x,y)$Lisp + x <= y == byteLessEqual(x,y)$Lisp + x >= y == byteGreaterEqual(x,y)$Lisp min() == per 0 max() == per 255 bitand(x,y) == bitand(x,y)$Lisp diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index ee06f056..6965144e 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -181,6 +181,9 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with random(x) == RANDOM(x)$Lisp x = y == EQL(x,y)$Lisp x < y == (x<y)$Lisp + x > y == (x > y)$Lisp -- Don't rely on default; help the inliner + x <= y == (x <= y)$Lisp -- Ditto + x >= y == (x >= y)$Lisp -- Ditto - x == (-x)$Lisp x + y == (x+y)$Lisp x - y == (x-y)$Lisp diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 35c59b87..507957ad 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -342,6 +342,9 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, coerce(x:%):OutputForm == outputForm x convert(x:%):InputForm == convert(x pretend DoubleFloat)$InputForm x < y == (x<y)$Lisp + x > y == (x > y)$Lisp -- help inliner + x <= y == (x <= y)$Lisp -- ditto + x >= y == (x >= y)$Lisp -- ditto - x == (-x)$Lisp x + y == (x+y)$Lisp x:% - y:% == (x-y)$Lisp diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 605f78e5..63e6c1db 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -288,6 +288,9 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,Logic,OpenMath) with Or(x,y) == LOGIOR(x,y)$Lisp xor(x,y) == LOGXOR(x,y)$Lisp x < y == QSLESSP(x,y)$Lisp + x > y == QSGREATERP(x,y)$Lisp + x <= y == (x <= y)$Lisp + x >= y == (x >= y)$Lisp inc x == QSADD1(x)$Lisp dec x == QSSUB1(x)$Lisp - x == QSMINUS(x)$Lisp diff --git a/src/algebra/strap/CHAR.lsp b/src/algebra/strap/CHAR.lsp index 6e24716c..7bd2bfbe 100644 --- a/src/algebra/strap/CHAR.lsp +++ b/src/algebra/strap/CHAR.lsp @@ -11,79 +11,94 @@ (PUT '|CHAR;<;2$B;2| '|SPADreplace| 'CHAR<) +(DECLAIM (FTYPE (FUNCTION (|%Char| |%Char| |%Shell|) |%Boolean|) + |CHAR;>;2$B;3|)) + +(PUT '|CHAR;>;2$B;3| '|SPADreplace| 'CHAR>) + +(DECLAIM (FTYPE (FUNCTION (|%Char| |%Char| |%Shell|) |%Boolean|) + |CHAR;<=;2$B;4|)) + +(PUT '|CHAR;<=;2$B;4| '|SPADreplace| 'CHAR<=) + +(DECLAIM (FTYPE (FUNCTION (|%Char| |%Char| |%Shell|) |%Boolean|) + |CHAR;>=;2$B;5|)) + +(PUT '|CHAR;>=;2$B;5| '|SPADreplace| 'CHAR>=) + (DECLAIM (FTYPE (FUNCTION (|%Shell|) (|%IntegerSection| 0)) - |CHAR;size;Nni;3|)) + |CHAR;size;Nni;6|)) -(PUT '|CHAR;size;Nni;3| '|SPADreplace| '(XLAM NIL 256)) +(PUT '|CHAR;size;Nni;6| '|SPADreplace| '(XLAM NIL 256)) (DECLAIM (FTYPE (FUNCTION ((|%IntegerSection| 1) |%Shell|) |%Char|) - |CHAR;index;Pi$;4|)) + |CHAR;index;Pi$;7|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) (|%IntegerSection| 1)) - |CHAR;lookup;$Pi;5|)) + |CHAR;lookup;$Pi;8|)) (DECLAIM (FTYPE (FUNCTION ((|%IntegerSection| 0) |%Shell|) |%Char|) - |CHAR;char;Nni$;6|)) + |CHAR;char;Nni$;9|)) -(PUT '|CHAR;char;Nni$;6| '|SPADreplace| 'CODE-CHAR) +(PUT '|CHAR;char;Nni$;9| '|SPADreplace| 'CODE-CHAR) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) (|%IntegerSection| 0)) - |CHAR;ord;$Nni;7|)) + |CHAR;ord;$Nni;10|)) -(PUT '|CHAR;ord;$Nni;7| '|SPADreplace| 'CHAR-CODE) +(PUT '|CHAR;ord;$Nni;10| '|SPADreplace| 'CHAR-CODE) -(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;random;$;8|)) +(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;random;$;11|)) -(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;space;$;9|)) +(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;space;$;12|)) -(PUT '|CHAR;space;$;9| '|SPADreplace| '(XLAM NIL (CHAR " " 0))) +(PUT '|CHAR;space;$;12| '|SPADreplace| '(XLAM NIL (CHAR " " 0))) -(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;quote;$;10|)) +(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;quote;$;13|)) -(PUT '|CHAR;quote;$;10| '|SPADreplace| '(XLAM NIL (CHAR "\" " 0))) +(PUT '|CHAR;quote;$;13| '|SPADreplace| '(XLAM NIL (CHAR "\" " 0))) -(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;escape;$;11|)) +(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;escape;$;14|)) -(PUT '|CHAR;escape;$;11| '|SPADreplace| '(XLAM NIL (CHAR "_ " 0))) +(PUT '|CHAR;escape;$;14| '|SPADreplace| '(XLAM NIL (CHAR "_ " 0))) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Thing|) - |CHAR;coerce;$Of;12|)) + |CHAR;coerce;$Of;15|)) -(PUT '|CHAR;coerce;$Of;12| '|SPADreplace| '(XLAM (|c|) |c|)) +(PUT '|CHAR;coerce;$Of;15| '|SPADreplace| '(XLAM (|c|) |c|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;digit?;$B;13|)) + |CHAR;digit?;$B;16|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;hexDigit?;$B;14|)) + |CHAR;hexDigit?;$B;17|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;upperCase?;$B;15|)) + |CHAR;upperCase?;$B;18|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;lowerCase?;$B;16|)) + |CHAR;lowerCase?;$B;19|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;alphabetic?;$B;17|)) + |CHAR;alphabetic?;$B;20|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|) - |CHAR;alphanumeric?;$B;18|)) + |CHAR;alphanumeric?;$B;21|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%String|) - |CHAR;latex;$S;19|)) + |CHAR;latex;$S;22|)) (DECLAIM (FTYPE (FUNCTION (|%String| |%Shell|) |%Char|) - |CHAR;char;S$;20|)) + |CHAR;char;S$;23|)) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Char|) - |CHAR;upperCase;2$;21|)) + |CHAR;upperCase;2$;24|)) -(PUT '|CHAR;upperCase;2$;21| '|SPADreplace| 'CHAR-UPCASE) +(PUT '|CHAR;upperCase;2$;24| '|SPADreplace| 'CHAR-UPCASE) (DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Char|) - |CHAR;lowerCase;2$;22|)) + |CHAR;lowerCase;2$;25|)) -(PUT '|CHAR;lowerCase;2$;22| '|SPADreplace| 'CHAR-DOWNCASE) +(PUT '|CHAR;lowerCase;2$;25| '|SPADreplace| 'CHAR-DOWNCASE) (DEFUN |CHAR;=;2$B;1| (|a| |b| $) (DECLARE (IGNORE $)) @@ -93,78 +108,92 @@ (DECLARE (IGNORE $)) (CHAR< |a| |b|)) -(DEFUN |CHAR;size;Nni;3| ($) (DECLARE (IGNORE $)) 256) +(DEFUN |CHAR;>;2$B;3| (|a| |b| $) + (DECLARE (IGNORE $)) + (CHAR> |a| |b|)) + +(DEFUN |CHAR;<=;2$B;4| (|a| |b| $) + (DECLARE (IGNORE $)) + (CHAR<= |a| |b|)) + +(DEFUN |CHAR;>=;2$B;5| (|a| |b| $) + (DECLARE (IGNORE $)) + (CHAR>= |a| |b|)) + +(DEFUN |CHAR;size;Nni;6| ($) (DECLARE (IGNORE $)) 256) -(DEFUN |CHAR;index;Pi$;4| (|n| $) - (PROG (#0=#:G1402) +(DEFUN |CHAR;index;Pi$;7| (|n| $) + (PROG (#0=#:G1405) (RETURN (CODE-CHAR - (PROG1 (LETT #0# (- |n| 1) |CHAR;index;Pi$;4|) + (PROG1 (LETT #0# (- |n| 1) |CHAR;index;Pi$;7|) (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)))))) -(DEFUN |CHAR;lookup;$Pi;5| (|c| $) - (PROG (#0=#:G1404) +(DEFUN |CHAR;lookup;$Pi;8| (|c| $) + (PROG (#0=#:G1407) (RETURN - (PROG1 (LETT #0# (+ 1 (CHAR-CODE |c|)) |CHAR;lookup;$Pi;5|) + (PROG1 (LETT #0# (+ 1 (CHAR-CODE |c|)) |CHAR;lookup;$Pi;8|) (|check-subtype| (< 0 #0#) '(|PositiveInteger|) #0#))))) -(DEFUN |CHAR;char;Nni$;6| (|n| $) +(DEFUN |CHAR;char;Nni$;9| (|n| $) (DECLARE (IGNORE $)) (CODE-CHAR |n|)) -(DEFUN |CHAR;ord;$Nni;7| (|c| $) (DECLARE (IGNORE $)) (CHAR-CODE |c|)) +(DEFUN |CHAR;ord;$Nni;10| (|c| $) + (DECLARE (IGNORE $)) + (CHAR-CODE |c|)) -(DEFUN |CHAR;random;$;8| ($) (CODE-CHAR (RANDOM 256))) +(DEFUN |CHAR;random;$;11| ($) (CODE-CHAR (RANDOM 256))) -(DEFUN |CHAR;space;$;9| ($) (DECLARE (IGNORE $)) (CHAR " " 0)) +(DEFUN |CHAR;space;$;12| ($) (DECLARE (IGNORE $)) (CHAR " " 0)) -(DEFUN |CHAR;quote;$;10| ($) (DECLARE (IGNORE $)) (CHAR "\" " 0)) +(DEFUN |CHAR;quote;$;13| ($) (DECLARE (IGNORE $)) (CHAR "\" " 0)) -(DEFUN |CHAR;escape;$;11| ($) (DECLARE (IGNORE $)) (CHAR "_ " 0)) +(DEFUN |CHAR;escape;$;14| ($) (DECLARE (IGNORE $)) (CHAR "_ " 0)) -(DEFUN |CHAR;coerce;$Of;12| (|c| $) (DECLARE (IGNORE $)) |c|) +(DEFUN |CHAR;coerce;$Of;15| (|c| $) (DECLARE (IGNORE $)) |c|) -(DEFUN |CHAR;digit?;$B;13| (|c| $) - (SPADCALL |c| (|spadConstant| $ 29) (|getShellEntry| $ 31))) +(DEFUN |CHAR;digit?;$B;16| (|c| $) + (SPADCALL |c| (|spadConstant| $ 32) (|getShellEntry| $ 34))) -(DEFUN |CHAR;hexDigit?;$B;14| (|c| $) - (SPADCALL |c| (|spadConstant| $ 33) (|getShellEntry| $ 31))) +(DEFUN |CHAR;hexDigit?;$B;17| (|c| $) + (SPADCALL |c| (|spadConstant| $ 36) (|getShellEntry| $ 34))) -(DEFUN |CHAR;upperCase?;$B;15| (|c| $) - (SPADCALL |c| (|spadConstant| $ 35) (|getShellEntry| $ 31))) +(DEFUN |CHAR;upperCase?;$B;18| (|c| $) + (SPADCALL |c| (|spadConstant| $ 38) (|getShellEntry| $ 34))) -(DEFUN |CHAR;lowerCase?;$B;16| (|c| $) - (SPADCALL |c| (|spadConstant| $ 37) (|getShellEntry| $ 31))) +(DEFUN |CHAR;lowerCase?;$B;19| (|c| $) + (SPADCALL |c| (|spadConstant| $ 40) (|getShellEntry| $ 34))) -(DEFUN |CHAR;alphabetic?;$B;17| (|c| $) - (SPADCALL |c| (|spadConstant| $ 39) (|getShellEntry| $ 31))) +(DEFUN |CHAR;alphabetic?;$B;20| (|c| $) + (SPADCALL |c| (|spadConstant| $ 42) (|getShellEntry| $ 34))) -(DEFUN |CHAR;alphanumeric?;$B;18| (|c| $) - (SPADCALL |c| (|spadConstant| $ 41) (|getShellEntry| $ 31))) +(DEFUN |CHAR;alphanumeric?;$B;21| (|c| $) + (SPADCALL |c| (|spadConstant| $ 44) (|getShellEntry| $ 34))) -(DEFUN |CHAR;latex;$S;19| (|c| $) +(DEFUN |CHAR;latex;$S;22| (|c| $) (STRCONC "\\mbox{`" (STRCONC (MAKE-FULL-CVEC 1 |c|) "'}"))) -(DEFUN |CHAR;char;S$;20| (|s| $) +(DEFUN |CHAR;char;S$;23| (|s| $) (COND ((EQL (QCSIZE |s|) 1) - (SPADCALL |s| (SPADCALL |s| (|getShellEntry| $ 49)) - (|getShellEntry| $ 50))) + (SPADCALL |s| (SPADCALL |s| (|getShellEntry| $ 52)) + (|getShellEntry| $ 53))) ('T (|userError| "String is not a single character")))) -(DEFUN |CHAR;upperCase;2$;21| (|c| $) +(DEFUN |CHAR;upperCase;2$;24| (|c| $) (DECLARE (IGNORE $)) (CHAR-UPCASE |c|)) -(DEFUN |CHAR;lowerCase;2$;22| (|c| $) +(DEFUN |CHAR;lowerCase;2$;25| (|c| $) (DECLARE (IGNORE $)) (CHAR-DOWNCASE |c|)) (DEFUN |Character| () (PROG () (RETURN - (PROG (#0=#:G1425) + (PROG (#0=#:G1428) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|Character|) @@ -184,7 +213,7 @@ (RETURN (PROGN (LETT |dv$| '(|Character|) . #0=(|Character|)) - (LETT $ (|newShell| 55) . #0#) + (LETT $ (|newShell| 58) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -194,23 +223,24 @@ (MAKEPROP '|Character| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|Boolean|) |CHAR;=;2$B;1| - |CHAR;<;2$B;2| (|NonNegativeInteger|) |CHAR;size;Nni;3| + |CHAR;<;2$B;2| |CHAR;>;2$B;3| |CHAR;<=;2$B;4| + |CHAR;>=;2$B;5| (|NonNegativeInteger|) |CHAR;size;Nni;6| (|PositiveInteger|) (0 . |One|) (4 . |One|) (|Integer|) - (8 . -) |CHAR;char;Nni$;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;$S;19| + (8 . -) |CHAR;char;Nni$;9| |CHAR;index;Pi$;7| + |CHAR;ord;$Nni;10| (14 . +) |CHAR;lookup;$Pi;8| + (20 . |random|) |CHAR;random;$;11| |CHAR;space;$;12| + |CHAR;quote;$;13| |CHAR;escape;$;14| (|OutputForm|) + |CHAR;coerce;$Of;15| (|CharacterClass|) (25 . |digit|) + (|Character|) (29 . |member?|) |CHAR;digit?;$B;16| + (35 . |hexDigit|) |CHAR;hexDigit?;$B;17| + (39 . |upperCase|) |CHAR;upperCase?;$B;18| + (43 . |lowerCase|) |CHAR;lowerCase?;$B;19| + (47 . |alphabetic|) |CHAR;alphabetic?;$B;20| + (51 . |alphanumeric|) |CHAR;alphanumeric?;$B;21| + (|String|) (55 . |new|) (61 . |concat|) |CHAR;latex;$S;22| (67 . |#|) (72 . |one?|) (77 . |minIndex|) (82 . |elt|) - |CHAR;char;S$;20| |CHAR;upperCase;2$;21| - |CHAR;lowerCase;2$;22| (|SingleInteger|)) + |CHAR;char;S$;23| |CHAR;upperCase;2$;24| + |CHAR;lowerCase;2$;25| (|SingleInteger|)) '#(~= 88 |upperCase?| 94 |upperCase| 99 |space| 104 |size| 108 |random| 112 |quote| 116 |ord| 120 |min| 125 |max| 135 |lowerCase?| 145 |lowerCase| 150 |lookup| 155 |latex| 160 @@ -224,24 +254,24 @@ |BasicType&| NIL) (CONS '#((|OrderedFinite|) (|OrderedSet|) (|Finite|) (|SetCategory|) (|BasicType|) - (|CoercibleTo| 26)) - (|makeByteWordVec2| 54 - '(0 11 0 12 0 9 0 13 2 14 0 0 0 15 2 9 - 0 0 0 19 1 9 0 0 21 0 28 0 29 2 28 6 - 30 0 31 0 28 0 33 0 28 0 35 0 28 0 37 - 0 28 0 39 0 28 0 41 2 43 0 9 30 44 2 - 43 0 0 0 45 1 43 9 0 47 1 9 6 0 48 1 - 43 14 0 49 2 43 30 0 14 50 2 0 6 0 0 - 1 1 0 6 0 36 1 0 0 0 52 0 0 0 23 0 0 - 9 10 0 0 0 22 0 0 0 24 1 0 9 0 18 0 0 - 0 1 2 0 0 0 0 1 0 0 0 1 2 0 0 0 0 1 1 - 0 6 0 38 1 0 0 0 53 1 0 11 0 20 1 0 - 43 0 46 1 0 0 11 17 1 0 6 0 34 1 0 54 - 0 1 0 0 0 25 1 0 6 0 32 1 0 26 0 27 1 - 0 0 43 51 1 0 0 9 16 2 0 6 0 0 1 1 0 - 6 0 42 1 0 6 0 40 2 0 6 0 0 1 2 0 6 0 - 0 1 2 0 6 0 0 7 2 0 6 0 0 1 2 0 6 0 0 - 8))))) + (|CoercibleTo| 29)) + (|makeByteWordVec2| 57 + '(0 14 0 15 0 12 0 16 2 17 0 0 0 18 2 + 12 0 0 0 22 1 12 0 0 24 0 31 0 32 2 + 31 6 33 0 34 0 31 0 36 0 31 0 38 0 31 + 0 40 0 31 0 42 0 31 0 44 2 46 0 12 33 + 47 2 46 0 0 0 48 1 46 12 0 50 1 12 6 + 0 51 1 46 17 0 52 2 46 33 0 17 53 2 0 + 6 0 0 1 1 0 6 0 39 1 0 0 0 55 0 0 0 + 26 0 0 12 13 0 0 0 25 0 0 0 27 1 0 12 + 0 21 0 0 0 1 2 0 0 0 0 1 0 0 0 1 2 0 + 0 0 0 1 1 0 6 0 41 1 0 0 0 56 1 0 14 + 0 23 1 0 46 0 49 1 0 0 14 20 1 0 6 0 + 37 1 0 57 0 1 0 0 0 28 1 0 6 0 35 1 0 + 29 0 30 1 0 0 46 54 1 0 0 12 19 2 0 6 + 0 0 1 1 0 6 0 45 1 0 6 0 43 2 0 6 0 0 + 11 2 0 6 0 0 9 2 0 6 0 0 7 2 0 6 0 0 + 10 2 0 6 0 0 8))))) '|lookupComplete|)) (MAKEPROP '|Character| 'NILADIC T) diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index 582076db..3096aacb 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -83,284 +83,298 @@ (PUT '|DFLOAT;<;2$B;20| '|SPADreplace| '<) +(DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) + |%Boolean|) + |DFLOAT;>;2$B;21|)) + +(PUT '|DFLOAT;>;2$B;21| '|SPADreplace| '>) + +(DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) + |%Boolean|) + |DFLOAT;<=;2$B;22|)) + +(DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) + |%Boolean|) + |DFLOAT;>=;2$B;23|)) + (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;-;2$;21|)) + |DFLOAT;-;2$;24|)) -(PUT '|DFLOAT;-;2$;21| '|SPADreplace| '-) +(PUT '|DFLOAT;-;2$;24| '|SPADreplace| '-) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;+;3$;22|)) + |DFLOAT;+;3$;25|)) -(PUT '|DFLOAT;+;3$;22| '|SPADreplace| '+) +(PUT '|DFLOAT;+;3$;25| '|SPADreplace| '+) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;-;3$;23|)) + |DFLOAT;-;3$;26|)) -(PUT '|DFLOAT;-;3$;23| '|SPADreplace| '-) +(PUT '|DFLOAT;-;3$;26| '|SPADreplace| '-) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;*;3$;24|)) + |DFLOAT;*;3$;27|)) -(PUT '|DFLOAT;*;3$;24| '|SPADreplace| '*) +(PUT '|DFLOAT;*;3$;27| '|SPADreplace| '*) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;*;I2$;25|)) + |DFLOAT;*;I2$;28|)) -(PUT '|DFLOAT;*;I2$;25| '|SPADreplace| '*) +(PUT '|DFLOAT;*;I2$;28| '|SPADreplace| '*) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;max;3$;26|)) + |DFLOAT;max;3$;29|)) -(PUT '|DFLOAT;max;3$;26| '|SPADreplace| 'MAX) +(PUT '|DFLOAT;max;3$;29| '|SPADreplace| 'MAX) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;min;3$;27|)) + |DFLOAT;min;3$;30|)) -(PUT '|DFLOAT;min;3$;27| '|SPADreplace| 'MIN) +(PUT '|DFLOAT;min;3$;30| '|SPADreplace| 'MIN) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%Boolean|) - |DFLOAT;=;2$B;28|)) + |DFLOAT;=;2$B;31|)) -(PUT '|DFLOAT;=;2$B;28| '|SPADreplace| '=) +(PUT '|DFLOAT;=;2$B;31| '|SPADreplace| '=) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Integer| |%Shell|) |%DoubleFloat|) - |DFLOAT;/;$I$;29|)) + |DFLOAT;/;$I$;32|)) -(PUT '|DFLOAT;/;$I$;29| '|SPADreplace| '/) +(PUT '|DFLOAT;/;$I$;32| '|SPADreplace| '/) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;sqrt;2$;30|)) + |DFLOAT;sqrt;2$;33|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;log10;2$;31|)) + |DFLOAT;log10;2$;34|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Integer| |%Shell|) |%DoubleFloat|) - |DFLOAT;**;$I$;32|)) + |DFLOAT;**;$I$;35|)) -(PUT '|DFLOAT;**;$I$;32| '|SPADreplace| 'EXPT) +(PUT '|DFLOAT;**;$I$;35| '|SPADreplace| 'EXPT) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;**;3$;33|)) + |DFLOAT;**;3$;36|)) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%DoubleFloat|) - |DFLOAT;coerce;I$;34|)) + |DFLOAT;coerce;I$;37|)) -(PUT '|DFLOAT;coerce;I$;34| '|SPADreplace| +(PUT '|DFLOAT;coerce;I$;37| '|SPADreplace| '(XLAM (|i|) (FLOAT |i| |$DoubleFloatMaximum|))) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;exp;2$;35|)) + |DFLOAT;exp;2$;38|)) -(PUT '|DFLOAT;exp;2$;35| '|SPADreplace| 'EXP) +(PUT '|DFLOAT;exp;2$;38| '|SPADreplace| 'EXP) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;log;2$;36|)) + |DFLOAT;log;2$;39|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;log2;2$;37|)) + |DFLOAT;log2;2$;40|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;sin;2$;38|)) + |DFLOAT;sin;2$;41|)) -(PUT '|DFLOAT;sin;2$;38| '|SPADreplace| 'SIN) +(PUT '|DFLOAT;sin;2$;41| '|SPADreplace| 'SIN) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;cos;2$;39|)) + |DFLOAT;cos;2$;42|)) -(PUT '|DFLOAT;cos;2$;39| '|SPADreplace| 'COS) +(PUT '|DFLOAT;cos;2$;42| '|SPADreplace| 'COS) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;tan;2$;40|)) + |DFLOAT;tan;2$;43|)) -(PUT '|DFLOAT;tan;2$;40| '|SPADreplace| 'TAN) +(PUT '|DFLOAT;tan;2$;43| '|SPADreplace| 'TAN) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;cot;2$;41|)) + |DFLOAT;cot;2$;44|)) -(PUT '|DFLOAT;cot;2$;41| '|SPADreplace| 'COT) +(PUT '|DFLOAT;cot;2$;44| '|SPADreplace| 'COT) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;sec;2$;42|)) + |DFLOAT;sec;2$;45|)) -(PUT '|DFLOAT;sec;2$;42| '|SPADreplace| 'SEC) +(PUT '|DFLOAT;sec;2$;45| '|SPADreplace| 'SEC) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;csc;2$;43|)) + |DFLOAT;csc;2$;46|)) -(PUT '|DFLOAT;csc;2$;43| '|SPADreplace| 'CSC) +(PUT '|DFLOAT;csc;2$;46| '|SPADreplace| 'CSC) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;asin;2$;44|)) + |DFLOAT;asin;2$;47|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acos;2$;45|)) + |DFLOAT;acos;2$;48|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;atan;2$;46|)) + |DFLOAT;atan;2$;49|)) -(PUT '|DFLOAT;atan;2$;46| '|SPADreplace| 'ATAN) +(PUT '|DFLOAT;atan;2$;49| '|SPADreplace| 'ATAN) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acsc;2$;47|)) + |DFLOAT;acsc;2$;50|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acot;2$;48|)) + |DFLOAT;acot;2$;51|)) -(PUT '|DFLOAT;acot;2$;48| '|SPADreplace| 'ACOT) +(PUT '|DFLOAT;acot;2$;51| '|SPADreplace| 'ACOT) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;asec;2$;49|)) + |DFLOAT;asec;2$;52|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;sinh;2$;50|)) + |DFLOAT;sinh;2$;53|)) -(PUT '|DFLOAT;sinh;2$;50| '|SPADreplace| 'SINH) +(PUT '|DFLOAT;sinh;2$;53| '|SPADreplace| 'SINH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;cosh;2$;51|)) + |DFLOAT;cosh;2$;54|)) -(PUT '|DFLOAT;cosh;2$;51| '|SPADreplace| 'COSH) +(PUT '|DFLOAT;cosh;2$;54| '|SPADreplace| 'COSH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;tanh;2$;52|)) + |DFLOAT;tanh;2$;55|)) -(PUT '|DFLOAT;tanh;2$;52| '|SPADreplace| 'TANH) +(PUT '|DFLOAT;tanh;2$;55| '|SPADreplace| 'TANH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;csch;2$;53|)) + |DFLOAT;csch;2$;56|)) -(PUT '|DFLOAT;csch;2$;53| '|SPADreplace| 'CSCH) +(PUT '|DFLOAT;csch;2$;56| '|SPADreplace| 'CSCH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;coth;2$;54|)) + |DFLOAT;coth;2$;57|)) -(PUT '|DFLOAT;coth;2$;54| '|SPADreplace| 'COTH) +(PUT '|DFLOAT;coth;2$;57| '|SPADreplace| 'COTH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;sech;2$;55|)) + |DFLOAT;sech;2$;58|)) -(PUT '|DFLOAT;sech;2$;55| '|SPADreplace| 'SECH) +(PUT '|DFLOAT;sech;2$;58| '|SPADreplace| 'SECH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;asinh;2$;56|)) + |DFLOAT;asinh;2$;59|)) -(PUT '|DFLOAT;asinh;2$;56| '|SPADreplace| 'ASINH) +(PUT '|DFLOAT;asinh;2$;59| '|SPADreplace| 'ASINH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acosh;2$;57|)) + |DFLOAT;acosh;2$;60|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;atanh;2$;58|)) + |DFLOAT;atanh;2$;61|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acsch;2$;59|)) + |DFLOAT;acsch;2$;62|)) -(PUT '|DFLOAT;acsch;2$;59| '|SPADreplace| 'ACSCH) +(PUT '|DFLOAT;acsch;2$;62| '|SPADreplace| 'ACSCH) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;acoth;2$;60|)) + |DFLOAT;acoth;2$;63|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;asech;2$;61|)) + |DFLOAT;asech;2$;64|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;/;3$;62|)) + |DFLOAT;/;3$;65|)) -(PUT '|DFLOAT;/;3$;62| '|SPADreplace| '/) +(PUT '|DFLOAT;/;3$;65| '|SPADreplace| '/) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Boolean|) - |DFLOAT;negative?;$B;63|)) + |DFLOAT;negative?;$B;66|)) -(PUT '|DFLOAT;negative?;$B;63| '|SPADreplace| 'MINUSP) +(PUT '|DFLOAT;negative?;$B;66| '|SPADreplace| 'MINUSP) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Boolean|) - |DFLOAT;zero?;$B;64|)) + |DFLOAT;zero?;$B;67|)) -(PUT '|DFLOAT;zero?;$B;64| '|SPADreplace| 'ZEROP) +(PUT '|DFLOAT;zero?;$B;67| '|SPADreplace| 'ZEROP) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Boolean|) - |DFLOAT;one?;$B;65|)) + |DFLOAT;one?;$B;68|)) -(PUT '|DFLOAT;one?;$B;65| '|SPADreplace| '(XLAM (|x|) (= |x| 1.0))) +(PUT '|DFLOAT;one?;$B;68| '|SPADreplace| '(XLAM (|x|) (= |x| 1.0))) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Short|) - |DFLOAT;hash;$Si;66|)) + |DFLOAT;hash;$Si;69|)) -(PUT '|DFLOAT;hash;$Si;66| '|SPADreplace| 'HASHEQ) +(PUT '|DFLOAT;hash;$Si;69| '|SPADreplace| 'HASHEQ) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Pair|) - |DFLOAT;recip;$U;67|)) + |DFLOAT;recip;$U;70|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;differentiate;2$;68|)) + |DFLOAT;differentiate;2$;71|)) -(PUT '|DFLOAT;differentiate;2$;68| '|SPADreplace| '(XLAM (|x|) 0.0)) +(PUT '|DFLOAT;differentiate;2$;71| '|SPADreplace| '(XLAM (|x|) 0.0)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;Gamma;2$;69|)) + |DFLOAT;Gamma;2$;72|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;Beta;3$;70|)) + |DFLOAT;Beta;3$;73|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Integer|) - |DFLOAT;wholePart;$I;71|)) + |DFLOAT;wholePart;$I;74|)) -(PUT '|DFLOAT;wholePart;$I;71| '|SPADreplace| 'FIX) +(PUT '|DFLOAT;wholePart;$I;74| '|SPADreplace| 'FIX) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| (|%IntegerSection| 1) |%Shell|) |%DoubleFloat|) - |DFLOAT;float;2IPi$;72|)) + |DFLOAT;float;2IPi$;75|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;convert;2$;73|)) + |DFLOAT;convert;2$;76|)) -(PUT '|DFLOAT;convert;2$;73| '|SPADreplace| '(XLAM (|x|) |x|)) +(PUT '|DFLOAT;convert;2$;76| '|SPADreplace| '(XLAM (|x|) |x|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Thing|) - |DFLOAT;convert;$F;74|)) + |DFLOAT;convert;$F;77|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| (|%IntegerSection| 0) |%Shell|) |%Thing|) - |DFLOAT;rationalApproximation;$NniF;75|)) + |DFLOAT;rationalApproximation;$NniF;78|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;atan;3$;76|)) + |DFLOAT;atan;3$;79|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Thing|) - |DFLOAT;retract;$F;77|)) + |DFLOAT;retract;$F;80|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Pair|) - |DFLOAT;retractIfCan;$U;78|)) + |DFLOAT;retractIfCan;$U;81|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Integer|) - |DFLOAT;retract;$I;79|)) + |DFLOAT;retract;$I;82|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Pair|) - |DFLOAT;retractIfCan;$U;80|)) + |DFLOAT;retractIfCan;$U;83|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Integer|) - |DFLOAT;sign;$I;81|)) + |DFLOAT;sign;$I;84|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) - |DFLOAT;abs;2$;82|)) + |DFLOAT;abs;2$;85|)) -(PUT '|DFLOAT;abs;2$;82| '|SPADreplace| +(PUT '|DFLOAT;abs;2$;85| '|SPADreplace| '(XLAM (|x|) (FLOAT-SIGN 1.0 |x|))) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%Pair|) @@ -370,11 +384,11 @@ (|%DoubleFloat| (|%IntegerSection| 0) (|%IntegerSection| 0) |%Shell|) |%Thing|) - |DFLOAT;rationalApproximation;$2NniF;84|)) + |DFLOAT;rationalApproximation;$2NniF;87|)) (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Thing| |%Shell|) |%DoubleFloat|) - |DFLOAT;**;$F$;85|)) + |DFLOAT;**;$F$;88|)) (DEFUN |DFLOAT;OMwrite;$S;1| (|x| $) (PROG (|sp| |dev| |s|) @@ -444,7 +458,7 @@ ('T (PROG1 (LETT #0# (FIX (SPADCALL (FLOAT-DIGITS 0.0) - (|DFLOAT;log2;2$;37| + (|DFLOAT;log2;2$;40| (FLOAT (FLOAT-RADIX 0.0) |$DoubleFloatMaximum|) $) @@ -486,211 +500,217 @@ (DEFUN |DFLOAT;<;2$B;20| (|x| |y| $) (DECLARE (IGNORE $)) (< |x| |y|)) -(DEFUN |DFLOAT;-;2$;21| (|x| $) (DECLARE (IGNORE $)) (- |x|)) +(DEFUN |DFLOAT;>;2$B;21| (|x| |y| $) (DECLARE (IGNORE $)) (> |x| |y|)) + +(DEFUN |DFLOAT;<=;2$B;22| (|x| |y| $) (NOT (> |x| |y|))) + +(DEFUN |DFLOAT;>=;2$B;23| (|x| |y| $) (NOT (< |x| |y|))) + +(DEFUN |DFLOAT;-;2$;24| (|x| $) (DECLARE (IGNORE $)) (- |x|)) -(DEFUN |DFLOAT;+;3$;22| (|x| |y| $) (DECLARE (IGNORE $)) (+ |x| |y|)) +(DEFUN |DFLOAT;+;3$;25| (|x| |y| $) (DECLARE (IGNORE $)) (+ |x| |y|)) -(DEFUN |DFLOAT;-;3$;23| (|x| |y| $) (DECLARE (IGNORE $)) (- |x| |y|)) +(DEFUN |DFLOAT;-;3$;26| (|x| |y| $) (DECLARE (IGNORE $)) (- |x| |y|)) -(DEFUN |DFLOAT;*;3$;24| (|x| |y| $) (DECLARE (IGNORE $)) (* |x| |y|)) +(DEFUN |DFLOAT;*;3$;27| (|x| |y| $) (DECLARE (IGNORE $)) (* |x| |y|)) -(DEFUN |DFLOAT;*;I2$;25| (|i| |x| $) (DECLARE (IGNORE $)) (* |i| |x|)) +(DEFUN |DFLOAT;*;I2$;28| (|i| |x| $) (DECLARE (IGNORE $)) (* |i| |x|)) -(DEFUN |DFLOAT;max;3$;26| (|x| |y| $) +(DEFUN |DFLOAT;max;3$;29| (|x| |y| $) (DECLARE (IGNORE $)) (MAX |x| |y|)) -(DEFUN |DFLOAT;min;3$;27| (|x| |y| $) +(DEFUN |DFLOAT;min;3$;30| (|x| |y| $) (DECLARE (IGNORE $)) (MIN |x| |y|)) -(DEFUN |DFLOAT;=;2$B;28| (|x| |y| $) (DECLARE (IGNORE $)) (= |x| |y|)) +(DEFUN |DFLOAT;=;2$B;31| (|x| |y| $) (DECLARE (IGNORE $)) (= |x| |y|)) -(DEFUN |DFLOAT;/;$I$;29| (|x| |i| $) (DECLARE (IGNORE $)) (/ |x| |i|)) +(DEFUN |DFLOAT;/;$I$;32| (|x| |i| $) (DECLARE (IGNORE $)) (/ |x| |i|)) -(DEFUN |DFLOAT;sqrt;2$;30| (|x| $) (C-TO-R (SQRT |x|))) +(DEFUN |DFLOAT;sqrt;2$;33| (|x| $) (C-TO-R (SQRT |x|))) -(DEFUN |DFLOAT;log10;2$;31| (|x| $) (C-TO-R (|log| |x|))) +(DEFUN |DFLOAT;log10;2$;34| (|x| $) (C-TO-R (|log| |x|))) -(DEFUN |DFLOAT;**;$I$;32| (|x| |i| $) +(DEFUN |DFLOAT;**;$I$;35| (|x| |i| $) (DECLARE (IGNORE $)) (EXPT |x| |i|)) -(DEFUN |DFLOAT;**;3$;33| (|x| |y| $) (C-TO-R (EXPT |x| |y|))) +(DEFUN |DFLOAT;**;3$;36| (|x| |y| $) (C-TO-R (EXPT |x| |y|))) -(DEFUN |DFLOAT;coerce;I$;34| (|i| $) +(DEFUN |DFLOAT;coerce;I$;37| (|i| $) (DECLARE (IGNORE $)) (FLOAT |i| |$DoubleFloatMaximum|)) -(DEFUN |DFLOAT;exp;2$;35| (|x| $) (DECLARE (IGNORE $)) (EXP |x|)) +(DEFUN |DFLOAT;exp;2$;38| (|x| $) (DECLARE (IGNORE $)) (EXP |x|)) -(DEFUN |DFLOAT;log;2$;36| (|x| $) (C-TO-R (LN |x|))) +(DEFUN |DFLOAT;log;2$;39| (|x| $) (C-TO-R (LN |x|))) -(DEFUN |DFLOAT;log2;2$;37| (|x| $) (C-TO-R (LOG2 |x|))) +(DEFUN |DFLOAT;log2;2$;40| (|x| $) (C-TO-R (LOG2 |x|))) -(DEFUN |DFLOAT;sin;2$;38| (|x| $) (DECLARE (IGNORE $)) (SIN |x|)) +(DEFUN |DFLOAT;sin;2$;41| (|x| $) (DECLARE (IGNORE $)) (SIN |x|)) -(DEFUN |DFLOAT;cos;2$;39| (|x| $) (DECLARE (IGNORE $)) (COS |x|)) +(DEFUN |DFLOAT;cos;2$;42| (|x| $) (DECLARE (IGNORE $)) (COS |x|)) -(DEFUN |DFLOAT;tan;2$;40| (|x| $) (DECLARE (IGNORE $)) (TAN |x|)) +(DEFUN |DFLOAT;tan;2$;43| (|x| $) (DECLARE (IGNORE $)) (TAN |x|)) -(DEFUN |DFLOAT;cot;2$;41| (|x| $) (DECLARE (IGNORE $)) (COT |x|)) +(DEFUN |DFLOAT;cot;2$;44| (|x| $) (DECLARE (IGNORE $)) (COT |x|)) -(DEFUN |DFLOAT;sec;2$;42| (|x| $) (DECLARE (IGNORE $)) (SEC |x|)) +(DEFUN |DFLOAT;sec;2$;45| (|x| $) (DECLARE (IGNORE $)) (SEC |x|)) -(DEFUN |DFLOAT;csc;2$;43| (|x| $) (DECLARE (IGNORE $)) (CSC |x|)) +(DEFUN |DFLOAT;csc;2$;46| (|x| $) (DECLARE (IGNORE $)) (CSC |x|)) -(DEFUN |DFLOAT;asin;2$;44| (|x| $) (C-TO-R (ASIN |x|))) +(DEFUN |DFLOAT;asin;2$;47| (|x| $) (C-TO-R (ASIN |x|))) -(DEFUN |DFLOAT;acos;2$;45| (|x| $) (C-TO-R (ACOS |x|))) +(DEFUN |DFLOAT;acos;2$;48| (|x| $) (C-TO-R (ACOS |x|))) -(DEFUN |DFLOAT;atan;2$;46| (|x| $) (DECLARE (IGNORE $)) (ATAN |x|)) +(DEFUN |DFLOAT;atan;2$;49| (|x| $) (DECLARE (IGNORE $)) (ATAN |x|)) -(DEFUN |DFLOAT;acsc;2$;47| (|x| $) (C-TO-R (ACSC |x|))) +(DEFUN |DFLOAT;acsc;2$;50| (|x| $) (C-TO-R (ACSC |x|))) -(DEFUN |DFLOAT;acot;2$;48| (|x| $) (DECLARE (IGNORE $)) (ACOT |x|)) +(DEFUN |DFLOAT;acot;2$;51| (|x| $) (DECLARE (IGNORE $)) (ACOT |x|)) -(DEFUN |DFLOAT;asec;2$;49| (|x| $) (C-TO-R (ASEC |x|))) +(DEFUN |DFLOAT;asec;2$;52| (|x| $) (C-TO-R (ASEC |x|))) -(DEFUN |DFLOAT;sinh;2$;50| (|x| $) (DECLARE (IGNORE $)) (SINH |x|)) +(DEFUN |DFLOAT;sinh;2$;53| (|x| $) (DECLARE (IGNORE $)) (SINH |x|)) -(DEFUN |DFLOAT;cosh;2$;51| (|x| $) (DECLARE (IGNORE $)) (COSH |x|)) +(DEFUN |DFLOAT;cosh;2$;54| (|x| $) (DECLARE (IGNORE $)) (COSH |x|)) -(DEFUN |DFLOAT;tanh;2$;52| (|x| $) (DECLARE (IGNORE $)) (TANH |x|)) +(DEFUN |DFLOAT;tanh;2$;55| (|x| $) (DECLARE (IGNORE $)) (TANH |x|)) -(DEFUN |DFLOAT;csch;2$;53| (|x| $) (DECLARE (IGNORE $)) (CSCH |x|)) +(DEFUN |DFLOAT;csch;2$;56| (|x| $) (DECLARE (IGNORE $)) (CSCH |x|)) -(DEFUN |DFLOAT;coth;2$;54| (|x| $) (DECLARE (IGNORE $)) (COTH |x|)) +(DEFUN |DFLOAT;coth;2$;57| (|x| $) (DECLARE (IGNORE $)) (COTH |x|)) -(DEFUN |DFLOAT;sech;2$;55| (|x| $) (DECLARE (IGNORE $)) (SECH |x|)) +(DEFUN |DFLOAT;sech;2$;58| (|x| $) (DECLARE (IGNORE $)) (SECH |x|)) -(DEFUN |DFLOAT;asinh;2$;56| (|x| $) (DECLARE (IGNORE $)) (ASINH |x|)) +(DEFUN |DFLOAT;asinh;2$;59| (|x| $) (DECLARE (IGNORE $)) (ASINH |x|)) -(DEFUN |DFLOAT;acosh;2$;57| (|x| $) (C-TO-R (ACOSH |x|))) +(DEFUN |DFLOAT;acosh;2$;60| (|x| $) (C-TO-R (ACOSH |x|))) -(DEFUN |DFLOAT;atanh;2$;58| (|x| $) (C-TO-R (ATANH |x|))) +(DEFUN |DFLOAT;atanh;2$;61| (|x| $) (C-TO-R (ATANH |x|))) -(DEFUN |DFLOAT;acsch;2$;59| (|x| $) (DECLARE (IGNORE $)) (ACSCH |x|)) +(DEFUN |DFLOAT;acsch;2$;62| (|x| $) (DECLARE (IGNORE $)) (ACSCH |x|)) -(DEFUN |DFLOAT;acoth;2$;60| (|x| $) (C-TO-R (ACOTH |x|))) +(DEFUN |DFLOAT;acoth;2$;63| (|x| $) (C-TO-R (ACOTH |x|))) -(DEFUN |DFLOAT;asech;2$;61| (|x| $) (C-TO-R (ASECH |x|))) +(DEFUN |DFLOAT;asech;2$;64| (|x| $) (C-TO-R (ASECH |x|))) -(DEFUN |DFLOAT;/;3$;62| (|x| |y| $) (DECLARE (IGNORE $)) (/ |x| |y|)) +(DEFUN |DFLOAT;/;3$;65| (|x| |y| $) (DECLARE (IGNORE $)) (/ |x| |y|)) -(DEFUN |DFLOAT;negative?;$B;63| (|x| $) +(DEFUN |DFLOAT;negative?;$B;66| (|x| $) (DECLARE (IGNORE $)) (MINUSP |x|)) -(DEFUN |DFLOAT;zero?;$B;64| (|x| $) (DECLARE (IGNORE $)) (ZEROP |x|)) +(DEFUN |DFLOAT;zero?;$B;67| (|x| $) (DECLARE (IGNORE $)) (ZEROP |x|)) -(DEFUN |DFLOAT;one?;$B;65| (|x| $) (DECLARE (IGNORE $)) (= |x| 1.0)) +(DEFUN |DFLOAT;one?;$B;68| (|x| $) (DECLARE (IGNORE $)) (= |x| 1.0)) -(DEFUN |DFLOAT;hash;$Si;66| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) +(DEFUN |DFLOAT;hash;$Si;69| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) -(DEFUN |DFLOAT;recip;$U;67| (|x| $) +(DEFUN |DFLOAT;recip;$U;70| (|x| $) (COND ((ZEROP |x|) (CONS 1 "failed")) ('T (CONS 0 (/ 1.0 |x|))))) -(DEFUN |DFLOAT;differentiate;2$;68| (|x| $) (DECLARE (IGNORE $)) 0.0) +(DEFUN |DFLOAT;differentiate;2$;71| (|x| $) (DECLARE (IGNORE $)) 0.0) -(DEFUN |DFLOAT;Gamma;2$;69| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 104))) +(DEFUN |DFLOAT;Gamma;2$;72| (|x| $) + (SPADCALL |x| (|getShellEntry| $ 108))) -(DEFUN |DFLOAT;Beta;3$;70| (|x| |y| $) - (SPADCALL |x| |y| (|getShellEntry| $ 106))) +(DEFUN |DFLOAT;Beta;3$;73| (|x| |y| $) + (SPADCALL |x| |y| (|getShellEntry| $ 110))) -(DEFUN |DFLOAT;wholePart;$I;71| (|x| $) +(DEFUN |DFLOAT;wholePart;$I;74| (|x| $) (DECLARE (IGNORE $)) (FIX |x|)) -(DEFUN |DFLOAT;float;2IPi$;72| (|ma| |ex| |b| $) +(DEFUN |DFLOAT;float;2IPi$;75| (|ma| |ex| |b| $) (* |ma| (EXPT (FLOAT |b| |$DoubleFloatMaximum|) |ex|))) -(DEFUN |DFLOAT;convert;2$;73| (|x| $) (DECLARE (IGNORE $)) |x|) +(DEFUN |DFLOAT;convert;2$;76| (|x| $) (DECLARE (IGNORE $)) |x|) -(DEFUN |DFLOAT;convert;$F;74| (|x| $) - (SPADCALL |x| (|getShellEntry| $ 110))) +(DEFUN |DFLOAT;convert;$F;77| (|x| $) + (SPADCALL |x| (|getShellEntry| $ 114))) -(DEFUN |DFLOAT;rationalApproximation;$NniF;75| (|x| |d| $) - (|DFLOAT;rationalApproximation;$2NniF;84| |x| |d| 10 $)) +(DEFUN |DFLOAT;rationalApproximation;$NniF;78| (|x| |d| $) + (|DFLOAT;rationalApproximation;$2NniF;87| |x| |d| 10 $)) -(DEFUN |DFLOAT;atan;3$;76| (|x| |y| $) +(DEFUN |DFLOAT;atan;3$;79| (|x| |y| $) (PROG (|theta|) (RETURN (SEQ (COND ((= |x| 0.0) (COND - ((< 0.0 |y|) (/ PI 2)) + ((> |y| 0.0) (/ PI 2)) ((< |y| 0.0) (- (/ PI 2))) ('T 0.0))) ('T (SEQ (LETT |theta| (ATAN (FLOAT-SIGN 1.0 (/ |y| |x|))) - |DFLOAT;atan;3$;76|) + |DFLOAT;atan;3$;79|) (COND ((< |x| 0.0) - (LETT |theta| (- PI |theta|) |DFLOAT;atan;3$;76|))) + (LETT |theta| (- PI |theta|) |DFLOAT;atan;3$;79|))) (COND ((< |y| 0.0) - (LETT |theta| (- |theta|) |DFLOAT;atan;3$;76|))) + (LETT |theta| (- |theta|) |DFLOAT;atan;3$;79|))) (EXIT |theta|)))))))) -(DEFUN |DFLOAT;retract;$F;77| (|x| $) - (PROG (#0=#:G1501) +(DEFUN |DFLOAT;retract;$F;80| (|x| $) + (PROG (#0=#:G1504) (RETURN - (|DFLOAT;rationalApproximation;$2NniF;84| |x| + (|DFLOAT;rationalApproximation;$2NniF;87| |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) - |DFLOAT;retract;$F;77|) + |DFLOAT;retract;$F;80|) (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (FLOAT-RADIX 0.0) $)))) -(DEFUN |DFLOAT;retractIfCan;$U;78| (|x| $) - (PROG (#0=#:G1506) +(DEFUN |DFLOAT;retractIfCan;$U;81| (|x| $) + (PROG (#0=#:G1509) (RETURN (CONS 0 - (|DFLOAT;rationalApproximation;$2NniF;84| |x| + (|DFLOAT;rationalApproximation;$2NniF;87| |x| (PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1) - |DFLOAT;retractIfCan;$U;78|) + |DFLOAT;retractIfCan;$U;81|) (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#)) (FLOAT-RADIX 0.0) $))))) -(DEFUN |DFLOAT;retract;$I;79| (|x| $) +(DEFUN |DFLOAT;retract;$I;82| (|x| $) (PROG (|n|) (RETURN - (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;79|) + (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;82|) (EXIT (COND ((= |x| (FLOAT |n| |$DoubleFloatMaximum|)) |n|) ('T (|error| "Not an integer")))))))) -(DEFUN |DFLOAT;retractIfCan;$U;80| (|x| $) +(DEFUN |DFLOAT;retractIfCan;$U;83| (|x| $) (PROG (|n|) (RETURN - (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;80|) + (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;83|) (EXIT (COND ((= |x| (FLOAT |n| |$DoubleFloatMaximum|)) (CONS 0 |n|)) ('T (CONS 1 "failed")))))))) -(DEFUN |DFLOAT;sign;$I;81| (|x| $) - (|DFLOAT;retract;$I;79| (FLOAT-SIGN |x| 1.0) $)) +(DEFUN |DFLOAT;sign;$I;84| (|x| $) + (|DFLOAT;retract;$I;82| (FLOAT-SIGN |x| 1.0) $)) -(DEFUN |DFLOAT;abs;2$;82| (|x| $) +(DEFUN |DFLOAT;abs;2$;85| (|x| $) (DECLARE (IGNORE $)) (FLOAT-SIGN 1.0 |x|)) (DEFUN |DFLOAT;manexp| (|x| $) - (PROG (|s| #0=#:G1527 |me| |two53|) + (PROG (|s| #0=#:G1530 |me| |two53|) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (CONS 0 0)) ('T - (SEQ (LETT |s| (|DFLOAT;sign;$I;81| |x| $) + (SEQ (LETT |s| (|DFLOAT;sign;$I;84| |x| $) |DFLOAT;manexp|) (LETT |x| (FLOAT-SIGN 1.0 |x|) |DFLOAT;manexp|) (COND - ((< |$DoubleFloatMaximum| |x|) + ((> |x| |$DoubleFloatMaximum|) (PROGN (LETT #0# (CONS @@ -713,32 +733,32 @@ (- (QCDR |me|) (FLOAT-DIGITS 0.0)))))))) #0# (EXIT #0#))))) -(DEFUN |DFLOAT;rationalApproximation;$2NniF;84| (|f| |d| |b| $) - (PROG (|#G103| |nu| |ex| BASE #0=#:G1530 |de| |tol| |#G104| |q| |r| - |p2| |q2| #1=#:G1539 |#G105| |#G106| |p0| |p1| |#G107| - |#G108| |q0| |q1| |#G109| |#G110| |s| |t|) +(DEFUN |DFLOAT;rationalApproximation;$2NniF;87| (|f| |d| |b| $) + (PROG (|#G109| |nu| |ex| BASE #0=#:G1533 |de| |tol| |#G110| |q| |r| + |p2| |q2| #1=#:G1542 |#G111| |#G112| |p0| |p1| |#G113| + |#G114| |q0| |q1| |#G115| |#G116| |s| |t|) (RETURN (SEQ (EXIT (SEQ (PROGN - (LETT |#G103| (|DFLOAT;manexp| |f| $) - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |nu| (QCAR |#G103|) - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |ex| (QCDR |#G103|) - |DFLOAT;rationalApproximation;$2NniF;84|) - |#G103|) + (LETT |#G109| (|DFLOAT;manexp| |f| $) + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |nu| (QCAR |#G109|) + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |ex| (QCDR |#G109|) + |DFLOAT;rationalApproximation;$2NniF;87|) + |#G109|) (LETT BASE (FLOAT-RADIX 0.0) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (EXIT (COND ((< |ex| 0) (SEQ (LETT |de| (EXPT BASE (PROG1 (LETT #0# (- |ex|) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (|check-subtype| (NOT (< #0# 0)) '(|NonNegativeInteger|) #0#))) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (EXIT (COND ((< |b| 2) @@ -746,37 +766,37 @@ ('T (SEQ (LETT |tol| (EXPT |b| |d|) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |s| |nu| - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |t| |de| - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |p0| 0 - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |p1| 1 - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |q0| 1 - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |q1| 0 - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (EXIT (SEQ G190 NIL (SEQ (PROGN - (LETT |#G104| + (LETT |#G110| (DIVIDE2 |s| |t|) - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |q| (QCAR |#G104|) - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |r| (QCDR |#G104|) - |DFLOAT;rationalApproximation;$2NniF;84|) - |#G104|) + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |q| (QCAR |#G110|) + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |r| (QCDR |#G110|) + |DFLOAT;rationalApproximation;$2NniF;87|) + |#G110|) (LETT |p2| (+ (* |q| |p1|) |p0|) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (LETT |q2| (+ (* |q| |q1|) |q0|) - |DFLOAT;rationalApproximation;$2NniF;84|) + |DFLOAT;rationalApproximation;$2NniF;87|) (COND ((OR (EQL |r| 0) (< @@ -785,44 +805,44 @@ (- (* |nu| |q2|) (* |de| |p2|))) (|getShellEntry| $ - 141)) + 145)) (* |de| (ABS |p2|)))) (EXIT (PROGN (LETT #1# (SPADCALL |p2| |q2| (|getShellEntry| $ - 139)) - |DFLOAT;rationalApproximation;$2NniF;84|) + 143)) + |DFLOAT;rationalApproximation;$2NniF;87|) (GO #1#))))) (PROGN - (LETT |#G105| |p1| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |#G106| |p2| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |p0| |#G105| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |p1| |#G106| - |DFLOAT;rationalApproximation;$2NniF;84|)) + (LETT |#G111| |p1| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |#G112| |p2| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |p0| |#G111| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |p1| |#G112| + |DFLOAT;rationalApproximation;$2NniF;87|)) (PROGN - (LETT |#G107| |q1| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |#G108| |q2| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |q0| |#G107| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |q1| |#G108| - |DFLOAT;rationalApproximation;$2NniF;84|)) + (LETT |#G113| |q1| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |#G114| |q2| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |q0| |#G113| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |q1| |#G114| + |DFLOAT;rationalApproximation;$2NniF;87|)) (EXIT (PROGN - (LETT |#G109| |t| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |#G110| |r| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |s| |#G109| - |DFLOAT;rationalApproximation;$2NniF;84|) - (LETT |t| |#G110| - |DFLOAT;rationalApproximation;$2NniF;84|)))) + (LETT |#G115| |t| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |#G116| |r| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |s| |#G115| + |DFLOAT;rationalApproximation;$2NniF;87|) + (LETT |t| |#G116| + |DFLOAT;rationalApproximation;$2NniF;87|)))) NIL (GO G190) G191 (EXIT NIL))))))))) ('T @@ -833,35 +853,35 @@ (|check-subtype| (NOT (< |ex| 0)) '(|NonNegativeInteger|) |ex|)))) - (|getShellEntry| $ 142))))))) + (|getShellEntry| $ 146))))))) #1# (EXIT #1#))))) -(DEFUN |DFLOAT;**;$F$;85| (|x| |r| $) - (PROG (|n| |d| #0=#:G1549) +(DEFUN |DFLOAT;**;$F$;88| (|x| |r| $) + (PROG (|n| |d| #0=#:G1552) (RETURN (SEQ (EXIT (COND ((ZEROP |x|) (COND - ((SPADCALL |r| (|getShellEntry| $ 143)) + ((SPADCALL |r| (|getShellEntry| $ 147)) (|error| "0**0 is undefined")) - ((SPADCALL |r| (|getShellEntry| $ 144)) + ((SPADCALL |r| (|getShellEntry| $ 148)) (|error| "division by 0")) ('T 0.0))) - ((OR (SPADCALL |r| (|getShellEntry| $ 143)) + ((OR (SPADCALL |r| (|getShellEntry| $ 147)) (= |x| 1.0)) 1.0) ('T (COND - ((SPADCALL |r| (|getShellEntry| $ 145)) |x|) + ((SPADCALL |r| (|getShellEntry| $ 149)) |x|) ('T (SEQ (LETT |n| (SPADCALL |r| - (|getShellEntry| $ 146)) - |DFLOAT;**;$F$;85|) + (|getShellEntry| $ 150)) + |DFLOAT;**;$F$;88|) (LETT |d| (SPADCALL |r| - (|getShellEntry| $ 147)) - |DFLOAT;**;$F$;85|) + (|getShellEntry| $ 151)) + |DFLOAT;**;$F$;88|) (EXIT (COND ((MINUSP |x|) (COND @@ -871,23 +891,23 @@ (PROGN (LETT #0# (- - (|DFLOAT;**;$F$;85| + (|DFLOAT;**;$F$;88| (- |x|) |r| $)) - |DFLOAT;**;$F$;85|) + |DFLOAT;**;$F$;88|) (GO #0#))) ('T (PROGN (LETT #0# - (|DFLOAT;**;$F$;85| + (|DFLOAT;**;$F$;88| (- |x|) |r| $) - |DFLOAT;**;$F$;85|) + |DFLOAT;**;$F$;88|) (GO #0#))))) ('T (|error| "negative root")))) ((EQL |d| 2) - (EXPT (|DFLOAT;sqrt;2$;30| |x| $) + (EXPT (|DFLOAT;sqrt;2$;33| |x| $) |n|)) ('T - (|DFLOAT;**;3$;33| |x| + (|DFLOAT;**;3$;36| |x| (/ (FLOAT |n| |$DoubleFloatMaximum|) @@ -899,7 +919,7 @@ (DEFUN |DoubleFloat| () (PROG () (RETURN - (PROG (#0=#:G1561) + (PROG (#0=#:G1564) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|DoubleFloat|) @@ -920,7 +940,7 @@ (RETURN (PROGN (LETT |dv$| '(|DoubleFloat|) . #0=(|DoubleFloat|)) - (LETT $ (|newShell| 161) . #0#) + (LETT $ (|newShell| 165) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -932,7 +952,7 @@ (LIST '#(NIL NIL NIL NIL NIL NIL (|OpenMathEncoding|) (0 . |OMencodingXML|) (|String|) (|OpenMathDevice|) (4 . |OMopenString|) (|Void|) (10 . |OMputObject|) - (|DoubleFloat|) |DFLOAT;convert;2$;73| (15 . |OMputFloat|) + (|DoubleFloat|) |DFLOAT;convert;2$;76| (15 . |OMputFloat|) (21 . |OMputEndObject|) (26 . |OMclose|) |DFLOAT;OMwrite;$S;1| (|Boolean|) |DFLOAT;OMwrite;$BS;2| |DFLOAT;OMwrite;Omd$V;3| |DFLOAT;OMwrite;Omd$BV;4| @@ -941,89 +961,91 @@ (|PositiveInteger|) |DFLOAT;base;Pi;6| (|Integer|) |DFLOAT;mantissa;$I;7| |DFLOAT;exponent;$I;8| |DFLOAT;precision;Pi;9| (31 . |base|) (35 . =) (41 . *) - (47 . |coerce|) |DFLOAT;log2;2$;37| (52 . *) - |DFLOAT;wholePart;$I;71| |DFLOAT;bits;Pi;10| + (47 . |coerce|) |DFLOAT;log2;2$;40| (52 . *) + |DFLOAT;wholePart;$I;74| |DFLOAT;bits;Pi;10| |DFLOAT;max;$;11| |DFLOAT;min;$;12| (58 . +) (64 . |One|) (68 . -) |DFLOAT;order;$I;13| (CONS IDENTITY (FUNCALL (|dispatchFunction| |DFLOAT;One;$;15|) $)) - |DFLOAT;/;3$;62| |DFLOAT;exp1;$;16| |DFLOAT;pi;$;17| + |DFLOAT;/;3$;65| |DFLOAT;exp1;$;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| - |DFLOAT;sec;2$;42| |DFLOAT;csc;2$;43| |DFLOAT;asin;2$;44| - |DFLOAT;acos;2$;45| |DFLOAT;atan;2$;46| - |DFLOAT;acsc;2$;47| |DFLOAT;acot;2$;48| - |DFLOAT;asec;2$;49| |DFLOAT;sinh;2$;50| - |DFLOAT;cosh;2$;51| |DFLOAT;tanh;2$;52| - |DFLOAT;csch;2$;53| |DFLOAT;coth;2$;54| - |DFLOAT;sech;2$;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;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) + |DFLOAT;<;2$B;20| |DFLOAT;>;2$B;21| (84 . |not|) + |DFLOAT;<=;2$B;22| |DFLOAT;>=;2$B;23| |DFLOAT;-;2$;24| + |DFLOAT;+;3$;25| |DFLOAT;-;3$;26| |DFLOAT;*;3$;27| + |DFLOAT;*;I2$;28| |DFLOAT;max;3$;29| |DFLOAT;min;3$;30| + |DFLOAT;=;2$B;31| |DFLOAT;/;$I$;32| |DFLOAT;sqrt;2$;33| + |DFLOAT;log10;2$;34| |DFLOAT;**;$I$;35| |DFLOAT;**;3$;36| + |DFLOAT;coerce;I$;37| |DFLOAT;exp;2$;38| + |DFLOAT;log;2$;39| |DFLOAT;sin;2$;41| |DFLOAT;cos;2$;42| + |DFLOAT;tan;2$;43| |DFLOAT;cot;2$;44| |DFLOAT;sec;2$;45| + |DFLOAT;csc;2$;46| |DFLOAT;asin;2$;47| |DFLOAT;acos;2$;48| + |DFLOAT;atan;2$;49| |DFLOAT;acsc;2$;50| + |DFLOAT;acot;2$;51| |DFLOAT;asec;2$;52| + |DFLOAT;sinh;2$;53| |DFLOAT;cosh;2$;54| + |DFLOAT;tanh;2$;55| |DFLOAT;csch;2$;56| + |DFLOAT;coth;2$;57| |DFLOAT;sech;2$;58| + |DFLOAT;asinh;2$;59| |DFLOAT;acosh;2$;60| + |DFLOAT;atanh;2$;61| |DFLOAT;acsch;2$;62| + |DFLOAT;acoth;2$;63| |DFLOAT;asech;2$;64| + |DFLOAT;negative?;$B;66| |DFLOAT;zero?;$B;67| + |DFLOAT;one?;$B;68| (|SingleInteger|) |DFLOAT;hash;$Si;69| + (|Union| $ '"failed") |DFLOAT;recip;$U;70| + |DFLOAT;differentiate;2$;71| + (|DoubleFloatSpecialFunctions|) (89 . |Gamma|) + |DFLOAT;Gamma;2$;72| (94 . |Beta|) |DFLOAT;Beta;3$;73| + |DFLOAT;float;2IPi$;75| (|Float|) (100 . |convert|) + |DFLOAT;convert;$F;77| (|Fraction| 26) (|NonNegativeInteger|) - |DFLOAT;rationalApproximation;$2NniF;84| - |DFLOAT;rationalApproximation;$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 . **) + |DFLOAT;rationalApproximation;$2NniF;87| + |DFLOAT;rationalApproximation;$NniF;78| (105 . |Zero|) + |DFLOAT;abs;2$;85| |DFLOAT;atan;3$;79| (109 . |One|) + |DFLOAT;retract;$F;80| (|Union| 116 '"failed") + |DFLOAT;retractIfCan;$U;81| |DFLOAT;retract;$I;82| + (|Union| 26 '"failed") |DFLOAT;retractIfCan;$U;83| + |DFLOAT;sign;$I;84| (113 . *) (119 . **) (125 . |Zero|) + (129 . |Zero|) (133 . <) (139 . -) (144 . **) (150 . <) + (156 . **) (|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| $) (|List| $) (|Union| 153 '"failed") + (162 . |divide|) (168 . =) (174 . /) (180 . |abs|) + (185 . *) (191 . |coerce|) (196 . |zero?|) + (201 . |negative?|) (206 . |one?|) (211 . |numer|) + (216 . |denom|) (221 . |odd?|) |DFLOAT;**;$F$;88| + (|PatternMatchResult| 113 $) (|Pattern| 113) + (|Factored| $) (|List| $) (|Union| 157 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 156 '"failed") - (|Record| (|:| |coef| 153) (|:| |generator| $)) + (|Union| 160 '"failed") + (|Record| (|:| |coef| 157) (|:| |generator| $)) (|SparseUnivariatePolynomial| $) (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $))) - '#(~= 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 |before?| 709 |base| 715 |atanh| 719 |atan| - 724 |associates?| 735 |asinh| 741 |asin| 746 |asech| 751 - |asec| 756 |acsch| 761 |acsc| 766 |acoth| 771 |acot| 776 - |acosh| 781 |acos| 786 |abs| 791 |Zero| 796 |One| 800 - |OMwrite| 804 |Gamma| 828 D 833 |Beta| 844 >= 850 > 856 = - 862 <= 868 < 874 / 880 - 892 + 903 ** 909 * 939) + '#(~= 226 |zero?| 232 |wholePart| 237 |unitNormal| 242 + |unitCanonical| 247 |unit?| 252 |truncate| 257 |tanh| 262 + |tan| 267 |subtractIfCan| 272 |squareFreePart| 278 + |squareFree| 283 |sqrt| 288 |sizeLess?| 293 |sinh| 299 + |sin| 304 |sign| 309 |sech| 314 |sec| 319 |sample| 324 + |round| 328 |retractIfCan| 333 |retract| 343 |rem| 353 + |recip| 359 |rationalApproximation| 364 |quo| 377 + |principalIdeal| 383 |prime?| 388 |precision| 393 + |positive?| 397 |pi| 402 |patternMatch| 406 |order| 413 + |one?| 418 |nthRoot| 423 |norm| 429 |negative?| 434 + |multiEuclidean| 439 |min| 445 |max| 455 |mantissa| 465 + |log2| 470 |log10| 475 |log| 480 |lcm| 485 |latex| 496 + |inv| 501 |hash| 506 |gcdPolynomial| 511 |gcd| 517 + |fractionPart| 528 |floor| 533 |float| 538 |factor| 551 + |extendedEuclidean| 556 |exquo| 569 |expressIdealMember| + 575 |exponent| 581 |exp1| 586 |exp| 590 |euclideanSize| + 595 |divide| 600 |digits| 606 |differentiate| 610 |csch| + 621 |csc| 626 |coth| 631 |cot| 636 |cosh| 641 |cos| 646 + |convert| 651 |coerce| 671 |characteristic| 701 |ceiling| + 705 |bits| 710 |before?| 714 |base| 720 |atanh| 724 |atan| + 729 |associates?| 740 |asinh| 746 |asin| 751 |asech| 756 + |asec| 761 |acsch| 766 |acsc| 771 |acoth| 776 |acot| 781 + |acosh| 786 |acos| 791 |abs| 796 |Zero| 801 |One| 805 + |OMwrite| 809 |Gamma| 833 D 838 |Beta| 849 >= 855 > 861 = + 867 <= 873 < 879 / 885 - 897 + 908 ** 914 * 944) '((|approximate| . 0) (|canonicalsClosed| . 0) (|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0) ((|commutative| "*") . 0) (|rightUnitary| . 0) @@ -1058,14 +1080,14 @@ (|PrincipalIdealDomain|) (|UniqueFactorizationDomain|) (|GcdDomain|) (|DivisionRing|) - (|IntegralDomain|) (|Algebra| 112) + (|IntegralDomain|) (|Algebra| 116) (|Algebra| $$) (|DifferentialRing|) (|CharacteristicZero|) (|OrderedRing|) - (|Module| 112) (|EntireRing|) + (|Module| 116) (|EntireRing|) (|CommutativeRing|) (|Module| $$) - (|BiModule| 112 112) (|BiModule| $$ $$) + (|BiModule| 116 116) (|BiModule| $$ $$) (|Ring|) (|OrderedAbelianGroup|) - (|RightModule| 112) (|LeftModule| 112) + (|RightModule| 116) (|LeftModule| 116) (|LeftModule| $$) (|Rng|) (|RightModule| $$) (|OrderedCancellationAbelianMonoid|) @@ -1073,17 +1095,17 @@ (|OrderedAbelianMonoid|) (|CancellationAbelianMonoid|) (|OrderedAbelianSemiGroup|) - (|LinearSet| 112) (|LinearSet| $$) + (|LinearSet| 116) (|LinearSet| $$) (|AbelianMonoid|) (|Monoid|) - (|PatternMatchable| 109) (|OrderedSet|) - (|LeftLinearSet| 112) - (|RightLinearSet| 112) + (|PatternMatchable| 113) (|OrderedSet|) + (|LeftLinearSet| 116) + (|RightLinearSet| 116) (|LeftLinearSet| $$) (|RightLinearSet| $$) (|AbelianSemiGroup|) (|SemiGroup|) (|LeftLinearSet| 26) (|TranscendentalFunctionCategory|) - (|RetractableTo| 112) + (|RetractableTo| 116) (|RetractableTo| 26) (|RealConstant|) (|SetCategory|) (|ConvertibleTo| 51) (|ElementaryFunctionCategory|) @@ -1091,79 +1113,79 @@ (|HyperbolicFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|TrigonometricFunctionCategory|) - (|OpenMath|) (|ConvertibleTo| 151) + (|OpenMath|) (|ConvertibleTo| 155) (|RadicalCategory|) - (|ConvertibleTo| 109) + (|ConvertibleTo| 113) (|ConvertibleTo| 13) - (|CoercibleFrom| 112) + (|CoercibleFrom| 116) (|CoercibleFrom| $$) (|CoercibleFrom| 26) (|BasicType|) (|CoercibleTo| 48)) - (|makeByteWordVec2| 160 + (|makeByteWordVec2| 164 '(0 6 0 7 2 9 0 8 6 10 1 9 11 0 12 2 9 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 0 158 153 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 - 154 153 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 1 0 0 153 1 - 2 0 0 0 0 1 1 0 8 0 1 1 0 0 0 1 1 0 - 98 0 99 2 0 159 159 159 1 1 0 0 153 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 2 0 155 0 0 1 3 0 157 0 0 0 1 2 0 - 100 0 0 1 2 0 154 153 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 2 - 0 19 0 0 1 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))))) + 49 1 51 0 13 52 1 19 0 0 56 1 107 13 + 13 108 2 107 13 13 13 110 1 113 0 13 + 114 0 26 0 120 0 24 0 123 2 26 0 26 0 + 131 2 26 0 0 117 132 0 116 0 133 0 + 117 0 134 2 26 19 0 0 135 1 26 0 0 + 136 2 24 0 0 117 137 2 117 19 0 0 138 + 2 117 0 0 117 139 2 26 140 0 0 141 2 + 26 19 0 0 142 2 116 0 26 26 143 1 26 + 0 0 144 2 26 0 117 0 145 1 116 0 26 + 146 1 116 19 0 147 1 116 19 0 148 1 + 116 19 0 149 1 116 26 0 150 1 116 26 + 0 151 1 26 19 0 152 2 0 19 0 0 1 1 0 + 19 0 100 1 0 26 0 36 1 0 164 0 1 1 0 + 0 0 1 1 0 19 0 1 1 0 0 0 1 1 0 0 0 89 + 1 0 0 0 77 2 0 104 0 0 1 1 0 0 0 1 1 + 0 156 0 1 1 0 0 0 68 2 0 19 0 0 1 1 0 + 0 0 87 1 0 0 0 75 1 0 26 0 130 1 0 0 + 0 92 1 0 0 0 79 0 0 0 1 1 0 0 0 1 1 0 + 125 0 126 1 0 128 0 129 1 0 116 0 124 + 1 0 26 0 127 2 0 0 0 0 1 1 0 104 0 + 105 2 0 116 0 117 119 3 0 116 0 117 + 117 118 2 0 0 0 0 1 1 0 162 157 1 1 0 + 19 0 1 0 0 24 29 1 0 19 0 1 0 0 0 47 + 3 0 154 0 155 154 1 1 0 26 0 43 1 0 + 19 0 101 2 0 0 0 26 1 1 0 0 0 1 1 0 + 19 0 99 2 0 158 157 0 1 0 0 0 39 2 0 + 0 0 0 65 0 0 0 38 2 0 0 0 0 64 1 0 26 + 0 27 1 0 0 0 34 1 0 0 0 69 1 0 0 0 74 + 1 0 0 157 1 2 0 0 0 0 1 1 0 8 0 1 1 0 + 0 0 1 1 0 102 0 103 2 0 163 163 163 1 + 1 0 0 157 1 2 0 0 0 0 1 1 0 0 0 1 1 0 + 0 0 1 3 0 0 26 26 24 112 2 0 0 26 26 + 1 1 0 156 0 1 2 0 159 0 0 1 3 0 161 0 + 0 0 1 2 0 104 0 0 1 2 0 158 157 0 1 1 + 0 26 0 28 0 0 0 46 1 0 0 0 73 1 0 117 + 0 1 2 0 140 0 0 1 0 0 24 1 1 0 0 0 + 106 2 0 0 0 117 1 1 0 0 0 90 1 0 0 0 + 80 1 0 0 0 91 1 0 0 0 78 1 0 0 0 88 1 + 0 0 0 76 1 0 51 0 53 1 0 155 0 1 1 0 + 113 0 115 1 0 13 0 14 1 0 0 116 1 1 0 + 0 26 72 1 0 0 116 1 1 0 0 0 1 1 0 0 + 26 72 1 0 48 0 50 0 0 117 1 1 0 0 0 1 + 0 0 24 37 2 0 19 0 0 1 0 0 24 25 1 0 + 0 0 95 2 0 0 0 0 122 1 0 0 0 83 2 0 + 19 0 0 1 1 0 0 0 93 1 0 0 0 81 1 0 0 + 0 98 1 0 0 0 86 1 0 0 0 96 1 0 0 0 84 + 1 0 0 0 97 1 0 0 0 85 1 0 0 0 94 1 0 + 0 0 82 1 0 0 0 121 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 0 109 1 0 0 + 0 1 2 0 0 0 117 1 2 0 0 0 0 111 2 0 + 19 0 0 58 2 0 19 0 0 55 2 0 19 0 0 66 + 2 0 19 0 0 57 2 0 19 0 0 54 2 0 0 0 + 26 67 2 0 0 0 0 45 2 0 0 0 0 61 1 0 0 + 0 59 2 0 0 0 0 60 2 0 0 0 0 71 2 0 0 + 0 116 153 2 0 0 0 26 70 2 0 0 0 117 1 + 2 0 0 0 24 1 2 0 0 116 0 1 2 0 0 0 + 116 1 2 0 0 0 0 62 2 0 0 26 0 63 2 0 + 0 117 0 1 2 0 0 24 0 35))))) '|lookupComplete|)) (MAKEPROP '|DoubleFloat| 'NILADIC T) diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp index 038285e5..6ec84ec3 100644 --- a/src/algebra/strap/INT.lsp +++ b/src/algebra/strap/INT.lsp @@ -149,87 +149,98 @@ (PUT '|INT;<;2$B;35| '|SPADreplace| '<) +(DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Boolean|) + |INT;>;2$B;36|)) + +(PUT '|INT;>;2$B;36| '|SPADreplace| '>) + +(DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Boolean|) + |INT;<=;2$B;37|)) + +(DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Boolean|) + |INT;>=;2$B;38|)) + (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Integer|) - |INT;-;2$;36|)) + |INT;-;2$;39|)) -(PUT '|INT;-;2$;36| '|SPADreplace| '-) +(PUT '|INT;-;2$;39| '|SPADreplace| '-) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;+;3$;37|)) + |INT;+;3$;40|)) -(PUT '|INT;+;3$;37| '|SPADreplace| '+) +(PUT '|INT;+;3$;40| '|SPADreplace| '+) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;-;3$;38|)) + |INT;-;3$;41|)) -(PUT '|INT;-;3$;38| '|SPADreplace| '-) +(PUT '|INT;-;3$;41| '|SPADreplace| '-) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;*;3$;39|)) + |INT;*;3$;42|)) -(PUT '|INT;*;3$;39| '|SPADreplace| '*) +(PUT '|INT;*;3$;42| '|SPADreplace| '*) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;*;3$;40|)) + |INT;*;3$;43|)) -(PUT '|INT;*;3$;40| '|SPADreplace| '*) +(PUT '|INT;*;3$;43| '|SPADreplace| '*) (DECLAIM (FTYPE (FUNCTION (|%Integer| (|%IntegerSection| 0) |%Shell|) |%Integer|) - |INT;**;$Nni$;41|)) + |INT;**;$Nni$;44|)) -(PUT '|INT;**;$Nni$;41| '|SPADreplace| 'EXPT) +(PUT '|INT;**;$Nni$;44| '|SPADreplace| 'EXPT) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Boolean|) - |INT;odd?;$B;42|)) + |INT;odd?;$B;45|)) -(PUT '|INT;odd?;$B;42| '|SPADreplace| 'ODDP) +(PUT '|INT;odd?;$B;45| '|SPADreplace| 'ODDP) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;max;3$;43|)) + |INT;max;3$;46|)) -(PUT '|INT;max;3$;43| '|SPADreplace| 'MAX) +(PUT '|INT;max;3$;46| '|SPADreplace| 'MAX) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;min;3$;44|)) + |INT;min;3$;47|)) -(PUT '|INT;min;3$;44| '|SPADreplace| 'MIN) +(PUT '|INT;min;3$;47| '|SPADreplace| 'MIN) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Pair|) - |INT;divide;2$R;45|)) + |INT;divide;2$R;48|)) -(PUT '|INT;divide;2$R;45| '|SPADreplace| 'DIVIDE2) +(PUT '|INT;divide;2$R;48| '|SPADreplace| 'DIVIDE2) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;quo;3$;46|)) + |INT;quo;3$;49|)) -(PUT '|INT;quo;3$;46| '|SPADreplace| 'QUOTIENT2) +(PUT '|INT;quo;3$;49| '|SPADreplace| 'QUOTIENT2) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;rem;3$;47|)) + |INT;rem;3$;50|)) -(PUT '|INT;rem;3$;47| '|SPADreplace| 'REMAINDER2) +(PUT '|INT;rem;3$;50| '|SPADreplace| 'REMAINDER2) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;shift;3$;48|)) + |INT;shift;3$;51|)) -(PUT '|INT;shift;3$;48| '|SPADreplace| 'ASH) +(PUT '|INT;shift;3$;51| '|SPADreplace| 'ASH) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Pair|) - |INT;recip;$U;49|)) + |INT;recip;$U;52|)) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|) - |INT;gcd;3$;50|)) + |INT;gcd;3$;53|)) -(PUT '|INT;gcd;3$;50| '|SPADreplace| 'GCD) +(PUT '|INT;gcd;3$;53| '|SPADreplace| 'GCD) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Shell|) - |INT;unitNormal;$R;51|)) + |INT;unitNormal;$R;54|)) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Integer|) - |INT;unitCanonical;2$;52|)) + |INT;unitCanonical;2$;55|)) -(PUT '|INT;unitCanonical;2$;52| '|SPADreplace| 'ABS) +(PUT '|INT;unitCanonical;2$;55| '|SPADreplace| 'ABS) (DECLAIM (FTYPE (FUNCTION (|%List| |%Thing| |%Shell|) |%Pair|) |INT;solveLinearPolynomialEquation|)) @@ -244,7 +255,7 @@ |INT;factorSquareFreePolynomial|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) - |INT;gcdPolynomial;3Sup;57|)) + |INT;gcdPolynomial;3Sup;60|)) (DEFUN |INT;writeOMInt| (|dev| |x| $) (SEQ (COND @@ -398,107 +409,113 @@ (DEFUN |INT;<;2$B;35| (|x| |y| $) (DECLARE (IGNORE $)) (< |x| |y|)) -(DEFUN |INT;-;2$;36| (|x| $) (DECLARE (IGNORE $)) (- |x|)) +(DEFUN |INT;>;2$B;36| (|x| |y| $) (DECLARE (IGNORE $)) (> |x| |y|)) + +(DEFUN |INT;<=;2$B;37| (|x| |y| $) (NOT (> |x| |y|))) + +(DEFUN |INT;>=;2$B;38| (|x| |y| $) (NOT (< |x| |y|))) + +(DEFUN |INT;-;2$;39| (|x| $) (DECLARE (IGNORE $)) (- |x|)) -(DEFUN |INT;+;3$;37| (|x| |y| $) (DECLARE (IGNORE $)) (+ |x| |y|)) +(DEFUN |INT;+;3$;40| (|x| |y| $) (DECLARE (IGNORE $)) (+ |x| |y|)) -(DEFUN |INT;-;3$;38| (|x| |y| $) (DECLARE (IGNORE $)) (- |x| |y|)) +(DEFUN |INT;-;3$;41| (|x| |y| $) (DECLARE (IGNORE $)) (- |x| |y|)) -(DEFUN |INT;*;3$;39| (|x| |y| $) (DECLARE (IGNORE $)) (* |x| |y|)) +(DEFUN |INT;*;3$;42| (|x| |y| $) (DECLARE (IGNORE $)) (* |x| |y|)) -(DEFUN |INT;*;3$;40| (|m| |y| $) (DECLARE (IGNORE $)) (* |m| |y|)) +(DEFUN |INT;*;3$;43| (|m| |y| $) (DECLARE (IGNORE $)) (* |m| |y|)) -(DEFUN |INT;**;$Nni$;41| (|x| |n| $) +(DEFUN |INT;**;$Nni$;44| (|x| |n| $) (DECLARE (IGNORE $)) (EXPT |x| |n|)) -(DEFUN |INT;odd?;$B;42| (|x| $) (DECLARE (IGNORE $)) (ODDP |x|)) +(DEFUN |INT;odd?;$B;45| (|x| $) (DECLARE (IGNORE $)) (ODDP |x|)) -(DEFUN |INT;max;3$;43| (|x| |y| $) (DECLARE (IGNORE $)) (MAX |x| |y|)) +(DEFUN |INT;max;3$;46| (|x| |y| $) (DECLARE (IGNORE $)) (MAX |x| |y|)) -(DEFUN |INT;min;3$;44| (|x| |y| $) (DECLARE (IGNORE $)) (MIN |x| |y|)) +(DEFUN |INT;min;3$;47| (|x| |y| $) (DECLARE (IGNORE $)) (MIN |x| |y|)) -(DEFUN |INT;divide;2$R;45| (|x| |y| $) +(DEFUN |INT;divide;2$R;48| (|x| |y| $) (DECLARE (IGNORE $)) (DIVIDE2 |x| |y|)) -(DEFUN |INT;quo;3$;46| (|x| |y| $) +(DEFUN |INT;quo;3$;49| (|x| |y| $) (DECLARE (IGNORE $)) (QUOTIENT2 |x| |y|)) -(DEFUN |INT;rem;3$;47| (|x| |y| $) +(DEFUN |INT;rem;3$;50| (|x| |y| $) (DECLARE (IGNORE $)) (REMAINDER2 |x| |y|)) -(DEFUN |INT;shift;3$;48| (|x| |y| $) +(DEFUN |INT;shift;3$;51| (|x| |y| $) (DECLARE (IGNORE $)) (ASH |x| |y|)) -(DEFUN |INT;recip;$U;49| (|x| $) +(DEFUN |INT;recip;$U;52| (|x| $) (COND ((OR (EQL |x| 1) (EQL |x| -1)) (CONS 0 |x|)) ('T (CONS 1 "failed")))) -(DEFUN |INT;gcd;3$;50| (|x| |y| $) (DECLARE (IGNORE $)) (GCD |x| |y|)) +(DEFUN |INT;gcd;3$;53| (|x| |y| $) (DECLARE (IGNORE $)) (GCD |x| |y|)) -(DEFUN |INT;unitNormal;$R;51| (|x| $) +(DEFUN |INT;unitNormal;$R;54| (|x| $) (COND ((< |x| 0) (VECTOR -1 (- |x|) -1)) ('T (VECTOR 1 |x| 1)))) -(DEFUN |INT;unitCanonical;2$;52| (|x| $) +(DEFUN |INT;unitCanonical;2$;55| (|x| $) (DECLARE (IGNORE $)) (ABS |x|)) (DEFUN |INT;solveLinearPolynomialEquation| (|lp| |p| $) - (SPADCALL |lp| |p| (|getShellEntry| $ 99))) + (SPADCALL |lp| |p| (|getShellEntry| $ 103))) (DEFUN |INT;squareFreePolynomial| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 103))) + (SPADCALL |p| (|getShellEntry| $ 107))) (DEFUN |INT;factorPolynomial| (|p| $) - (PROG (|pp| #0=#:G1498) + (PROG (|pp| #0=#:G1501) (RETURN - (SEQ (LETT |pp| (SPADCALL |p| (|getShellEntry| $ 104)) + (SEQ (LETT |pp| (SPADCALL |p| (|getShellEntry| $ 108)) |INT;factorPolynomial|) (EXIT (COND - ((EQL (SPADCALL |pp| (|getShellEntry| $ 105)) - (SPADCALL |p| (|getShellEntry| $ 105))) - (SPADCALL |p| (|getShellEntry| $ 107))) + ((EQL (SPADCALL |pp| (|getShellEntry| $ 109)) + (SPADCALL |p| (|getShellEntry| $ 109))) + (SPADCALL |p| (|getShellEntry| $ 111))) ('T - (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 107)) + (SPADCALL (SPADCALL |pp| (|getShellEntry| $ 111)) (SPADCALL (CONS #'|INT;factorPolynomial!0| $) (SPADCALL (PROG2 (LETT #0# (SPADCALL (SPADCALL |p| - (|getShellEntry| $ 105)) + (|getShellEntry| $ 109)) (SPADCALL |pp| - (|getShellEntry| $ 105)) - (|getShellEntry| $ 109)) + (|getShellEntry| $ 109)) + (|getShellEntry| $ 113)) |INT;factorPolynomial|) (QCDR #0#) (|check-union| (QEQCAR #0# 0) $ #0#)) - (|getShellEntry| $ 111)) - (|getShellEntry| $ 115)) - (|getShellEntry| $ 117))))))))) + (|getShellEntry| $ 115)) + (|getShellEntry| $ 119)) + (|getShellEntry| $ 121))))))))) (DEFUN |INT;factorPolynomial!0| (|#1| $) - (SPADCALL |#1| (|getShellEntry| $ 108))) + (SPADCALL |#1| (|getShellEntry| $ 112))) (DEFUN |INT;factorSquareFreePolynomial| (|p| $) - (SPADCALL |p| (|getShellEntry| $ 118))) + (SPADCALL |p| (|getShellEntry| $ 122))) -(DEFUN |INT;gcdPolynomial;3Sup;57| (|p| |q| $) +(DEFUN |INT;gcdPolynomial;3Sup;60| (|p| |q| $) (COND - ((SPADCALL |p| (|getShellEntry| $ 119)) - (SPADCALL |q| (|getShellEntry| $ 120))) - ((SPADCALL |q| (|getShellEntry| $ 119)) - (SPADCALL |p| (|getShellEntry| $ 120))) - ('T (SPADCALL (LIST |p| |q|) (|getShellEntry| $ 123))))) + ((SPADCALL |p| (|getShellEntry| $ 123)) + (SPADCALL |q| (|getShellEntry| $ 124))) + ((SPADCALL |q| (|getShellEntry| $ 123)) + (SPADCALL |p| (|getShellEntry| $ 124))) + ('T (SPADCALL (LIST |p| |q|) (|getShellEntry| $ 127))))) (DEFUN |Integer| () (PROG () (RETURN - (PROG (#0=#:G1523) + (PROG (#0=#:G1526) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|Integer|) |Integer|) @@ -517,15 +534,15 @@ (RETURN (PROGN (LETT |dv$| '(|Integer|) . #0=(|Integer|)) - (LETT $ (|newShell| 138) . #0#) + (LETT $ (|newShell| 142) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) (|haddProp| |$ConstructorCache| '|Integer| NIL (CONS 1 $)) (|stuffDomainSlots| $) - (|setShellEntry| $ 80 + (|setShellEntry| $ 84 (|setShellEntry| $ 52 - (CONS (|dispatchFunction| |INT;*;3$;40|) $))) + (CONS (|dispatchFunction| |INT;*;3$;43|) $))) $)))) (MAKEPROP '|Integer| '|infovec| @@ -535,7 +552,7 @@ (|NonNegativeInteger|) (0 . |Zero|) (|Boolean|) |INT;<;2$B;35| (|Void|) (|OpenMathDevice|) (4 . |OMputApp|) (|String|) (9 . |OMputSymbol|) - |INT;-;2$;36| (|Integer|) (16 . |OMputInteger|) + |INT;-;2$;39| (|Integer|) (16 . |OMputInteger|) (22 . |OMputEndApp|) (|OpenMathEncoding|) (27 . |OMencodingXML|) (31 . |OMopenString|) (37 . |OMputObject|) (42 . |OMputEndObject|) @@ -545,12 +562,12 @@ (CONS IDENTITY (FUNCALL (|dispatchFunction| |INT;One;$;9|) $)) (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| + |INT;base;$;10| |INT;copy;2$;11| |INT;+;3$;40| + |INT;inc;2$;12| |INT;-;3$;41| |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;addmod;4$;20| |INT;submod;4$;21| NIL |INT;rem;3$;50| |INT;mulmod;4$;22| (|Float|) (61 . |coerce|) |INT;convert;$F;23| (|DoubleFloat|) (66 . |coerce|) |INT;convert;$Df;24| (|InputForm|) (71 . |convert|) @@ -560,61 +577,63 @@ |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| NIL |INT;**;$Nni$;41| - |INT;odd?;$B;42| |INT;max;3$;43| |INT;min;3$;44| + |INT;random;$;32| |INT;random;2$;33| |INT;>;2$B;36| + (93 . |not|) |INT;<=;2$B;37| |INT;>=;2$B;38| NIL + |INT;**;$Nni$;44| |INT;odd?;$B;45| |INT;max;3$;46| + |INT;min;3$;47| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - |INT;divide;2$R;45| |INT;quo;3$;46| |INT;shift;3$;48| - (|Union| $ '"failed") |INT;recip;$U;49| |INT;gcd;3$;50| + |INT;divide;2$R;48| |INT;quo;3$;49| |INT;shift;3$;51| + (|Union| $ '"failed") |INT;recip;$U;52| |INT;gcd;3$;53| (|Record| (|:| |unit| $) (|:| |canonical| $) - (|:| |associate| $)) - |INT;unitNormal;$R;51| |INT;unitCanonical;2$;52| - (|SparseUnivariatePolynomial| 17) (|List| 95) - (|Union| 96 '"failed") + (|:| |associate| $)) + |INT;unitNormal;$R;54| |INT;unitCanonical;2$;55| + (|SparseUnivariatePolynomial| 17) (|List| 99) + (|Union| 100 '"failed") (|IntegerSolveLinearPolynomialEquation|) - (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|) + (98 . |solveLinearPolynomialEquation|) + (|SparseUnivariatePolynomial| $$) (|Factored| 104) + (|UnivariatePolynomialSquareFree| $$ 104) + (104 . |squareFree|) (109 . |primitivePart|) + (114 . |leadingCoefficient|) (|GaloisGroupFactorizer| 104) + (119 . |factor|) (124 . |coerce|) (129 . |exquo|) + (|Factored| $) (135 . |factor|) (|Mapping| 104 $$) + (|Factored| $$) (|FactoredFunctions2| $$ 104) + (140 . |map|) (|FactoredFunctionUtilities| 104) + (146 . |mergeFactors|) (152 . |factorSquareFree|) + (157 . |zero?|) (162 . |unitCanonical|) (|List| 104) + (|HeuGcd| 104) (167 . |gcd|) (|SparseUnivariatePolynomial| $) - |INT;gcdPolynomial;3Sup;57| (|Fraction| 17) - (|Union| 126 '"failed") (|PatternMatchResult| 17 $) + |INT;gcdPolynomial;3Sup;60| (|Fraction| 17) + (|Union| 130 '"failed") (|PatternMatchResult| 17 $) (|Pattern| 17) (|Union| 17 '"failed") (|List| $) - (|Union| 131 '"failed") - (|Record| (|:| |coef| 131) (|:| |generator| $)) + (|Union| 135 '"failed") + (|Record| (|:| |coef| 135) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 134 '"failed") + (|Union| 138 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|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 |before?| 592 |base| 598 - |associates?| 602 |addmod| 608 |abs| 615 |Zero| 620 |One| - 624 |OMwrite| 628 D 652 >= 663 > 669 = 675 <= 681 < 687 - - 693 + 704 ** 710 * 722) + '#(~= 172 |zero?| 178 |unitNormal| 183 |unitCanonical| 188 + |unit?| 193 |symmetricRemainder| 198 |subtractIfCan| 204 + |submod| 210 |squareFreePart| 217 |squareFree| 222 + |sizeLess?| 227 |sign| 233 |shift| 238 |sample| 244 + |retractIfCan| 248 |retract| 253 |rem| 258 |reducedSystem| + 264 |recip| 275 |rationalIfCan| 280 |rational?| 285 + |rational| 290 |random| 295 |quo| 304 |principalIdeal| 310 + |prime?| 315 |powmod| 320 |positiveRemainder| 327 + |positive?| 333 |permutation| 338 |patternMatch| 344 + |one?| 351 |odd?| 356 |nextItem| 361 |negative?| 366 + |multiEuclidean| 371 |mulmod| 377 |min| 384 |max| 390 + |mask| 396 |length| 401 |lcm| 406 |latex| 417 |invmod| 422 + |init| 428 |inc| 432 |hash| 437 |gcdPolynomial| 442 |gcd| + 448 |factorial| 459 |factor| 464 |extendedEuclidean| 469 + |exquo| 482 |expressIdealMember| 488 |even?| 494 + |euclideanSize| 499 |divide| 504 |differentiate| 510 |dec| + 521 |copy| 526 |convert| 531 |coerce| 561 |characteristic| + 581 |bit?| 585 |binomial| 591 |before?| 597 |base| 603 + |associates?| 607 |addmod| 613 |abs| 620 |Zero| 625 |One| + 629 |OMwrite| 633 D 657 >= 668 > 674 = 680 <= 686 < 692 - + 698 + 709 ** 715 * 727) '((|infinite| . 0) (|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) @@ -667,61 +686,61 @@ (|ConvertibleTo| 55) (|ConvertibleTo| 58) (|CombinatorialFunctionCategory|) - (|ConvertibleTo| 129) + (|ConvertibleTo| 133) (|ConvertibleTo| 61) (|ConvertibleTo| 17) (|CoercibleFrom| $$) (|CoercibleFrom| 17) (|BasicType|) (|CoercibleTo| 44)) - (|makeByteWordVec2| 137 + (|makeByteWordVec2| 141 '(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 0 133 - 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 0 132 131 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 1 0 0 131 1 2 0 - 0 0 0 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 1 0 0 131 1 2 0 0 0 0 91 1 0 - 0 0 1 1 0 110 0 111 3 0 135 0 0 0 1 2 - 0 136 0 0 1 2 0 89 0 0 109 2 0 132 - 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 2 0 9 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 1 0 0 0 16 2 0 0 0 0 39 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))))) + 2 14 0 0 0 67 1 9 0 0 81 2 102 101 + 100 99 103 1 106 105 104 107 1 104 0 + 0 108 1 104 2 0 109 1 110 105 104 111 + 1 104 0 2 112 2 0 93 0 0 113 1 0 114 + 0 115 2 118 105 116 117 119 2 120 105 + 105 105 121 1 110 105 104 122 1 104 9 + 0 123 1 104 0 0 124 1 126 104 125 127 + 2 0 9 0 0 1 1 0 9 0 30 1 0 96 0 97 1 + 0 0 0 98 1 0 9 0 1 2 0 0 0 0 1 2 0 93 + 0 0 1 3 0 0 0 0 0 51 1 0 0 0 1 1 0 + 114 0 1 2 0 9 0 0 1 1 0 17 0 1 2 0 0 + 0 0 92 0 0 0 1 1 0 134 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 93 0 94 1 0 131 0 1 1 0 9 0 + 1 1 0 130 0 1 0 0 0 78 1 0 0 0 79 2 0 + 0 0 0 91 1 0 137 135 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 0 132 0 133 132 1 1 0 9 0 + 34 1 0 9 0 86 1 0 93 0 1 1 0 9 0 43 2 + 0 136 135 0 1 3 0 0 0 0 0 54 2 0 0 0 + 0 88 2 0 0 0 0 87 1 0 0 0 1 1 0 0 0 + 49 1 0 0 135 1 2 0 0 0 0 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 0 128 128 128 129 1 0 0 135 + 1 2 0 0 0 0 95 1 0 0 0 1 1 0 114 0 + 115 3 0 139 0 0 0 1 2 0 140 0 0 1 2 0 + 93 0 0 113 2 0 136 135 0 1 1 0 9 0 1 + 1 0 7 0 1 2 0 89 0 0 90 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 0 133 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 2 0 9 + 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 83 2 0 9 0 0 80 2 0 9 0 0 + 33 2 0 9 0 0 82 2 0 9 0 0 10 1 0 0 0 + 16 2 0 0 0 0 39 2 0 0 0 0 37 2 0 0 0 + 7 85 2 0 0 0 141 1 2 0 0 0 0 52 2 0 0 + 17 0 84 2 0 0 7 0 1 2 0 0 141 0 1))))) '|lookupComplete|)) (MAKEPROP '|Integer| 'NILADIC T) diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp index cf309a77..591a5604 100644 --- a/src/algebra/strap/SINT.lsp +++ b/src/algebra/strap/SINT.lsp @@ -104,154 +104,165 @@ (PUT '|SINT;<;2$B;24| '|SPADreplace| 'QSLESSP) +(DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|) + |SINT;>;2$B;25|)) + +(PUT '|SINT;>;2$B;25| '|SPADreplace| 'QSGREATERP) + +(DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|) + |SINT;<=;2$B;26|)) + +(DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|) + |SINT;>=;2$B;27|)) + (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;inc;2$;25|)) + |SINT;inc;2$;28|)) -(PUT '|SINT;inc;2$;25| '|SPADreplace| 'QSADD1) +(PUT '|SINT;inc;2$;28| '|SPADreplace| 'QSADD1) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;dec;2$;26|)) + |SINT;dec;2$;29|)) -(PUT '|SINT;dec;2$;26| '|SPADreplace| 'QSSUB1) +(PUT '|SINT;dec;2$;29| '|SPADreplace| 'QSSUB1) -(DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) |SINT;-;2$;27|)) +(DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) |SINT;-;2$;30|)) -(PUT '|SINT;-;2$;27| '|SPADreplace| 'QSMINUS) +(PUT '|SINT;-;2$;30| '|SPADreplace| 'QSMINUS) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;+;3$;28|)) + |SINT;+;3$;31|)) -(PUT '|SINT;+;3$;28| '|SPADreplace| 'QSPLUS) +(PUT '|SINT;+;3$;31| '|SPADreplace| 'QSPLUS) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;-;3$;29|)) + |SINT;-;3$;32|)) -(PUT '|SINT;-;3$;29| '|SPADreplace| 'QSDIFFERENCE) +(PUT '|SINT;-;3$;32| '|SPADreplace| 'QSDIFFERENCE) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;*;3$;30|)) + |SINT;*;3$;33|)) -(PUT '|SINT;*;3$;30| '|SPADreplace| 'QSTIMES) +(PUT '|SINT;*;3$;33| '|SPADreplace| 'QSTIMES) (DECLAIM (FTYPE (FUNCTION (|%Short| (|%IntegerSection| 0) |%Shell|) |%Short|) - |SINT;**;$Nni$;31|)) + |SINT;**;$Nni$;34|)) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;quo;3$;32|)) + |SINT;quo;3$;35|)) -(PUT '|SINT;quo;3$;32| '|SPADreplace| 'QSQUOTIENT) +(PUT '|SINT;quo;3$;35| '|SPADreplace| 'QSQUOTIENT) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;rem;3$;33|)) + |SINT;rem;3$;36|)) -(PUT '|SINT;rem;3$;33| '|SPADreplace| 'QSREMAINDER) +(PUT '|SINT;rem;3$;36| '|SPADreplace| 'QSREMAINDER) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Pair|) - |SINT;divide;2$R;34|)) + |SINT;divide;2$R;37|)) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;gcd;3$;35|)) + |SINT;gcd;3$;38|)) -(PUT '|SINT;gcd;3$;35| '|SPADreplace| 'GCD) +(PUT '|SINT;gcd;3$;38| '|SPADreplace| 'GCD) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;abs;2$;36|)) + |SINT;abs;2$;39|)) -(PUT '|SINT;abs;2$;36| '|SPADreplace| 'QSABSVAL) +(PUT '|SINT;abs;2$;39| '|SPADreplace| 'QSABSVAL) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|) - |SINT;odd?;$B;37|)) + |SINT;odd?;$B;40|)) -(PUT '|SINT;odd?;$B;37| '|SPADreplace| 'QSODDP) +(PUT '|SINT;odd?;$B;40| '|SPADreplace| 'QSODDP) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|) - |SINT;zero?;$B;38|)) + |SINT;zero?;$B;41|)) -(PUT '|SINT;zero?;$B;38| '|SPADreplace| 'QSZEROP) +(PUT '|SINT;zero?;$B;41| '|SPADreplace| 'QSZEROP) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|) - |SINT;one?;$B;39|)) + |SINT;one?;$B;42|)) -(PUT '|SINT;one?;$B;39| '|SPADreplace| '(XLAM (|x|) (EQL |x| 1))) +(PUT '|SINT;one?;$B;42| '|SPADreplace| '(XLAM (|x|) (EQL |x| 1))) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;max;3$;40|)) + |SINT;max;3$;43|)) -(PUT '|SINT;max;3$;40| '|SPADreplace| 'QSMAX) +(PUT '|SINT;max;3$;43| '|SPADreplace| 'QSMAX) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;min;3$;41|)) + |SINT;min;3$;44|)) -(PUT '|SINT;min;3$;41| '|SPADreplace| 'QSMIN) +(PUT '|SINT;min;3$;44| '|SPADreplace| 'QSMIN) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;hash;2$;42|)) + |SINT;hash;2$;45|)) -(PUT '|SINT;hash;2$;42| '|SPADreplace| 'HASHEQ) +(PUT '|SINT;hash;2$;45| '|SPADreplace| 'HASHEQ) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;length;2$;43|)) + |SINT;length;2$;46|)) -(PUT '|SINT;length;2$;43| '|SPADreplace| 'INTEGER-LENGTH) +(PUT '|SINT;length;2$;46| '|SPADreplace| 'INTEGER-LENGTH) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;shift;3$;44|)) + |SINT;shift;3$;47|)) -(PUT '|SINT;shift;3$;44| '|SPADreplace| 'QSLEFTSHIFT) +(PUT '|SINT;shift;3$;47| '|SPADreplace| 'QSLEFTSHIFT) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|) |%Short|) - |SINT;mulmod;4$;45|)) + |SINT;mulmod;4$;48|)) -(PUT '|SINT;mulmod;4$;45| '|SPADreplace| 'QSMULTMOD) +(PUT '|SINT;mulmod;4$;48| '|SPADreplace| 'QSMULTMOD) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|) |%Short|) - |SINT;addmod;4$;46|)) + |SINT;addmod;4$;49|)) -(PUT '|SINT;addmod;4$;46| '|SPADreplace| 'QSADDMOD) +(PUT '|SINT;addmod;4$;49| '|SPADreplace| 'QSADDMOD) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|) |%Short|) - |SINT;submod;4$;47|)) + |SINT;submod;4$;50|)) -(PUT '|SINT;submod;4$;47| '|SPADreplace| 'QSDIFMOD) +(PUT '|SINT;submod;4$;50| '|SPADreplace| 'QSDIFMOD) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|) - |SINT;negative?;$B;48|)) + |SINT;negative?;$B;51|)) -(PUT '|SINT;negative?;$B;48| '|SPADreplace| 'QSMINUSP) +(PUT '|SINT;negative?;$B;51| '|SPADreplace| 'QSMINUSP) (DECLAIM (FTYPE (FUNCTION (|%Shell|) (|%IntegerSection| 0)) - |SINT;size;Nni;49|)) + |SINT;size;Nni;52|)) (DECLAIM (FTYPE (FUNCTION ((|%IntegerSection| 1) |%Shell|) |%Short|) - |SINT;index;Pi$;50|)) + |SINT;index;Pi$;53|)) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) (|%IntegerSection| 1)) - |SINT;lookup;$Pi;51|)) + |SINT;lookup;$Pi;54|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| (|%Vector| *) |%Shell|) |%Pair|) - |SINT;reducedSystem;MVR;52|)) + |SINT;reducedSystem;MVR;55|)) -(PUT '|SINT;reducedSystem;MVR;52| '|SPADreplace| 'CONS) +(PUT '|SINT;reducedSystem;MVR;55| '|SPADreplace| 'CONS) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|) - |SINT;positiveRemainder;3$;53|)) + |SINT;positiveRemainder;3$;56|)) (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Short|) - |SINT;coerce;I$;54|)) + |SINT;coerce;I$;57|)) -(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Short|) |SINT;random;$;55|)) +(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Short|) |SINT;random;$;58|)) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) - |SINT;random;2$;56|)) + |SINT;random;2$;59|)) -(PUT '|SINT;random;2$;56| '|SPADreplace| 'RANDOM) +(PUT '|SINT;random;2$;59| '|SPADreplace| 'RANDOM) (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Shell|) - |SINT;unitNormal;$R;57|)) + |SINT;unitNormal;$R;60|)) (DEFUN |SINT;writeOMSingleInt| (|dev| |x| $) (SEQ (COND @@ -358,105 +369,113 @@ (DECLARE (IGNORE $)) (QSLESSP |x| |y|)) -(DEFUN |SINT;inc;2$;25| (|x| $) (DECLARE (IGNORE $)) (QSADD1 |x|)) +(DEFUN |SINT;>;2$B;25| (|x| |y| $) + (DECLARE (IGNORE $)) + (QSGREATERP |x| |y|)) + +(DEFUN |SINT;<=;2$B;26| (|x| |y| $) (NOT (> |x| |y|))) + +(DEFUN |SINT;>=;2$B;27| (|x| |y| $) (NOT (< |x| |y|))) -(DEFUN |SINT;dec;2$;26| (|x| $) (DECLARE (IGNORE $)) (QSSUB1 |x|)) +(DEFUN |SINT;inc;2$;28| (|x| $) (DECLARE (IGNORE $)) (QSADD1 |x|)) -(DEFUN |SINT;-;2$;27| (|x| $) (DECLARE (IGNORE $)) (QSMINUS |x|)) +(DEFUN |SINT;dec;2$;29| (|x| $) (DECLARE (IGNORE $)) (QSSUB1 |x|)) -(DEFUN |SINT;+;3$;28| (|x| |y| $) +(DEFUN |SINT;-;2$;30| (|x| $) (DECLARE (IGNORE $)) (QSMINUS |x|)) + +(DEFUN |SINT;+;3$;31| (|x| |y| $) (DECLARE (IGNORE $)) (QSPLUS |x| |y|)) -(DEFUN |SINT;-;3$;29| (|x| |y| $) +(DEFUN |SINT;-;3$;32| (|x| |y| $) (DECLARE (IGNORE $)) (QSDIFFERENCE |x| |y|)) -(DEFUN |SINT;*;3$;30| (|x| |y| $) +(DEFUN |SINT;*;3$;33| (|x| |y| $) (DECLARE (IGNORE $)) (QSTIMES |x| |y|)) -(DEFUN |SINT;**;$Nni$;31| (|x| |n| $) +(DEFUN |SINT;**;$Nni$;34| (|x| |n| $) (SPADCALL (EXPT |x| |n|) (|getShellEntry| $ 36))) -(DEFUN |SINT;quo;3$;32| (|x| |y| $) +(DEFUN |SINT;quo;3$;35| (|x| |y| $) (DECLARE (IGNORE $)) (QSQUOTIENT |x| |y|)) -(DEFUN |SINT;rem;3$;33| (|x| |y| $) +(DEFUN |SINT;rem;3$;36| (|x| |y| $) (DECLARE (IGNORE $)) (QSREMAINDER |x| |y|)) -(DEFUN |SINT;divide;2$R;34| (|x| |y| $) +(DEFUN |SINT;divide;2$R;37| (|x| |y| $) (CONS (QSQUOTIENT |x| |y|) (QSREMAINDER |x| |y|))) -(DEFUN |SINT;gcd;3$;35| (|x| |y| $) +(DEFUN |SINT;gcd;3$;38| (|x| |y| $) (DECLARE (IGNORE $)) (GCD |x| |y|)) -(DEFUN |SINT;abs;2$;36| (|x| $) (DECLARE (IGNORE $)) (QSABSVAL |x|)) +(DEFUN |SINT;abs;2$;39| (|x| $) (DECLARE (IGNORE $)) (QSABSVAL |x|)) -(DEFUN |SINT;odd?;$B;37| (|x| $) (DECLARE (IGNORE $)) (QSODDP |x|)) +(DEFUN |SINT;odd?;$B;40| (|x| $) (DECLARE (IGNORE $)) (QSODDP |x|)) -(DEFUN |SINT;zero?;$B;38| (|x| $) (DECLARE (IGNORE $)) (QSZEROP |x|)) +(DEFUN |SINT;zero?;$B;41| (|x| $) (DECLARE (IGNORE $)) (QSZEROP |x|)) -(DEFUN |SINT;one?;$B;39| (|x| $) (DECLARE (IGNORE $)) (EQL |x| 1)) +(DEFUN |SINT;one?;$B;42| (|x| $) (DECLARE (IGNORE $)) (EQL |x| 1)) -(DEFUN |SINT;max;3$;40| (|x| |y| $) +(DEFUN |SINT;max;3$;43| (|x| |y| $) (DECLARE (IGNORE $)) (QSMAX |x| |y|)) -(DEFUN |SINT;min;3$;41| (|x| |y| $) +(DEFUN |SINT;min;3$;44| (|x| |y| $) (DECLARE (IGNORE $)) (QSMIN |x| |y|)) -(DEFUN |SINT;hash;2$;42| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) +(DEFUN |SINT;hash;2$;45| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) -(DEFUN |SINT;length;2$;43| (|x| $) +(DEFUN |SINT;length;2$;46| (|x| $) (DECLARE (IGNORE $)) (INTEGER-LENGTH |x|)) -(DEFUN |SINT;shift;3$;44| (|x| |n| $) +(DEFUN |SINT;shift;3$;47| (|x| |n| $) (DECLARE (IGNORE $)) (QSLEFTSHIFT |x| |n|)) -(DEFUN |SINT;mulmod;4$;45| (|a| |b| |p| $) +(DEFUN |SINT;mulmod;4$;48| (|a| |b| |p| $) (DECLARE (IGNORE $)) (QSMULTMOD |a| |b| |p|)) -(DEFUN |SINT;addmod;4$;46| (|a| |b| |p| $) +(DEFUN |SINT;addmod;4$;49| (|a| |b| |p| $) (DECLARE (IGNORE $)) (QSADDMOD |a| |b| |p|)) -(DEFUN |SINT;submod;4$;47| (|a| |b| |p| $) +(DEFUN |SINT;submod;4$;50| (|a| |b| |p| $) (DECLARE (IGNORE $)) (QSDIFMOD |a| |b| |p|)) -(DEFUN |SINT;negative?;$B;48| (|x| $) +(DEFUN |SINT;negative?;$B;51| (|x| $) (DECLARE (IGNORE $)) (QSMINUSP |x|)) -(DEFUN |SINT;size;Nni;49| ($) +(DEFUN |SINT;size;Nni;52| ($) (+ (- |$ShortMaximum| |$ShortMinimum|) 1)) -(DEFUN |SINT;index;Pi$;50| (|i| $) - (PROG (#0=#:G1456) +(DEFUN |SINT;index;Pi$;53| (|i| $) + (PROG (#0=#:G1459) (RETURN (PROG1 (LETT #0# (- (+ |i| |$ShortMinimum|) 1) - |SINT;index;Pi$;50|) + |SINT;index;Pi$;53|) (|check-subtype| (SMINTP #0#) '(|SingleInteger|) #0#))))) -(DEFUN |SINT;lookup;$Pi;51| (|x| $) (+ (- |x| |$ShortMinimum|) 1)) +(DEFUN |SINT;lookup;$Pi;54| (|x| $) (+ (- |x| |$ShortMinimum|) 1)) -(DEFUN |SINT;reducedSystem;MVR;52| (|m| |v| $) +(DEFUN |SINT;reducedSystem;MVR;55| (|m| |v| $) (DECLARE (IGNORE $)) (CONS |m| |v|)) -(DEFUN |SINT;positiveRemainder;3$;53| (|x| |n| $) +(DEFUN |SINT;positiveRemainder;3$;56| (|x| |n| $) (PROG (|r|) (RETURN (SEQ (LETT |r| (QSREMAINDER |x| |n|) - |SINT;positiveRemainder;3$;53|) + |SINT;positiveRemainder;3$;56|) (EXIT (COND ((QSMINUSP |r|) (COND @@ -464,18 +483,18 @@ ('T (QSPLUS |r| |n|)))) ('T |r|))))))) -(DEFUN |SINT;coerce;I$;54| (|x| $) +(DEFUN |SINT;coerce;I$;57| (|x| $) (PROG1 |x| (|check-subtype| (SMINTP |x|) '(|SingleInteger|) |x|))) -(DEFUN |SINT;random;$;55| ($) +(DEFUN |SINT;random;$;58| ($) (SEQ (|setShellEntry| $ 6 (REMAINDER (TIMES 314159269 (|getShellEntry| $ 6)) 2147483647)) (EXIT (REMAINDER (|getShellEntry| $ 6) 67108864)))) -(DEFUN |SINT;random;2$;56| (|n| $) (DECLARE (IGNORE $)) (RANDOM |n|)) +(DEFUN |SINT;random;2$;59| (|n| $) (DECLARE (IGNORE $)) (RANDOM |n|)) -(DEFUN |SINT;unitNormal;$R;57| (|x| $) +(DEFUN |SINT;unitNormal;$R;60| (|x| $) (COND ((QSLESSP |x| 0) (VECTOR -1 (QSMINUS |x|) -1)) ('T (VECTOR 1 |x| 1)))) @@ -483,7 +502,7 @@ (DEFUN |SingleInteger| () (PROG () (RETURN - (PROG (#0=#:G1491) + (PROG (#0=#:G1494) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|SingleInteger|) @@ -505,7 +524,7 @@ (RETURN (PROGN (LETT |dv$| '(|SingleInteger|) . #0=(|SingleInteger|)) - (LETT $ (|newShell| 111) . #0#) + (LETT $ (|newShell| 115) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) @@ -521,7 +540,7 @@ (FUNCALL (|dispatchFunction| |SINT;Zero;$;10|) $)) (0 . |Zero|) (|Boolean|) |SINT;<;2$B;24| (|Void|) (|OpenMathDevice|) (4 . |OMputApp|) (|String|) - (9 . |OMputSymbol|) |SINT;-;2$;27| |SINT;convert;$I;8| + (9 . |OMputSymbol|) |SINT;-;2$;30| |SINT;convert;$I;8| (16 . |OMputInteger|) (22 . |OMputEndApp|) (|OpenMathEncoding|) (27 . |OMencodingXML|) (31 . |OMopenString|) (37 . |OMputObject|) @@ -530,7 +549,7 @@ |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| + (57 . |coerce|) |SINT;*;3$;33| |SINT;*;I2$;9| (CONS IDENTITY (FUNCALL (|dispatchFunction| |SINT;One;$;11|) $)) |SINT;base;$;12| @@ -541,57 +560,58 @@ |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$;23| - |SINT;inc;2$;25| |SINT;dec;2$;26| |SINT;+;3$;28| - |SINT;-;3$;29| (|NonNegativeInteger|) |SINT;**;$Nni$;31| - |SINT;quo;3$;32| |SINT;rem;3$;33| + |SINT;>;2$B;25| (62 . |not|) |SINT;<=;2$B;26| + |SINT;>=;2$B;27| |SINT;inc;2$;28| |SINT;dec;2$;29| + |SINT;+;3$;31| |SINT;-;3$;32| (|NonNegativeInteger|) + |SINT;**;$Nni$;34| |SINT;quo;3$;35| |SINT;rem;3$;36| (|Record| (|:| |quotient| $) (|:| |remainder| $)) - |SINT;divide;2$R;34| |SINT;gcd;3$;35| |SINT;abs;2$;36| - |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|) (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$;56| + |SINT;divide;2$R;37| |SINT;gcd;3$;38| |SINT;abs;2$;39| + |SINT;odd?;$B;40| |SINT;zero?;$B;41| (67 . |One|) + |SINT;one?;$B;42| |SINT;max;3$;43| |SINT;min;3$;44| + (|SingleInteger|) |SINT;hash;2$;45| |SINT;length;2$;46| + |SINT;shift;3$;47| |SINT;mulmod;4$;48| |SINT;addmod;4$;49| + |SINT;submod;4$;50| |SINT;negative?;$B;51| + |SINT;size;Nni;52| (|PositiveInteger|) (71 . +) (77 . -) + |SINT;index;Pi$;53| |SINT;lookup;$Pi;54| (|Vector| 5) + (|Record| (|:| |mat| 30) (|:| |vec| 88)) (|Vector| $) + |SINT;reducedSystem;MVR;55| |SINT;positiveRemainder;3$;56| + |SINT;coerce;I$;57| |SINT;random;$;58| |SINT;random;2$;59| (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) - |SINT;unitNormal;$R;57| (|Fraction| 5) - (|Union| 94 '"failed") (|DoubleFloat|) + |SINT;unitNormal;$R;60| (|Fraction| 5) + (|Union| 98 '"failed") (|DoubleFloat|) (|Union| $ '"failed") (|Float|) (|PatternMatchResult| 5 $) (|Pattern| 5) (|InputForm|) (|Union| 5 '"failed") - (|List| $) (|Union| 103 '"failed") - (|Record| (|:| |coef| 103) (|:| |generator| $)) + (|List| $) (|Union| 107 '"failed") + (|Record| (|:| |coef| 107) (|:| |generator| $)) (|Record| (|:| |coef1| $) (|:| |coef2| $)) - (|Union| 106 '"failed") + (|Union| 110 '"failed") (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) (|Factored| $) (|SparseUnivariatePolynomial| $)) - '#(~= 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 |before?| 536 |base| 542 - |associates?| 546 |addmod| 552 |abs| 559 |\\/| 564 |Zero| - 570 |Or| 574 |One| 580 |OMwrite| 584 |Not| 608 D 613 |And| - 624 >= 630 > 636 = 642 <= 648 < 654 |/\\| 660 - 666 + 677 - ** 683 * 695) + '#(~= 83 ~ 89 |zero?| 94 |xor| 99 |unitNormal| 105 + |unitCanonical| 110 |unit?| 115 |symmetricRemainder| 120 + |subtractIfCan| 126 |submod| 132 |squareFreePart| 139 + |squareFree| 144 |sizeLess?| 149 |size| 155 |sign| 159 + |shift| 164 |sample| 170 |retractIfCan| 174 |retract| 179 + |rem| 184 |reducedSystem| 190 |recip| 201 |rationalIfCan| + 206 |rational?| 211 |rational| 216 |random| 221 |quo| 230 + |principalIdeal| 236 |prime?| 241 |powmod| 246 + |positiveRemainder| 253 |positive?| 259 |permutation| 264 + |patternMatch| 270 |one?| 277 |odd?| 282 |not| 287 + |nextItem| 292 |negative?| 297 |multiEuclidean| 302 + |mulmod| 308 |min| 315 |max| 325 |mask| 335 |lookup| 340 + |length| 345 |lcm| 350 |latex| 361 |invmod| 366 |init| 372 + |index| 376 |inc| 381 |hash| 386 |gcdPolynomial| 391 |gcd| + 397 |factorial| 408 |factor| 413 |extendedEuclidean| 418 + |exquo| 431 |expressIdealMember| 437 |even?| 443 + |euclideanSize| 448 |divide| 453 |differentiate| 459 |dec| + 470 |copy| 475 |convert| 480 |coerce| 505 |characteristic| + 525 |bit?| 529 |binomial| 535 |before?| 541 |base| 547 + |associates?| 551 |addmod| 557 |abs| 564 |\\/| 569 |Zero| + 575 |Or| 579 |One| 585 |OMwrite| 589 |Not| 613 D 618 |And| + 629 >= 635 > 641 = 647 <= 653 < 659 |/\\| 665 - 671 + 682 + ** 688 * 700) '((|noetherian| . 0) (|canonicalsClosed| . 0) (|canonical| . 0) (|canonicalUnitNormal| . 0) (|multiplicativeValuation| . 0) (|noZeroDivisors| . 0) @@ -641,59 +661,59 @@ (|LeftLinearSet| 5) (|Logic|) (|RealConstant|) (|RetractableTo| 5) (|SetCategory|) (|OpenMath|) - (|ConvertibleTo| 98) - (|ConvertibleTo| 96) - (|CombinatorialFunctionCategory|) + (|ConvertibleTo| 102) (|ConvertibleTo| 100) - (|ConvertibleTo| 101) + (|CombinatorialFunctionCategory|) + (|ConvertibleTo| 104) + (|ConvertibleTo| 105) (|ConvertibleTo| 5) (|CoercibleFrom| $$) (|CoercibleFrom| 5) (|BasicType|) (|CoercibleTo| 33)) - (|makeByteWordVec2| 110 + (|makeByteWordVec2| 114 '(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 97 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 2 0 85 31 86 87 1 0 30 31 - 32 1 0 97 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 0 105 103 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 99 0 100 99 1 1 0 9 0 67 1 0 - 9 0 64 1 0 0 0 45 1 0 97 0 1 1 0 9 0 - 77 2 0 104 103 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 2 - 0 0 0 0 1 1 0 0 103 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 2 0 - 0 0 0 62 1 0 0 103 1 1 0 0 0 1 1 0 - 109 0 1 3 0 107 0 0 0 1 2 0 108 0 0 1 - 2 0 97 0 0 1 2 0 104 103 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 - 96 0 1 1 0 98 0 1 1 0 101 0 1 1 0 100 - 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 2 0 9 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 2 - 0 0 0 0 55 1 0 0 0 16 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))))) + 0 5 36 1 9 0 0 53 0 5 0 70 2 83 0 0 0 + 84 2 5 0 0 0 85 2 0 9 0 0 1 1 0 0 0 + 44 1 0 9 0 69 2 0 0 0 0 51 1 0 96 0 + 97 1 0 0 0 1 1 0 9 0 1 2 0 0 0 0 1 2 + 0 101 0 0 1 3 0 0 0 0 0 80 1 0 0 0 1 + 1 0 113 0 1 2 0 9 0 0 1 0 0 60 82 1 0 + 5 0 1 2 0 0 0 0 77 0 0 0 1 1 0 106 0 + 1 1 0 5 0 1 2 0 0 0 0 63 2 0 89 31 90 + 91 1 0 30 31 32 1 0 101 0 1 1 0 99 0 + 1 1 0 9 0 1 1 0 98 0 1 1 0 0 0 95 0 0 + 0 94 2 0 0 0 0 62 1 0 109 107 1 1 0 9 + 0 1 3 0 0 0 0 0 1 2 0 0 0 0 92 1 0 9 + 0 1 2 0 0 0 0 1 3 0 103 0 104 103 1 1 + 0 9 0 71 1 0 9 0 68 1 0 0 0 45 1 0 + 101 0 1 1 0 9 0 81 2 0 108 107 0 1 3 + 0 0 0 0 0 78 0 0 0 42 2 0 0 0 0 73 0 + 0 0 41 2 0 0 0 0 72 1 0 0 0 1 1 0 83 + 0 87 1 0 0 0 76 2 0 0 0 0 1 1 0 0 107 + 1 1 0 14 0 1 2 0 0 0 0 1 0 0 0 1 1 0 + 0 83 86 1 0 0 0 56 1 0 74 0 75 2 0 + 114 114 114 1 2 0 0 0 0 66 1 0 0 107 + 1 1 0 0 0 1 1 0 113 0 1 3 0 111 0 0 0 + 1 2 0 112 0 0 1 2 0 101 0 0 1 2 0 108 + 107 0 1 1 0 9 0 1 1 0 60 0 1 2 0 64 0 + 0 65 1 0 0 0 1 2 0 0 0 60 1 1 0 0 0 + 57 1 0 0 0 1 1 0 100 0 1 1 0 102 0 1 + 1 0 105 0 1 1 0 104 0 1 1 0 5 0 17 1 + 0 0 5 93 1 0 0 0 1 1 0 0 5 93 1 0 33 + 0 35 0 0 60 1 2 0 9 0 0 1 2 0 0 0 0 1 + 2 0 9 0 0 1 0 0 0 40 2 0 9 0 0 1 3 0 + 0 0 0 0 79 1 0 0 0 67 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 60 1 2 0 0 0 0 49 2 0 9 0 0 55 2 0 + 9 0 0 52 2 0 9 0 0 43 2 0 9 0 0 54 2 + 0 9 0 0 10 2 0 0 0 0 46 2 0 0 0 0 59 + 1 0 0 0 16 2 0 0 0 0 58 2 0 0 0 60 61 + 2 0 0 0 83 1 2 0 0 0 0 37 2 0 0 5 0 + 38 2 0 0 60 0 1 2 0 0 83 0 1))))) '|lookupComplete|)) (MAKEPROP '|SingleInteger| 'NILADIC T) diff --git a/src/algebra/string.spad.pamphlet b/src/algebra/string.spad.pamphlet index 48a09e30..1e08bf30 100644 --- a/src/algebra/string.spad.pamphlet +++ b/src/algebra/string.spad.pamphlet @@ -82,6 +82,9 @@ Character: OrderedFinite() with a = b == CHAR_=(a,b)$Lisp a < b == CHAR_<(a,b)$Lisp + a > b == CHAR_>(a,b)$Lisp + a <= b == CHAR_<_=(a,b)$Lisp + a >= b == CHAR_>_=(a,b)$Lisp size() == 256 index n == char((n - 1)::NNI) lookup c == (1 + ord c)::PositiveInteger diff --git a/src/interp/compiler.boot b/src/interp/compiler.boot index 1aa087cb..2d42c1fa 100644 --- a/src/interp/compiler.boot +++ b/src/interp/compiler.boot @@ -1454,6 +1454,11 @@ compExclusiveOr(x,m,e) == bT := comp(b,$EmptyMode,e) or return nil compResolveCall("xor",[aT,bT],m,bT.env) +compGreaterThan: (%Form, %Mode, %Env) -> %Maybe %Triple +compGreaterThan(x,m,e) == + x isnt [">", a, b] => nil + $normalizeTree and resolve(m,$Boolean) = $Boolean => comp(["<",b,a],m,e) + compForm(x,m,e) --% Case compCase: (%Form,%Mode,%Env) -> %Maybe %Triple @@ -2445,6 +2450,7 @@ for x in [["|", :"compSuchthat"],_ ["@", :"compAtSign"],_ [":", :"compColon"],_ ["::", :"compCoerce"],_ + [">", :"compGreaterThan"],_ ["QUOTE", :"compQuote"],_ ["add", :"compAdd"],_ ["CAPSULE", :"compCapsule"],_ diff --git a/src/interp/parse.boot b/src/interp/parse.boot index 92c040bd..f8491813 100644 --- a/src/interp/parse.boot +++ b/src/interp/parse.boot @@ -262,11 +262,6 @@ parseDropAssertions x == [y,:parseDropAssertions r] x -parseGreaterThan: %ParseForm -> %Form -parseGreaterThan t == - t isnt [op,x,y] => systemErrorHere ["parseGreaterThan",t] - [substitute("<",">",op),parseTran y,parseTran x] - parseGreaterEqual: %ParseForm -> %Form parseGreaterEqual u == parseTran ["not",[substitute("<",">=",first u),:rest u]] @@ -482,7 +477,6 @@ parseVCONS l == --% Register special parsers. for x in [["<=", :"parseLessEqual"],_ - [">", :"parseGreaterThan"],_ [">=", :"parseGreaterEqual"],_ ["^=", :"parseNotEqual"],_ [":", :"parseColon"],_ diff --git a/src/interp/postpar.boot b/src/interp/postpar.boot index 7a5ae403..e54d24fd 100644 --- a/src/interp/postpar.boot +++ b/src/interp/postpar.boot @@ -1,6 +1,6 @@ -- Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd. -- All rights reserved. --- Copyright (C) 2007-2008, Gabriel Dos Reis. +-- Copyright (C) 2007-2009, Gabriel Dos Reis. -- All rights reserved. -- -- Redistribution and use in source and binary forms, with or without diff --git a/src/interp/sys-macros.lisp b/src/interp/sys-macros.lisp index db4b08ec..4f237206 100644 --- a/src/interp/sys-macros.lisp +++ b/src/interp/sys-macros.lisp @@ -71,6 +71,9 @@ (defmacro |byteGreaterEqual| (|x| |y|) `(>= (the |%Byte| ,|x|) (the |%Byte| ,|y|))) +(defmacro |byteGreaterThan| (|x| |y|) + `(> (the |%Byte| ,|x|) (the |%Byte| ,|y|))) + ;; ;; -*- BigFloat Constructors -*- ;; diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 1fd81673..46e04939 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2284136 . 3452782368) +(2284136 . 3452796868) (-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 @@ -56,7 +56,7 @@ 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 -2234) +(-32 R -2372) ((|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 -1036) (QUOTE (-564))))) @@ -88,11 +88,11 @@ 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 -2234 UP UPUP -1472) +(-40 -2372 UP UPUP -3615) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2706 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2706 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2706 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2234) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2805 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2805 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2805 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2805 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -2372) ((|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| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-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."))) ((-4410 . T) (-4411 . T)) -((-2706 (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|))))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|))))))) +((-2805 (-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2234) +(-54 |Base| R -2372) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) -(-61 -2461) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +(-61 -2617) ((|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 -(-62 -2461) +(-62 -2617) ((|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 -(-63 -2461) +(-63 -2617) ((|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 -(-64 -2461) +(-64 -2617) ((|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 -2461) +(-65 -2617) ((|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 -2461) +(-66 -2617) ((|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 -2461) +(-67 -2617) ((|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 -2461) +(-68 -2617) ((|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 -2461) +(-69 -2617) ((|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 -2461) +(-70 -2617) ((|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 -2461) +(-71 -2617) ((|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 -2461) +(-72 -2617) ((|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 -2461) +(-73 -2617) ((|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 -2461) +(-74 -2617) ((|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 @@ -236,55 +236,55 @@ NIL ((|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 -(-77 -2461) +(-77 -2617) ((|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 -(-78 -2461) +(-78 -2617) ((|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 -2461) +(-79 -2617) ((|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 -2461) +(-80 -2617) ((|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 -2461) +(-81 -2617) ((|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 -2461) +(-82 -2617) ((|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 -(-83 -2461) +(-83 -2617) ((|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 -(-84 -2461) +(-84 -2617) ((|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 -(-85 -2461) +(-85 -2617) ((|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 -(-86 -2461) +(-86 -2617) ((|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 -(-87 -2461) +(-87 -2617) ((|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 -(-88 -2461) +(-88 -2617) ((|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 -2461) +(-89 -2617) ((|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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2805 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (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| (($ (|Identifier|) (|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| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|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!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|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|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|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}."))) NIL NIL -(-115 -2234 UP) +(-115 -2372 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}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-907))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1020))) (|HasCategory| (-116 |#1|) (QUOTE (-818))) (-2706 (|HasCategory| (-116 |#1|) (QUOTE (-818))) (|HasCategory| (-116 |#1|) (QUOTE (-848)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1148))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (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 (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-907))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1020))) (|HasCategory| (-116 |#1|) (QUOTE (-818))) (-2805 (|HasCategory| (-116 |#1|) (QUOTE (-818))) (|HasCategory| (-116 |#1|) (QUOTE (-848)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1148))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (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 (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (|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"))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2706 (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097)))) (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-2805 (-12 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2805 (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097)))) (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|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 @@ -468,11 +468,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4412 "*") . T)) NIL -(-135 |minix| -3554 S T$) +(-135 |minix| -2256 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3554 R) +(-136 |minix| -2256 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -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}."))) ((-4410 . T) (-4400 . T) (-4411 . T)) -((-2706 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2805 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|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."))) ((-4407 . T)) NIL -(-148 -2234 UP UPUP) +(-148 -2372 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 @@ -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 -2234) +(-158 R -2372) ((|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 @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-1197))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556)))) (-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})"))) -((-4403 -2706 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4409 |has| |#1| (-6 -4409)) (-3609 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-4403 -2805 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4409 |has| |#1| (-6 -4409)) (-3639 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . 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."))) @@ -606,8 +606,8 @@ 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}."))) -((-4403 -2706 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4409 |has| |#1| (-6 -4409)) (-3609 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . 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T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|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 -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-907)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-907))))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-1057))) (-12 (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasAttribute| |#1| (QUOTE -4409)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|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 @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2234) +(-188 R -2372) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2234 UP UPUP R) +(-215 -2372 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 -2234 FP) +(-216 -2372 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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2805 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2234) +(-219 R -2372) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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}."))) ((-4407 . T)) NIL -(-224 R -2234) +(-224 R -2372) ((|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}."))) -((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-3629 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . 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}"))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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 -3554 R) +(-237 S -2256 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 (-791))) (|HasCategory| |#3| (QUOTE (-846))) (|HasAttribute| |#3| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-1097)))) -(-238 -3554 R) +(-238 -2256 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"))) ((-4404 |has| |#2| (-1047)) (-4405 |has| |#2| (-1047)) (-4407 |has| |#2| (-6 -4407)) ((-4412 "*") |has| |#2| (-172)) (-4410 . T)) NIL -(-239 -3554 A B) +(-239 -2256 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\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| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\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 -(-240 -3554 R) +(-240 -2256 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."))) ((-4404 |has| |#2| (-1047)) (-4405 |has| |#2| (-1047)) (-4407 |has| |#2| (-6 -4407)) ((-4412 "*") |has| |#2| (-172)) (-4410 . T)) -((-2706 (-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 (-724))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-791))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (-2706 (-12 (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1047)))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-363))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1047)))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-791))) (-2706 (|HasCategory| |#2| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-724))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1047)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE 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(((|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 @@ -911,7 +911,7 @@ 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}"))) ((-4411 . T) (-4410 . 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(|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 @@ -919,7 +919,7 @@ 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.")) 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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 -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2805 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-724))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-2805 (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097)))) (-2805 (|HasAttribute| |#3| (QUOTE -4407)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|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 @@ -987,7 +987,7 @@ 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"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|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 -2234) +(-276 R -2372) ((|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 -2234) +(-277 R -2372) ((|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 @@ -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| -1790 -2740 |exactQuo|) +(-289 S R |Mod| -3661 -3516 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) (-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 -2234 S) +(-297 -2372 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 -(-298 E -2234) +(-298 E -2372) ((|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 @@ -1168,7 +1168,7 @@ 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 -2234) +(-310 -2372) ((|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 @@ -1183,7 +1183,7 @@ 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))}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-1020))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-818))) (-2706 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-818))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-848)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-1148))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-848))) (-12 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|HasCategory| $ (QUOTE (-145)))) (-2706 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-1020))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-818))) (-2805 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-818))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-848)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-1148))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1248) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-848))) (-12 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|HasCategory| $ (QUOTE (-145)))) (-2805 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1248 |#1| |#2| |#3| |#4|) (QUOTE (-907))) (|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 @@ -1194,9 +1194,9 @@ NIL NIL (-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."))) -((-4407 -2706 (-2275 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2706 (-2275 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1047)) (|has| |#1| (-473)))) (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4408 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(-25))) (-12 (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2706 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1036) (QUOTE (-564))))) -(-317 R -2234) +((-4407 -2805 (-2425 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2805 (-2425 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1047)) (|has| |#1| (-473)))) (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) 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(-1109)))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2805 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1036) (QUOTE (-564))))) +(-317 R -2372) ((|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 @@ -1207,7 +1207,7 @@ 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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|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 @@ -1239,12 +1239,12 @@ 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."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2234) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -2372) ((|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 -2234) +(-329 -2372) ((|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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL @@ -1264,15 +1264,15 @@ NIL ((|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 -(-334 S -2234 UP UPUP R) +(-334 S -2372 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 -(-335 -2234 UP UPUP R) +(-335 -2372 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 -2234 UP UPUP R) +(-336 -2372 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 @@ -1292,26 +1292,26 @@ NIL ((|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 -2234 UP UPUP) +(-341 S -2372 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 -2234 UP UPUP) +(-342 -2372 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."))) ((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) +((-2805 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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 @@ -1328,31 +1328,31 @@ NIL ((|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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL -(-350 R UP -2234) +(-350 R UP -2372) ((|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 (-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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) +((-2805 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) +((-2805 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2234 GF) +((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2372 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 @@ -1360,14 +1360,14 @@ NIL ((|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 -2234 FP FPP) +(-358 -2372 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}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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 @@ -1446,7 +1446,7 @@ 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}."))) -((-4393 . T) (-4401 . T) (-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-4393 . T) (-4401 . T) (-3629 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . 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}."))) @@ -1496,7 +1496,7 @@ 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 -2234 UP UPUP R) +(-392 -2372 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 @@ -1520,11 +1520,11 @@ NIL ((|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 -2461 |returnType| -2737 |symbols|) +(-398 -2617 |returnType| -4048 |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 -2234 UP) +(-399 -2372 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4393)) (|HasAttribute| |#1| (QUOTE -4401))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-3629 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-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."))) @@ -1559,7 +1559,7 @@ 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."))) ((-4397 -12 (|has| |#1| (-6 -4408)) (|has| |#1| (-452)) (|has| |#1| (-6 -4397))) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-818))) (-2706 (|HasCategory| |#1| (QUOTE (-818))) (|HasCategory| |#1| (QUOTE (-848)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 (-826)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-818))) (-2805 (|HasCategory| |#1| (QUOTE (-818))) (|HasCategory| |#1| (QUOTE (-848)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 (-826)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2234 UP A) +(-413 R -2372 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4407 . T)) NIL -(-414 R -2234 UP A |ibasis|) +(-414 R -2372 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 -1036) (|devaluate| |#2|)))) @@ -1603,7 +1603,7 @@ 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."))) ((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1216))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1216)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1216))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1216)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 -898) (QUOTE (-1173)))) (|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 @@ -1632,7 +1632,7 @@ NIL ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4410 . T) (-4400 . T) (-4411 . T)) NIL -(-426 R -2234) +(-426 R -2372) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4397 -12 (|has| |#1| (-6 -4397)) (|has| |#2| (-6 -4397))) (-4404 . T) (-4405 . T) (-4407 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#2| (QUOTE -4397)))) -(-428 R -2234) +(-428 R -2372) ((|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 @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -612) (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}."))) -((-4407 -2706 (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-556)) (-4402 |has| |#1| (-556))) +((-4407 -2805 (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-556)) (-4402 |has| |#1| (-556))) NIL -(-431 R -2234) +(-431 R -2372) ((|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 -2234) +(-432 R -2372) ((|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 -2234) +(-433 R -2372) ((|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 @@ -1668,7 +1668,7 @@ 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 -2234 UP) +(-435 R -2372 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 -1036) (QUOTE (-48))))) @@ -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 -2234) +(-443 R UP -2372) ((|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 @@ -1747,7 +1747,7 @@ NIL (-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"))) (((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-907))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|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 @@ -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| -2234 R) +(-471 |lv| -2372 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 @@ -1827,11 +1827,11 @@ 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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) (-475 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097)))) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097)))) (-476 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. 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)}"))) ((-4411 . T) (-4410 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) (-480) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. 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 @@ -1855,11 +1855,11 @@ 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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . 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(QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-791))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-848))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1047)))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2805 (|HasCategory| |#2| (QUOTE (-1047))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) -(-485 -2234 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +(-485 -2372 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 @@ -1879,7 +1879,7 @@ 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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2805 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,7 +1904,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -2234 UP |AlExt| |AlPol|) +(-494 -2372 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 @@ -1915,16 +1915,16 @@ NIL (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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 -2234) +(-499 R UP -2372) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2234 |Expon| |VarSet| |DPoly|) +(-504 -2372 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1173))))) @@ -1995,7 +1995,7 @@ NIL (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|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}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((-2706 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-2805 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-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 -2234 |Par|) +(-532 K -2372 |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 @@ -2080,7 +2080,7 @@ NIL ((|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 -2234 |Par|) +(-538 K -2372 |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 @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) -(-551 R -2234) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) +(-551 R -2372) ((|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 -2234 UP UPUP R) +(-552 R0 -2372 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 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."))) -((-3601 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-3629 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-555 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."))) @@ -2156,7 +2156,7 @@ NIL ((|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."))) ((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL -(-557 R -2234) +(-557 R -2372) ((|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 @@ -2168,7 +2168,7 @@ NIL ((|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 -2234 L) +(-560 R -2372 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 -654) (|devaluate| |#2|)))) @@ -2176,11 +2176,11 @@ NIL ((|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 -2234 UP UPUP R) +(-562 -2372 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 -2234 UP) +(-563 -2372 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 @@ -2192,15 +2192,15 @@ NIL ((|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 -(-566 R -2234 L) +(-566 R -2372 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 -654) (|devaluate| |#2|)))) -(-567 R -2234) +(-567 R -2372) ((|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 -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1136)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2234 UP) +(-568 -2372 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 @@ -2208,27 +2208,27 @@ 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 -(-570 -2234) +(-570 -2372) ((|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 (-571 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."))) -((-3601 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-3629 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-572) ((|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 -(-573 R -2234) +(-573 R -2372) ((|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| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2234 UP) +(-574 -2372 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 -(-575 R -2234) +(-575 R -2372) ((|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 @@ -2260,15 +2260,15 @@ 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 -(-583 R -2234) +(-583 R -2372) ((|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 E -2234) +(-584 E -2372) ((|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 -(-585 -2234) +(-585 -2372) ((|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}."))) ((-4405 . T) (-4404 . T)) ((|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-1173))))) @@ -2299,7 +2299,7 @@ NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2706 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2805 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2805 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 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 @@ -2307,7 +2307,7 @@ NIL (-594 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2805 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |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.}"))) ((-4405 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4407 . T)) @@ -2320,7 +2320,7 @@ 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 -(-598 R -2234 FG) +(-598 R -2372 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 @@ -2331,7 +2331,7 @@ NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,12 +2350,12 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4407 -2706 (-2275 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) -((-2706 (|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|)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4407 -2805 (-2425 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) +((-2805 (|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|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| (-1155) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| (-1155) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|)) (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|)) (LIST (QUOTE -611) (QUOTE (-860))))) (-607 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 @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2234 UP) +(-613 -2372 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2408,7 +2408,7 @@ NIL ((|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}."))) ((-4404 . T) (-4405 . T) (-4407 . T)) ((|HasCategory| |#1| (QUOTE (-846)))) -(-620 R -2234) +(-620 R -2372) ((|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 @@ -2440,18 +2440,18 @@ NIL ((|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 -(-628 R -2234) +(-628 R -2372) ((|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 -(-629 |lv| -2234) +(-629 |lv| -2372) ((|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 (-630) ((|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."))) ((-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1155) (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097)))) +((-12 (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -2806) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1155) (QUOTE (-848))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 (-1155)) (|:| -2806 (-52))) (QUOTE (-1097)))) (-631 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,8 +2462,8 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4407 -2706 (-2275 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) -((-2706 (|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|)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4407 -2805 (-2425 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) +((-2805 (|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|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 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|) "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 @@ -2475,7 +2475,7 @@ NIL (-636 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 -((-2268 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2414 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4407 . T)) @@ -2499,7 +2499,7 @@ NIL (-642 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-643 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2511,7 +2511,7 @@ NIL (-645 S) ((|substitute| (($ |#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."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-646 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"))) NIL @@ -2528,7 +2528,7 @@ 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 -(-650 R -2234 L) +(-650 R -2372 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 @@ -2548,11 +2548,11 @@ NIL ((|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}."))) ((-4404 . T) (-4405 . T) (-4407 . T)) NIL -(-655 -2234 UP) +(-655 -2372 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)))) -(-656 A -2297) +(-656 A -1756) ((|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}}"))) ((-4404 . T) (-4405 . T) (-4407 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2588,11 +2588,11 @@ 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}."))) ((-4411 . T) (-4410 . T)) NIL -(-665 -2234) +(-665 -2372) ((|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 -(-666 -2234 |Row| |Col| M) +(-666 -2372 |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 @@ -2603,7 +2603,7 @@ NIL (-668 |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."))) ((-4407 . T) (-4410 . T) (-4404 . T) (-4405 . T)) -((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2706 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2805 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-669) ((|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 @@ -2623,7 +2623,7 @@ NIL (-673 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 -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-674) ((|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 @@ -2679,7 +2679,7 @@ NIL (-687 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."))) ((-4410 . T) (-4411 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-688 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 @@ -2688,7 +2688,7 @@ 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 -(-690 S -2234 FLAF FLAS) +(-690 S -2372 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 @@ -2698,8 +2698,8 @@ NIL NIL (-692) ((|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"))) -((-4403 . T) (-4408 |has| (-697) (-363)) (-4402 |has| (-697) (-363)) (-3609 . T) (-4409 |has| (-697) (-6 -4409)) (-4406 |has| (-697) (-6 -4406)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-697) (QUOTE (-147))) (|HasCategory| (-697) (QUOTE (-145))) (|HasCategory| (-697) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-697) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-697) (QUOTE (-368))) (|HasCategory| (-697) (QUOTE (-363))) (-2706 (|HasCategory| (-697) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-697) (QUOTE (-363)))) (|HasCategory| (-697) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-697) (QUOTE (-233))) (-2706 (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-349)))) (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (LIST (QUOTE -286) (QUOTE (-697)) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -309) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-697) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-697) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-697) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (-2706 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-349)))) (|HasCategory| (-697) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-697) (QUOTE (-1020))) (|HasCategory| (-697) (QUOTE (-1197))) (-12 (|HasCategory| (-697) (QUOTE (-1000))) (|HasCategory| (-697) (QUOTE (-1197)))) (-2706 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-363))) (-12 (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (QUOTE (-907))))) (-2706 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (-12 (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-907)))) (-12 (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (QUOTE (-907))))) (|HasCategory| (-697) (QUOTE (-545))) (-12 (|HasCategory| (-697) (QUOTE (-1057))) (|HasCategory| (-697) (QUOTE (-1197)))) (|HasCategory| (-697) (QUOTE (-1057))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907))) (-2706 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-363)))) (-2706 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-556)))) (-12 (|HasCategory| (-697) (QUOTE (-233))) (|HasCategory| (-697) (QUOTE (-363)))) (-12 (|HasCategory| (-697) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-697) (QUOTE (-363)))) (|HasCategory| (-697) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-697) (QUOTE (-556))) (|HasAttribute| (-697) (QUOTE -4409)) (|HasAttribute| (-697) (QUOTE -4406)) (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-145)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-349))))) +((-4403 . T) (-4408 |has| (-697) (-363)) (-4402 |has| (-697) (-363)) (-3639 . T) (-4409 |has| (-697) (-6 -4409)) (-4406 |has| (-697) (-6 -4406)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((|HasCategory| (-697) (QUOTE (-147))) (|HasCategory| (-697) (QUOTE (-145))) (|HasCategory| (-697) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-697) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-697) (QUOTE (-368))) (|HasCategory| (-697) (QUOTE (-363))) (-2805 (|HasCategory| (-697) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-697) (QUOTE (-363)))) (|HasCategory| (-697) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-697) (QUOTE (-233))) (-2805 (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-349)))) (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (LIST (QUOTE -286) (QUOTE (-697)) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -309) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-697)))) (|HasCategory| (-697) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-697) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-697) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-697) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (-2805 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-349)))) (|HasCategory| (-697) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-697) (QUOTE (-1020))) (|HasCategory| (-697) (QUOTE (-1197))) (-12 (|HasCategory| (-697) (QUOTE (-1000))) (|HasCategory| (-697) (QUOTE (-1197)))) (-2805 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-363))) (-12 (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (QUOTE (-907))))) (-2805 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (-12 (|HasCategory| (-697) (QUOTE (-363))) (|HasCategory| (-697) (QUOTE (-907)))) (-12 (|HasCategory| (-697) (QUOTE (-349))) (|HasCategory| (-697) (QUOTE (-907))))) (|HasCategory| (-697) (QUOTE (-545))) (-12 (|HasCategory| (-697) (QUOTE (-1057))) (|HasCategory| (-697) (QUOTE (-1197)))) (|HasCategory| (-697) (QUOTE (-1057))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907))) (-2805 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-363)))) (-2805 (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-556)))) (-12 (|HasCategory| (-697) (QUOTE (-233))) (|HasCategory| (-697) (QUOTE (-363)))) (-12 (|HasCategory| (-697) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-697) (QUOTE (-363)))) (|HasCategory| (-697) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-697) (QUOTE (-556))) (|HasAttribute| (-697) (QUOTE -4409)) (|HasAttribute| (-697) (QUOTE -4406)) (-12 (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-697) (QUOTE (-307))) (|HasCategory| (-697) (QUOTE (-907)))) (|HasCategory| (-697) (QUOTE (-349))))) (-693 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}."))) ((-4411 . T)) @@ -2712,13 +2712,13 @@ NIL ((|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 -(-696 OV E -2234 PG) +(-696 OV E -2372 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 (-697) ((|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}"))) -((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) +((-3629 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-698 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."))) @@ -2744,7 +2744,7 @@ 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 -(-704 S -4044 I) +(-704 S -2830 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 @@ -2764,14 +2764,14 @@ 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 -(-709 R |Mod| -1790 -2740 |exactQuo|) +(-709 R |Mod| -3661 -3516 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-710 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) (-711 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2780,7 +2780,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-713 R |Mod| -1790 -2740 |exactQuo|) +(-713 R |Mod| -3661 -3516 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4407 . T)) NIL @@ -2792,7 +2792,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4405 . T) (-4404 . T)) NIL -(-716 -2234) +(-716 -2372) ((|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]]}."))) ((-4407 . T)) NIL @@ -2828,7 +2828,7 @@ 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 -(-725 -2234 UP) +(-725 -2372 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 @@ -2847,7 +2847,7 @@ NIL (-729 |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."))) (((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-907))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) (-730 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 @@ -2980,11 +2980,11 @@ 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 -(-763 -2234) +(-763 -2372) ((|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 -(-764 P -2234) +(-764 P -2372) ((|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 @@ -2992,7 +2992,7 @@ NIL NIL NIL NIL -(-766 UP -2234) +(-766 UP -2372) ((|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 @@ -3008,7 +3008,7 @@ 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."))) (((-4412 "*") . T)) NIL -(-770 R -2234) +(-770 R -2372) ((|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 @@ -3028,7 +3028,7 @@ 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 -(-775 -2234 |ExtF| |SUEx| |ExtP| |n|) +(-775 -2372 |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 @@ -3043,7 +3043,7 @@ NIL (-778 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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . 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(-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2414 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2414 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2414 (|HasCategory| |#1| (LIST (QUOTE -990) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) (-779 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 @@ -3051,7 +3051,7 @@ NIL (-780 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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3112,23 +3112,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4404 . T) (-4405 . T) (-4407 . T)) NIL -(-796 -2706 R OS S) +(-796 -2805 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-797 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2706 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2805 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (-798) ((|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 -(-799 R -2234 L) +(-799 R -2372 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 -(-800 R -2234) +(-800 R -2372) ((|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 @@ -3136,7 +3136,7 @@ NIL ((|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 -(-802 R -2234) +(-802 R -2372) ((|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 @@ -3144,11 +3144,11 @@ 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 -(-804 -2234 UP UPUP R) +(-804 -2372 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 -(-805 -2234 UP L LQ) +(-805 -2372 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 @@ -3156,38 +3156,38 @@ 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 -(-807 -2234 UP L LQ) +(-807 -2372 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 -(-808 -2234 UP) +(-808 -2372 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 -(-809 -2234 L UP A LO) +(-809 -2372 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 -(-810 -2234 UP) +(-810 -2372 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)))) -(-811 -2234 LO) +(-811 -2372 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 -(-812 -2234 LODO) +(-812 -2372 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)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) (-815 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4412 "*") |has| |#2| (-363)) (-4403 |has| |#2| (-363)) (-4408 |has| |#2| (-363)) (-4402 |has| |#2| (-363)) (-4407 . T) (-4405 . T) (-4404 . T)) @@ -3255,7 +3255,7 @@ NIL (-831 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."))) ((-4407 |has| |#1| (-846))) -((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2706 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2805 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) (-832 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.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,{}n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3295,12 +3295,12 @@ NIL (-841 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4407 |has| |#1| (-846))) -((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2706 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2805 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) (-842) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-843 -3554 S) +(-843 -2256 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 @@ -3336,11 +3336,11 @@ NIL ((|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)))) -(-852 R |sigma| -1926) +(-852 R |sigma| -2958) ((|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."))) ((-4404 . T) (-4405 . T) (-4407 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-853 |x| R |sigma| -1926) +(-853 |x| R |sigma| -2958) ((|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}."))) ((-4404 . T) (-4405 . T) (-4407 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3407,15 +3407,15 @@ NIL (-869 |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)."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-868 |#1|) (QUOTE (-907))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-147))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-868 |#1|) (QUOTE (-1020))) (|HasCategory| (-868 |#1|) (QUOTE (-818))) (-2706 (|HasCategory| (-868 |#1|) (QUOTE (-818))) (|HasCategory| (-868 |#1|) (QUOTE (-848)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-1148))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-233))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -868) (|devaluate| |#1|)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (QUOTE (-307))) (|HasCategory| (-868 |#1|) (QUOTE (-545))) (|HasCategory| (-868 |#1|) (QUOTE (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))))) +((|HasCategory| (-868 |#1|) (QUOTE (-907))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-147))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-868 |#1|) (QUOTE (-1020))) (|HasCategory| (-868 |#1|) (QUOTE (-818))) (-2805 (|HasCategory| (-868 |#1|) (QUOTE (-818))) (|HasCategory| (-868 |#1|) (QUOTE (-848)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-1148))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-233))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -868) (|devaluate| |#1|)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (QUOTE (-307))) (|HasCategory| (-868 |#1|) (QUOTE (-545))) (|HasCategory| (-868 |#1|) (QUOTE (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))))) (-870 |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)}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-818))) (-2706 (|HasCategory| |#2| (QUOTE (-818))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-818))) (-2805 (|HasCategory| |#2| (QUOTE (-818))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) (-871 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 (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) (-872) ((|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 @@ -3471,7 +3471,7 @@ NIL (-885 |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 (-2268 (|HasCategory| |#2| (QUOTE (-1047)))) (-2268 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (-2268 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173))))) +((-12 (-2414 (|HasCategory| |#2| (QUOTE (-1047)))) (-2414 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (-2414 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173))))) (-886 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 @@ -3480,7 +3480,7 @@ NIL ((|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 -(-888 R -4044) +(-888 R -2830) ((|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 @@ -3504,7 +3504,7 @@ 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 -(-894 UP -2234) +(-894 UP -2372) ((|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 @@ -3527,7 +3527,7 @@ NIL (-899 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 (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-900 |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 @@ -3543,7 +3543,7 @@ NIL (-903 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."))) ((-4407 . T)) -((-2706 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) +((-2805 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) (-904 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 @@ -3564,7 +3564,7 @@ NIL ((|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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-909 R0 -2234 UP UPUP R) +(-909 R0 -2372 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 @@ -3592,7 +3592,7 @@ 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 -(-916 -2234) +(-916 -2372) ((|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 @@ -3608,11 +3608,11 @@ NIL ((|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}."))) (((-4412 "*") . T)) NIL -(-920 -2234 P) +(-920 -2372 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-921 |xx| -2234) +(-921 |xx| -2372) ((|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 @@ -3636,7 +3636,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-927 R -2234) +(-927 R -2372) ((|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| (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3648,7 +3648,7 @@ NIL ((|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 -(-930 S R -2234) +(-930 S R -2372) ((|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 @@ -3668,11 +3668,11 @@ 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 -884) (|devaluate| |#1|)))) -(-935 R -2234 -4044) +(-935 R -2372 -2830) ((|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 -(-936 -4044) +(-936 -2830) ((|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 @@ -3695,7 +3695,7 @@ NIL (-941 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-942 |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 @@ -3720,7 +3720,7 @@ NIL ((|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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) NIL -(-948 E V R P -2234) +(-948 E V R P -2372) ((|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 @@ -3731,8 +3731,8 @@ NIL (-950 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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-951 E V R P -2234) +((|HasCategory| |#1| (QUOTE (-907))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-951 E V R P -2372) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3755,12 +3755,12 @@ NIL (-956 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-957) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-958 -2234) +(-958 -2372) ((|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 @@ -3775,11 +3775,11 @@ NIL (-961 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}"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4408))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4408))) (-962 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"))) ((-4407 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2706 (-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 (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2706 (-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 (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2805 (-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 (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2805 (-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 (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) (-963) ((|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| (($ (|Identifier|) (|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| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3860,7 +3860,7 @@ 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 -(-983 K R UP -2234) +(-983 K R UP -2372) ((|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 @@ -3919,11 +3919,11 @@ NIL (-997 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.}"))) ((-4403 |has| |#1| (-290)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|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 -898) (QUOTE (-1173)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545)))) (-998 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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-999 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3932,14 +3932,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1001 -2234 UP UPUP |radicnd| |n|) +(-1001 -2372 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2706 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2706 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2706 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-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))) (-2805 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2805 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2805 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2805 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1002 |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."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2805 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1003) ((|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 @@ -3972,19 +3972,19 @@ 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}}"))) ((-4403 . T) (-4408 . T) (-4402 . T) (-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4407 . T)) NIL -(-1011 R -2234) +(-1011 R -2372) ((|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 -(-1012 R -2234) +(-1012 R -2372) ((|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 -(-1013 -2234 UP) +(-1013 -2372 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 -(-1014 -2234 UP) +(-1014 -2372 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 @@ -4019,8 +4019,8 @@ NIL (-1022 |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"))) ((-4403 . T) (-4408 . T) (-4402 . T) (-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4407 . T)) -((-2706 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564))))) -(-1023 -2234 L) +((-2805 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564))))) +(-1023 -2372 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 @@ -4056,14 +4056,14 @@ 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 -(-1032 -2234 |Expon| |VarSet| |FPol| |LFPol|) +(-1032 -2372 |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"))) (((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL (-1033) ((|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.}"))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -2806) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) (-1034) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4120,7 +4120,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4407 . T)) NIL -(-1048 |xx| -2234) +(-1048 |xx| -2372) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4139,7 +4139,7 @@ NIL (-1052 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4410 . T) (-4405 . T) (-4404 . T)) -((|HasCategory| |#3| (QUOTE (-172))) (-2706 (-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 (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860))))) +((|HasCategory| |#3| (QUOTE (-172))) (-2805 (-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 (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860))))) (-1053 |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 @@ -4171,7 +4171,7 @@ NIL (-1060) ((|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}"))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -2806) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) (-1061 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 @@ -4220,11 +4220,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1073 |Base| R -2234) +(-1073 |Base| R -2372) ((|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 -(-1074 |Base| R -2234) +(-1074 |Base| R -2372) ((|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 @@ -4239,7 +4239,7 @@ NIL (-1077 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."))) ((-4403 |has| |#1| (-363)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1078 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 @@ -4267,7 +4267,7 @@ NIL (-1084 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"))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1085 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 @@ -4327,7 +4327,7 @@ NIL (-1099 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)}}"))) ((-4410 . T) (-4400 . T) (-4411 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1100 |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 @@ -4371,7 +4371,7 @@ NIL (-1110 |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}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-848))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2805 (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097)))) (|HasAttribute| |#3| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1111 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 @@ -4380,7 +4380,7 @@ NIL ((|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 -(-1113 R -2234) +(-1113 R -2372) ((|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 @@ -4419,16 +4419,16 @@ NIL (-1122 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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-907))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1123 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1124 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}"))) ((-4411 . T) (-4410 . T)) NIL -(-1125 UP -2234) +(-1125 UP -2372) ((|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 @@ -4483,11 +4483,11 @@ NIL (-1138 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))) (-2706 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))))) (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))) (-2805 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))))) (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860))))) (-1139 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4407 . T) (-4399 |has| |#2| (-6 (-4412 "*"))) (-4410 . T) (-4404 . T) (-4405 . T)) -((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (-2706 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (-2805 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1140 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-1145 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 @@ -4519,7 +4519,7 @@ NIL (-1147 |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."))) ((-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097)))) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097)))) (-1148) ((|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 @@ -4543,7 +4543,7 @@ NIL (-1153 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."))) ((-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-1154) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4411 . T) (-4410 . T)) @@ -4551,11 +4551,11 @@ NIL (-1155) NIL ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2805 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1156 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4410 . T) (-4411 . 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(|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 @@ -4586,9 +4586,9 @@ NIL NIL (-1164 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\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{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with 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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4412 "*") -2706 (-2275 (|has| |#1| (-363)) (|has| (-1171 |#1| |#2| |#3|) (-818))) (|has| |#1| (-172)) (-2275 (|has| |#1| (-363)) (|has| (-1171 |#1| |#2| |#3|) (-907)))) (-4403 -2706 (-2275 (|has| |#1| (-363)) (|has| (-1171 |#1| |#2| |#3|) (-818))) (|has| |#1| (-556)) (-2275 (|has| |#1| (-363)) (|has| (-1171 |#1| |#2| |#3|) (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . 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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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) (-1171 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2805 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) (-1172) ((|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}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-969) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4408))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-969) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4408))) (-1176) ((|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 @@ -4671,7 +4671,7 @@ NIL (-1185 |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}"))) ((-4410 . T) (-4411 . T)) -((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1993) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2806) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2805 (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) (-1186 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 @@ -4723,7 +4723,7 @@ NIL (-1198 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4411 . T) (-4410 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) +((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (-1199 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4732,7 +4732,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1201 R -2234) +(-1201 R -2372) ((|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 @@ -4740,7 +4740,7 @@ 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 -(-1203 R -2234) +(-1203 R -2372) ((|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 -612) (LIST (QUOTE -890) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -884) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -884) (|devaluate| |#1|))))) @@ -4755,7 +4755,7 @@ NIL (-1206 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1207 |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 @@ -4768,7 +4768,7 @@ NIL ((|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 (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) -(-1210 -2234) +(-1210 -2372) ((|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}.")) 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(LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-818))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1227 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 @@ -4871,7 +4871,7 @@ NIL (-1235 |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}"))) (((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4406 |has| |#2| (-363)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) -((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1236 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 @@ -4887,7 +4887,7 @@ NIL (-1239 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 -898) (QUOTE (-1173)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2327) (LIST (|devaluate| |#2|) (QUOTE (-1173)))))) +((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2502) (LIST (|devaluate| |#2|) (QUOTE (-1173)))))) (-1240 |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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) @@ -4915,15 +4915,15 @@ NIL (-1246 |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)}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1247 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2805 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) (-1248 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))}."))) (((-4412 "*") |has| (-1247 |#2| |#3| |#4|) (-172)) (-4403 |has| (-1247 |#2| |#3| |#4|) (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-172))) (-2706 (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-556)))) +((|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-172))) (-2805 (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-556)))) (-1249 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4939,7 +4939,7 @@ NIL (-1252 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-957))) (|HasCategory| |#2| (QUOTE (-1197))) (|HasSignature| |#2| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4107) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1173))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-957))) (|HasCategory| |#2| (QUOTE (-1197))) (|HasSignature| |#2| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4384) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1173))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1253 |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."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) @@ -4947,12 +4947,12 @@ NIL (-1254 |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}."))) (((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2805 (|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 -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2502) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4384) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -2510) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) (-1255 |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 -(-1256 -2234 UP L UTS) +(-1256 -2372 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)))) @@ -4979,7 +4979,7 @@ NIL (-1262 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."))) ((-4411 . T) (-4410 . T)) -((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1263) ((|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 @@ -5012,7 +5012,7 @@ 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 -(-1271 K R UP -2234) +(-1271 K R UP -2372) ((|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 @@ -5048,11 +5048,11 @@ NIL ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) NIL -(-1280 S -2234) +(-1280 S -2372) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1281 -2234) +(-1281 -2372) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 392259cf..114f3f5f 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(187993 . 3452782375) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((#0=(-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) #0#) |has| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (-309 (-2 (|:| -1907 |#1|) (|:| -3778 |#2|))))) -((((-564)) . T) (($) -2706 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2706 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1036 (-407 (-564))))) ((|#1|) . T)) +(187993 . 3452796875) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((#0=(-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) #0#) |has| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (-309 (-2 (|:| -1993 |#1|) (|:| -2806 |#2|))))) +((((-564)) . T) (($) -2805 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2805 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1036 (-407 (-564))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-564)) . T)) -((($ $) -2706 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) +((($ $) -2805 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T)) -((($) -2706 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) +((($) -2805 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) (|has| |#1| (-907)) ((((-860)) . T)) ((((-860)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-860)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (((|#1|) . T)) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-846))) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2706 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -(-2706 (|has| |#1| (-818)) (|has| |#1| (-848))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-846))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2805 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +(-2805 (|has| |#1| (-818)) (|has| |#1| (-848))) ((((-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) (((-564)) |has| |#1| (-1036 (-564))) ((|#1|) . T)) ((((-860)) . T)) ((((-860)) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-846)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) ((((-316 |#1|)) . T) (((-564)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-564)) . T) (((-868 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) -((($) . T) (((-407 (-564))) -2706 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) . T) (((-407 (-564))) -2805 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-407 (-564))) . T) (((-697)) . T) (($) . T)) ((((-860)) . T)) ((((-1178)) . T)) @@ -49,14 +49,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1178)) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-1036 (-564))) (((-407 (-564))) |has| |#1| (-1036 (-407 (-564))))) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) -(((|#2| (-482 (-2127 |#1|) (-769))) . T)) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) +(((|#2| (-482 (-2250 |#1|) (-769))) . T)) (((|#1| (-531 (-1173))) . T)) (((#0=(-868 |#1|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-1155)) . T) (((-956 (-129))) . T) (((-860)) . T)) ((((-860)) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (|has| |#4| (-368)) (|has| |#3| (-368)) (((|#1|) . T)) @@ -70,13 +70,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-556)) -((((-564)) . T) (((-407 (-564))) -2706 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1036 (-407 (-564))))) ((|#2|) . T) (($) -2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((-862 |#1|)) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) -((((-2 (|:| -2047 |#1|) (|:| -2700 |#2|))) . T)) +((((-564)) . T) (((-407 (-564))) -2805 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1036 (-407 (-564))))) ((|#2|) . T) (($) -2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((-862 |#1|)) . T)) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) +((((-2 (|:| -2145 |#1|) (|:| -4330 |#2|))) . T)) ((($) . T)) -((((-564)) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) ((|#1|) . T) (($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (((-1173)) . T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) +((((-564)) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) ((|#1|) . T) (($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (((-1173)) . T)) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) ((((-536)) |has| |#1| (-612 (-536)))) ((((-1173)) . T)) ((((-564)) . T) (($) . T)) @@ -96,12 +96,12 @@ (((|#1| |#2|) . T)) ((((-860)) . T)) (((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2706 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2805 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) (((|#1|) . T)) ((((-116 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) ((((-860)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) -((($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +((($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-116 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -109,45 +109,45 @@ ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (((|#2|) . T) (((-564)) . T) ((|#6|) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T) (($) -2706 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T) (($) -2805 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) ((($) . T)) (((|#2|) . T)) ((($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907)))) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907)))) ((($ $) . T)) ((($) . T)) ((((-564)) . T) (($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1254 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +((((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1254 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-368)) (((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +(((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . T)) -(-2706 (|has| |#1| (-848)) (|has| |#1| (-1097))) +(-2805 (|has| |#1| (-848)) (|has| |#1| (-1097))) (((|#1|) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-564)) . T)) ((((-860)) . T)) (((|#1| |#2|) . T)) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (((|#1|) . T) (((-564)) . T) (($) . T)) (|has| |#1| (-556)) (((|#1| |#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-846))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-846))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-848)) (|has| |#1| (-1097))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-848)) (|has| |#1| (-1097))) (|has| |#1| (-1097)) -(-2706 (|has| |#1| (-848)) (|has| |#1| (-1097))) +(-2805 (|has| |#1| (-848)) (|has| |#1| (-1097))) (|has| |#1| (-1097)) -(-2706 (|has| |#1| (-848)) (|has| |#1| (-1097))) +(-2805 (|has| |#1| (-848)) (|has| |#1| (-1097))) (|has| |#1| (-846)) ((($) . T) (((-407 (-564))) . T)) ((((-860)) . T)) @@ -156,12 +156,12 @@ ((((-564) (-129)) . T)) ((($) . T) (((-407 (-564))) . T)) ((((-129)) . T)) -(-2706 (|has| |#4| (-791)) (|has| |#4| (-846))) -(-2706 (|has| |#4| (-791)) (|has| |#4| (-846))) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) +(-2805 (|has| |#4| (-791)) (|has| |#4| (-846))) +(-2805 (|has| |#4| (-791)) (|has| |#4| (-846))) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) (((|#1| |#2|) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1178)) . T)) (((|#2| |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) (((-1173) |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-514 (-1173) |#2|)))) (((|#1| |#2|) . T)) @@ -177,39 +177,39 @@ ((((-564)) . T)) ((((-564)) . T)) (((|#1|) . T)) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) (((|#1| (-769)) . T)) (|has| |#2| (-791)) -(-2706 (|has| |#2| (-791)) (|has| |#2| (-846))) +(-2805 (|has| |#2| (-791)) (|has| |#2| (-846))) (|has| |#2| (-846)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1155) |#1|) . T)) ((((-564) (-129)) . T)) (((|#1|) . T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) (((|#3| (-769)) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) ((($) . T) (((-407 (-564))) . T)) ((($) . T)) ((($) . T)) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-407 (-564))) . T) (($) . T)) ((($) . T)) ((($) . T)) (|has| |#1| (-1097)) ((((-407 (-564))) . T) (((-564)) . T)) ((((-564)) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-1036 (-407 (-564))))) -((((-564)) . 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T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564)))))) (((|#1|) . T) (($) . T)) ((((-564)) . T)) ((((-564)) . T)) -((($) -2706 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) ((((-564)) . T)) ((((-564)) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -230,13 +230,13 @@ ((((-860)) . T)) ((((-860)) . T)) (((|#1| |#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907)))) -((($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1| |#1|) . 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T)) (|has| |#1| (-556)) (|has| |#1| (-556)) @@ -288,21 +288,21 @@ ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (-12 (|has| |#1| (-1097)) (|has| |#2| (-1097))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1171 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1171 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) ((((-536)) |has| |#1| (-612 (-536)))) ((((-860)) . T) (((-1178)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) ((((-1178)) . 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T)) (((|#1| (-969)) . T)) ((((-564)) . T) ((|#2|) . T)) @@ -349,7 +349,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1148)) -((((-2 (|:| -1907 (-1155)) (|:| -3778 |#1|))) . T)) +((((-2 (|:| -1993 (-1155)) (|:| -2806 |#1|))) . T)) (|has| (-1248 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1248 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -361,27 +361,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1122 |#1| (-1173))) . T) (((-564)) . T) (((-816 (-1173))) . T) (($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-1173)) . T)) +((((-1122 |#1| (-1173))) . T) (((-564)) . T) (((-816 (-1173))) . T) (($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-1173)) . 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T)) (|has| (-407 |#2|) (-147)) (|has| (-407 |#2|) (-145)) @@ -850,15 +850,15 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-860)) . T)) -((((-2 (|:| -1907 (-1155)) (|:| -3778 |#1|))) . T)) +((((-2 (|:| -1993 (-1155)) (|:| -2806 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|))) . T)) +((((-388) (-2 (|:| -1993 (-1155)) (|:| -2806 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1148)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-860)) . T) (((-1178)) . T)) ((((-860)) . T) (((-1178)) . T)) ((((-860)) . T) (((-1178)) . T)) @@ -876,7 +876,7 @@ ((((-388) (-1155)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (|has| |#2| (-846)) (-12 (|has| |#1| (-791)) (|has| |#2| (-791))) (-12 (|has| |#1| (-791)) (|has| |#2| (-791))) -(-2706 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-724)) (|has| |#2| (-724)))) +(-2805 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-724)) (|has| |#2| (-724)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-172)) ((|#4|) . T) (((-564)) . T)) (((|#2|) |has| |#2| (-172))) @@ -1003,7 +1003,7 @@ (((|#1|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) -((($) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-826)) ((((-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) (((-564)) |has| |#1| (-1036 (-564))) ((|#1|) . T)) (|has| |#1| (-1097)) @@ -1014,13 +1014,13 @@ (((|#4|) |has| |#4| (-1097))) (((|#3|) |has| |#3| (-1097))) (|has| |#3| (-368)) -((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-564)) . T)) -((((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2706 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1254 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-564)) . T)) +((((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1254 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) ((((-860)) . T)) ((((-860)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2706 (|has| |#1| (-363)) (|has| |#1| (-556)))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2805 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-363)) @@ -1028,19 +1028,19 @@ (((|#1|) |has| |#1| (-172))) ((((-407 (-564))) . T) (((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) -((($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((($) . T) (((-564)) . 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T)) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1047))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1047))) (((|#1|) |has| |#1| (-172))) (|has| $ (-147)) (|has| $ (-147)) @@ -1050,15 +1050,15 @@ ((((-860)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1047)) (|has| |#1| (-1109))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1047)) (|has| |#1| (-1109))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-1173)) . T)) (|has| |#1| (-556)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -1069,7 +1069,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-846)) -(((|#2| (-240 (-2127 |#1|) (-769)) (-862 |#1|)) . T)) +(((|#2| (-240 (-2250 |#1|) (-769)) (-862 |#1|)) . T)) (|has| |#3| (-846)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1084,20 +1084,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) -(-2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) -(-2706 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) +(-2805 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1139 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1047))) -(((|#2|) . T) (((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) +(((|#2|) . T) (((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) ((((-860)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-697)) . T)) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-846)) (|has| |#2| (-1047))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1121,11 +1121,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (((|#1|) . 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T)) @@ -1543,7 +1543,7 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) ((((-1254 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((#0=(-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) #0#) |has| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (-309 (-2 (|:| -1907 |#1|) (|:| -3778 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((#0=(-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) #0#) |has| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (-309 (-2 (|:| -1993 |#1|) (|:| -2806 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1097)) (|has| |#1| (-38 (-407 (-564)))) @@ -1555,14 +1555,14 @@ (((|#2|) . T)) (((|#1|) . 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T)) @@ -1588,19 +1588,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) #0#) |has| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (-309 (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097)))) -((($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) #0#) |has| (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)) (-309 (-2 (|:| -1993 |#1|) (|:| -2806 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097)))) +((($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-848)) (((|#2| (-769) (-1079)) . T)) (((|#1| |#2|) . T)) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-789)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2706 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-2706 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-2805 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-2805 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1155) |#1|) . T)) @@ -1614,24 +1614,24 @@ (((|#3|) . T)) ((((-1254 |#1| |#2| |#3|)) |has| |#1| (-363))) ((($) . T) (((-564)) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1171 |#1| |#2| |#3|)) |has| |#1| (-363)) (((-564)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097)))) @@ -1650,7 +1650,7 @@ ((((-564)) . T)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-2706 (|has| |#1| (-473)) (|has| |#1| (-724)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) +(-2805 (|has| |#1| (-473)) (|has| |#1| (-724)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) (|has| |#1| (-363)) ((((-860)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1661,8 +1661,8 @@ (|has| |#1| (-846)) ((((-860)) . T)) (((|#2|) . 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T)) -(((|#1|) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047))) (($) -2706 (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047))) (($) -2805 (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047)))) (((|#1|) . T) (((-564)) |has| |#1| (-1036 (-564))) (((-407 (-564))) |has| |#1| (-1036 (-407 (-564))))) (|has| |#1| (-848)) (|has| |#1| (-848)) @@ -1720,13 +1720,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1097)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1097)))) -(((|#3|) -2706 (|has| |#3| (-172)) (|has| |#3| (-363)))) -((($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -(-2706 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-907))) -((($) -2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) . 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T)) -(-2706 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-846)) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1744,14 +1744,14 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-1173)) |has| |#1| (-898 (-1173))) (((-1079)) . T)) (((|#1|) . 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T)) @@ -2463,10 +2463,10 @@ ((((-860)) . T)) ((((-860)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-1173) |#1|) |has| |#1| (-514 (-1173) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -2476,10 +2476,10 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-363))) -((($) -2706 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2706 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . 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T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-1248 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556)) (($) |has| |#1| (-556))) -((((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1|) . T)) +((((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1|) . T)) (|has| |#1| (-363)) -((($) |has| |#1| (-846)) (((-564)) -2706 (|has| |#1| (-21)) (|has| |#1| (-846)))) +((($) |has| |#1| (-846)) (((-564)) -2805 (|has| |#1| (-21)) (|has| |#1| (-846)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) @@ -2565,17 +2565,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097)))) (((|#2| |#3|) . 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T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-860)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-2706 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-2805 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-846)) @@ -2672,7 +2672,7 @@ ((((-860)) . T)) ((((-860)) . T)) ((((-187)) . T) (((-860)) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-860)) . T)) ((((-860)) . T)) @@ -2685,7 +2685,7 @@ ((((-860)) . T)) ((((-1155)) . T)) ((((-1173) |#1|) |has| |#1| (-514 (-1173) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -1907 (-1155)) (|:| -3778 |#1|))) . T)) +((((-2 (|:| -1993 (-1155)) (|:| -2806 |#1|))) . T)) (|has| |#1| (-848)) ((((-860)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2697,16 +2697,16 @@ (((|#2|) . T)) ((((-908 |#1|)) . 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T)) -(-2706 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-846)) (|has| |#2| (-1047))) (|has| |#1| (-907)) ((((-908 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-907)) @@ -2723,12 +2723,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (|has| |#1| (-818)) (((#0=(-908 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-846)) -((((-1198 |#1|)) . T) (((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-1198 |#1|)) . T) (((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-908 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1047)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1047)))) @@ -2744,28 +2744,28 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -1907 (-1173)) (|:| -3778 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1907 (-1173)) (|:| -3778 #0#))) . T)) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -1993 (-1173)) (|:| -2806 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1993 (-1173)) (|:| -2806 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-860)) . T)) (((|#1|) . T)) (((#0=(-1248 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) -(((|#1|) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047))) (($) -2706 (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) (((-564)) -2706 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047))) (($) -2805 (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047))) (((-564)) -2805 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-898 (-1173))) (|has| |#1| (-1047)))) (((#0=(-1079) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-697) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-860)) . T)) (|has| |#1| (-1097)) (((|#1|) . T)) -(((|#1|) -2706 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -2706 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2805 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2805 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-697)) . T) (($) . T)) ((((-579)) . T)) @@ -2790,7 +2790,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2834,7 +2834,7 @@ (|has| |#2| (-1020)) ((($) . T)) (|has| |#1| (-907)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2843,10 +2843,10 @@ (|has| |#1| (-363)) ((((-908 |#1|)) . T)) ((($) . T) (((-564)) . T) ((|#1|) . T) (((-407 (-564))) . T)) -((($) -2706 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) |has| |#1| (-846)) (((-564)) -2706 (|has| |#1| (-21)) (|has| |#1| (-846)))) +((($) -2805 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) |has| |#1| (-846)) (((-564)) -2805 (|has| |#1| (-21)) (|has| |#1| (-846)))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2706 (|has| |#1| (-368)) (|has| |#1| (-848))) +(-2805 (|has| |#1| (-368)) (|has| |#1| (-848))) (((|#1|) . T)) ((((-769)) . T)) ((((-860)) . T)) @@ -2857,17 +2857,17 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-769) |#1|) . T)) -(((|#2| (-240 (-2127 |#1|) (-769))) . T)) +(((|#2| (-240 (-2250 |#1|) (-769))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) +(-2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((((-1155)) . T) (((-860)) . T)) -(((#0=(-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) #0#) |has| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (-309 (-2 (|:| -1907 (-1173)) (|:| -3778 (-52)))))) +(((#0=(-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) #0#) |has| (-2 (|:| -1993 (-1173)) (|:| -2806 (-52))) (-309 (-2 (|:| -1993 (-1173)) (|:| -2806 (-52)))))) ((((-1155)) . T)) (|has| |#1| (-907)) (|has| |#2| (-363)) (((|#1|) . T) (($) . T) (((-564)) . T)) -(-2706 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-860)) . T)) (((|#1|) . T)) @@ -2884,11 +2884,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2706 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-826))) ((((-860)) . T)) -((((-1173)) -2706 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-898 (-1173)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-898 (-1173)))))) +((((-1173)) -2805 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-898 (-1173)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-898 (-1173)))))) (|has| |#1| (-363)) ((((-1173)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-898 (-1173))))) (|has| |#1| (-363)) @@ -2900,7 +2900,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2930,11 +2930,11 @@ (((|#2|) |has| |#1| (-363))) ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-884 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-884 (-564))))) (|has| |#1| (-363)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (((|#1|) . T)) ((($) . T) (((-564)) . T) ((|#2|) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (((|#3|) . T)) ((((-1155)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) @@ -2942,23 +2942,23 @@ (|has| |#1| (-556)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1097)))) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-2706 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) (((|#2|) . T)) (((|#2|) . T)) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) -((((-2 (|:| -1907 (-1155)) (|:| -3778 |#1|))) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) +((((-2 (|:| -1993 (-1155)) (|:| -2806 |#1|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) ((($) . T)) ((((-1155) |#1|) . T)) (|has| |#1| (-147)) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-368))) ((($) . T)) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) @@ -2972,7 +2972,7 @@ ((((-407 (-564))) |has| |#2| (-1036 (-564))) (((-564)) |has| |#2| (-1036 (-564))) (((-1173)) |has| |#2| (-1036 (-1173))) ((|#2|) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2706 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-860)) . T)) ((($) . T)) @@ -2997,7 +2997,7 @@ ((((-860)) . T)) ((((-908 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3019,7 +3019,7 @@ ((((-564)) . T)) ((((-860)) . T)) ((((-564)) . T)) -(-2706 (|has| |#2| (-791)) (|has| |#2| (-846))) +(-2805 (|has| |#2| (-791)) (|has| |#2| (-846))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-860)) . T)) ((((-860)) . T)) @@ -3031,9 +3031,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(((|#1|) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)))) (((|#1|) . T)) -(((|#1|) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1047)))) ((((-564)) . T) (((-407 (-564))) . T)) (((|#1|) . T)) (|has| |#1| (-556)) ((($) . T) (((-564)) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-363)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (|has| |#1| (-1097)) ((((-778 |#1| (-862 |#2|))) |has| (-778 |#1| (-862 |#2|)) (-309 (-778 |#1| (-862 |#2|))))) -(-2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) +(-2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3080,13 +3080,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -1907 (-1155)) (|:| -3778 (-52)))) . T)) +((((-2 (|:| -1993 (-1155)) (|:| -2806 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) ((((-860)) . T)) ((((-860)) . T)) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) ((((-860)) . T)) ((((-1117)) . T) (((-860)) . T)) ((((-536)) . T) (((-860)) . T)) @@ -3097,12 +3097,12 @@ ((((-564)) . T)) (((|#3|) . T)) ((((-860)) . T)) -(-2706 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) -((((-564)) . T) (((-407 (-564))) -2706 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1036 (-407 (-564))))) ((|#2|) . T) (($) -2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((-862 |#1|)) . T)) -((((-1122 |#1| |#2|)) . T) ((|#2|) . T) (($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) . T) (((-407 (-564))) -2706 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-564)) . T)) -((((-1169 |#1|)) . T) (((-564)) . T) (($) -2706 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (((-1079)) . T) ((|#1|) . 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T)) +((((-1169 |#1|)) . T) (((-564)) . T) (($) -2805 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) (((-1079)) . T) ((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564)))))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1047))) +((((-1122 |#1| (-1173))) . T) (((-564)) . T) (((-1085 (-1173))) . T) (($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) . T) (((-407 (-564))) -2805 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564))))) (((-1173)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -3120,7 +3120,7 @@ (((|#1|) . T)) ((((-860)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2706 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2805 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -3128,21 +3128,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -2706 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1| |#1|) . 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T)) @@ -3365,7 +3365,7 @@ (|has| |#1| (-1097)) (|has| |#1| (-1097)) (|has| |#2| (-363)) -(((|#1|) . T) (($) -2706 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -2805 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564)))) @@ -3374,32 +3374,32 @@ ((((-1173)) -12 (|has| |#3| (-898 (-1173))) (|has| |#3| (-1047)))) (((|#1|) . T)) (|has| |#1| (-233)) -(((|#2| (-240 (-2127 |#1|) (-769))) . T)) +(((|#2| (-240 (-2250 |#1|) (-769))) . T)) (((|#1| (-531 |#3|)) . T)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1|) . T) (($) . T)) (((|#1| (-531 |#2|)) . T)) -(-2706 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) (((|#1| (-769)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3606,17 +3606,17 @@ ((($) . T) (((-564)) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-860)) . T)) ((((-1254 |#1| |#2| |#3|)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) ((($) . T) (((-564)) . T)) -((($) -2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1101)) . T)) ((((-860)) . 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T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) ((((-1178)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1178)) . T)) @@ -3645,13 +3645,13 @@ ((((-1178)) . T)) ((((-1178)) . T)) ((((-1178)) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1178)) . T)) ((((-1178)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-2706 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-769)) . T)) @@ -3666,16 +3666,16 @@ ((((-890 (-379))) . T) (((-890 (-564))) . T) (((-1173)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-860)) . T)) -(-2706 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) -(-2706 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-791)) (|has| |#2| (-791)))) +(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-791)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-791)) (|has| |#2| (-791)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2706 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-724)) (|has| |#2| (-846)) (|has| |#2| (-1047))) ((((-1173)) -12 (|has| |#2| (-898 (-1173))) (|has| |#2| (-1047)))) -(-2706 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-724)) (|has| |#2| (-724)))) +(-2805 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-724)) (|has| |#2| (-724)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3706,7 +3706,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-2706 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2805 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3718,7 +3718,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-848)) (|has| |#1| (-1097)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-907)) (|has| |#1| (-907)) @@ -3729,14 +3729,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1178)) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-846))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-846))) (((|#2|) . T)) -(-2706 (|has| |#1| (-21)) (|has| |#1| (-846))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-846))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-860)) -2706 (-12 (|has| |#1| (-611 (-860))) (|has| |#2| (-611 (-860)))) (-12 (|has| |#1| (-1097)) (|has| |#2| (-1097))))) +((((-860)) -2805 (-12 (|has| |#1| (-611 (-860))) (|has| |#2| (-611 (-860)))) (-12 (|has| |#1| (-1097)) (|has| |#2| (-1097))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3750,19 +3750,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-2706 (|has| |#4| (-172)) (|has| |#4| (-724)) (|has| |#4| (-846)) (|has| |#4| (-1047))) -(-2706 (|has| |#3| (-172)) (|has| |#3| (-724)) (|has| |#3| (-846)) (|has| |#3| (-1047))) +(-2805 (|has| |#4| (-172)) (|has| |#4| (-724)) (|has| |#4| (-846)) (|has| |#4| (-1047))) +(-2805 (|has| |#3| (-172)) (|has| |#3| (-724)) (|has| |#3| (-846)) (|has| |#3| (-1047))) ((((-860)) . T) (((-1178)) . T)) (|has| |#4| (-791)) -(-2706 (|has| |#4| (-791)) (|has| |#4| (-846))) +(-2805 (|has| |#4| (-791)) (|has| |#4| (-846))) (|has| |#4| (-846)) (|has| |#3| (-791)) ((((-1178)) . T)) -(-2706 (|has| |#3| (-791)) (|has| |#3| (-846))) +(-2805 (|has| |#3| (-791)) (|has| |#3| (-846))) (|has| |#3| (-846)) ((((-564)) . T)) (((|#2|) . T)) -((((-1173)) -2706 (-12 (|has| (-1171 |#1| |#2| |#3|) (-898 (-1173))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-898 (-1173)))))) +((((-1173)) -2805 (-12 (|has| (-1171 |#1| |#2| |#3|) (-898 (-1173))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-898 (-1173)))))) ((((-1173)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-898 (-1173))))) ((((-1173)) -12 (|has| |#1| (-15 * (|#1| (-769) |#1|))) (|has| |#1| (-898 (-1173))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3777,11 +3777,11 @@ ((((-1171 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1137 |#1| |#2|)) . T)) ((((-1171 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) -((((-2 (|:| -1907 (-1173)) (|:| -3778 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) +((((-2 (|:| -1993 (-1173)) (|:| -2806 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1020)) -(((|#2|) . T) (((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) ((((-860)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-890 (-564))) |has| |#2| (-612 (-890 (-564)))) (((-890 (-379))) |has| |#2| (-612 (-890 (-379)))) (((-379)) . #0=(|has| |#2| (-1020))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3798,15 +3798,15 @@ ((((-1171 |#1| |#2| |#3|)) . T)) ((((-1171 |#1| |#2| |#3|)) . T) (((-1164 |#1| |#2| |#3|)) . T)) ((((-860)) . T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) ((((-564) |#1|) . T)) ((((-1171 |#1| |#2| |#3|)) |has| |#1| (-363))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-363)) -(((|#3|) . T) ((|#2|) . T) (($) -2706 (|has| |#4| (-172)) (|has| |#4| (-846)) (|has| |#4| (-1047))) ((|#4|) -2706 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1047)))) -(((|#2|) . T) (($) -2706 (|has| |#3| (-172)) (|has| |#3| (-846)) (|has| |#3| (-1047))) ((|#3|) -2706 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1047)))) +(((|#3|) . T) ((|#2|) . T) (($) -2805 (|has| |#4| (-172)) (|has| |#4| (-846)) (|has| |#4| (-1047))) ((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1047)))) +(((|#2|) . T) (($) -2805 (|has| |#3| (-172)) (|has| |#3| (-846)) (|has| |#3| (-1047))) ((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1047)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-363)) @@ -3821,7 +3821,7 @@ ((((-187)) . T) (((-860)) . T)) ((((-860)) . T)) (((|#1|) . T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) ((((-129)) . T) (((-860)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3830,13 +3830,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-907))) -(-2706 (|has| |#1| (-848)) (|has| |#1| (-1097))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-907))) +(-2805 (|has| |#1| (-848)) (|has| |#1| (-1097))) ((((-860)) . T)) ((((-860)) . T)) ((((-860)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -1907 (-1173)) (|:| -3778 (-52)))) . T)) +((((-2 (|:| -1993 (-1173)) (|:| -2806 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3851,8 +3851,8 @@ ((((-1178)) . T)) ((((-860)) . T) (((-1178)) . T)) ((((-860)) . T) (((-1178)) . T)) -(-2706 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) -(-2706 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) +(-2805 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) +(-2805 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-907))) ((($) . T)) (((|#2| (-531 (-862 |#1|))) . T)) ((((-1178)) . T)) @@ -3867,13 +3867,13 @@ ((((-1178)) . T)) ((((-860)) . T) (((-1178)) . T)) ((((-1178)) . T)) -((((-860)) -2706 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) +((((-860)) -2805 (|has| |#1| (-611 (-860))) (|has| |#1| (-1097)))) (((|#1|) . T)) (((|#2| (-769)) . T)) (((|#1| |#2|) . T)) ((((-1155) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -1907 |#1|) (|:| -3778 |#2|))) . T)) +((((-2 (|:| -1993 |#1|) (|:| -2806 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3884,14 +3884,14 @@ ((((-564)) . T) (($) . T)) (((|#2| $) |has| |#2| (-286 |#2| |#2|))) (((|#1| (-642 |#1|)) |has| |#1| (-846))) -(-2706 (|has| |#1| (-233)) (|has| |#1| (-349))) -(-2706 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-233)) (|has| |#1| (-349))) +(-2805 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1258 |#1|)) . T) (((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1036 (-407 (-564))))) (|has| |#1| (-1097)) (((|#1|) . T)) -((((-1258 |#1|)) . T) (((-564)) . T) (($) -2706 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((-1079)) . T) ((|#2|) . T) (((-407 (-564))) -2706 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1036 (-407 (-564)))))) +((((-1258 |#1|)) . T) (((-564)) . T) (($) -2805 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-907))) (((-1079)) . T) ((|#2|) . T) (((-407 (-564))) -2805 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1036 (-407 (-564)))))) ((((-407 (-564))) . T) (($) . T)) -((((-997 |#1|)) . T) ((|#1|) . T) (((-564)) -2706 (|has| (-997 |#1|) (-1036 (-564))) (|has| |#1| (-1036 (-564)))) (((-407 (-564))) -2706 (|has| (-997 |#1|) (-1036 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564)))))) +((((-997 |#1|)) . T) ((|#1|) . T) (((-564)) -2805 (|has| (-997 |#1|) (-1036 (-564))) (|has| |#1| (-1036 (-564)))) (((-407 (-564))) -2805 (|has| (-997 |#1|) (-1036 (-407 (-564)))) (|has| |#1| (-1036 (-407 (-564)))))) ((((-908 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) @@ -3907,10 +3907,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1137 |#1| |#2|) #0#) |has| (-1137 |#1| |#2|) (-309 (-1137 |#1| |#2|)))) (((|#1|) . 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. -611) 184050) ((-388 . -102) T) ((-1117 . -143) T) ((-126 . -611) 183982) ((-872 . -1097) T) ((-656 . -411) 183966) ((-712 . -611) 183948) ((-249 . -611) 183915) ((-187 . -611) 183897) ((-162 . -611) 183879) ((-157 . -611) 183861) ((-1277 . -724) T) ((-1099 . -34) T) ((-869 . -793) NIL) ((-869 . -790) NIL) ((-856 . -848) T) ((-729 . -884) NIL) ((-1286 . -131) T) ((-381 . -131) T) ((-890 . -614) 183829) ((-902 . -102) T) ((-729 . -1036) 183705) ((-531 . -131) T) ((-1084 . -411) 183689) ((-998 . -489) 183673) ((-117 . -400) 183650) ((-1164 . -1212) 183629) ((-780 . -411) 183613) ((-778 . -411) 183597) ((-941 . -34) T) ((-692 . -1148) NIL) ((-251 . -646) 183432) ((-250 . -646) 183254) ((-815 . -918) 183233) ((-454 . -411) 183217) ((-600 . -19) 183201) ((-1143 . -1205) 183170) ((-1164 . -884) NIL) ((-1164 . -882) 183122) ((-600 . -602) 183099) ((-1198 . -611) 183031) ((-1172 . -611) 183013) ((-62 . -395) T) ((-1170 . -1036) 182948) ((-1164 . -1036) 182914) ((-692 . -38) 182864) ((-40 . -644) 182794) ((-474 . -286) 182779) ((-1218 . -611) 182761) ((-729 . -377) 182745) ((-836 . -611) 182727) ((-656 . -1055) T) ((-1246 . -1000) 182693) ((-1225 . -1000) 182659) ((-1085 . -614) 182643) ((-1060 . -1188) 182618) ((-1073 . -614) 182595) ((-870 . -612) 182402) ((-870 . -611) 182384) ((-1185 . -489) 182321) ((-418 . -1020) 182299) ((-48 . -309) 182286) ((-1060 . -107) 182232) ((-479 . -489) 182169) ((-520 . -1212) T) ((-1164 . -338) 182121) ((-1138 . -489) 182092) ((-1164 . -377) 182044) ((-1084 . -1055) T) ((-437 . -102) T) ((-183 . -1097) T) ((-251 . -34) T) ((-250 . -34) T) ((-780 . -1055) T) ((-778 . -1055) T) ((-729 . -898) 182021) ((-454 . -1055) T) ((-59 . -489) 182005) ((-1032 . -1054) 181979) ((-519 . -489) 181963) ((-516 . -489) 181947) ((-497 . -489) 181931) ((-496 . -489) 181915) ((-245 . -514) 181848) ((-1032 . -111) 181815) ((-1171 . -898) 181728) ((-1170 . -898) 181634) ((-1164 . -898) 181467) ((-1123 . -898) 181451) ((-668 . -1109) T) ((-354 . -1148) T) ((-643 . -93) T) ((-322 . -1054) 181433) ((-251 . -789) 181412) ((-251 . -792) 181363) ((-31 . -490) 181344) ((-251 . -791) 181323) ((-250 . -789) 181302) ((-250 . -792) 181253) ((-250 . -791) 181232) ((-31 . -611) 181198) ((-50 . -1055) T) ((-251 . -724) 181108) ((-250 . -724) 181018) ((-1206 . -1097) T) ((-668 . -23) T) ((-581 . -1055) T) ((-518 . -1055) T) ((-379 . -1054) 180983) ((-322 . -111) 180958) ((-73 . -383) T) ((-73 . -395) T) ((-1022 . -38) 180895) ((-692 . -400) 180877) ((-99 . -102) T) ((-709 . -1097) T) ((-1290 . -1049) 180864) ((-1001 . -145) 180836) ((-1001 . -147) 180808) ((-868 . -644) 180780) ((-379 . -111) 180736) ((-319 . -1216) 180715) ((-474 . -1000) 180681) ((-354 . -38) 180646) ((-40 . -370) 180618) ((-871 . -611) 180490) ((-127 . -125) 180474) ((-121 . -125) 180458) ((-834 . -1054) 180428) ((-831 . -21) 180380) ((-825 . -1054) 180364) ((-831 . -25) 180316) ((-319 . -556) 180267) ((-517 . -614) 180248) ((-564 . -826) T) ((-240 . -1212) T) ((-1032 . -614) 180217) ((-834 . -111) 180182) ((-825 . -111) 180161) ((-1246 . -611) 180143) ((-1225 . -611) 180125) ((-1225 . -612) 179796) ((-1169 . -907) 179775) ((-1122 . -907) 179754) ((-48 . -38) 179719) ((-1284 . -1109) T) ((-600 . -611) 179631) ((-600 . -612) 179592) ((-1282 . -1109) T) ((-361 . -614) 179576) ((-322 . -614) 179560) ((-240 . -1036) 179387) ((-1169 . -646) 179312) ((-1122 . -646) 179237) ((-852 . -646) 179211) ((-716 . -611) 179193) ((-546 . -368) T) ((-1284 . -23) T) ((-1282 . -23) T) ((-491 . -1097) T) ((-379 . -614) 179143) ((-379 . -616) 179125) ((-1032 . -1047) T) ((-863 . -102) T) ((-1185 . -286) 179104) ((-169 . -368) 179055) ((-1002 . -1212) T) ((-834 . -614) 179009) ((-825 . -614) 178964) ((-44 . -23) T) ((-479 . -286) 178943) ((-585 . -1097) T) ((-1143 . -1106) 178912) ((-1101 . -1100) 178864) ((-390 . -21) T) ((-390 . -25) T) ((-152 . -1109) T) ((-1290 . -102) T) ((-1002 . -882) 178846) ((-1002 . -884) 178828) ((-1206 . -715) 178725) ((-621 . -231) 178709) ((-619 . -21) T) ((-289 . -556) T) ((-619 . -25) T) ((-1192 . -1097) T) ((-709 . -715) 178674) ((-240 . -377) 178643) ((-1002 . -1036) 178603) ((-379 . -1047) T) ((-223 . -1055) T) ((-117 . -231) 178580) ((-59 . -286) 178557) ((-152 . -23) T) ((-516 . -286) 178534) ((-327 . -514) 178467) ((-496 . -286) 178444) ((-379 . -243) T) ((-379 . -233) T) ((-834 . -1047) T) ((-825 . -1047) T) ((-710 . -947) 178413) ((-699 . -848) T) ((-474 . -611) 178395) ((-1248 . -1049) 178300) ((-580 . -644) 178272) ((-564 . -644) 178244) ((-495 . -644) 178194) ((-825 . -233) 178173) ((-134 . -848) T) ((-1248 . -638) 178065) ((-656 . -1097) T) ((-1185 . -602) 178044) ((-550 . -1188) 178023) ((-336 . -1097) T) ((-319 . -363) 178002) ((-407 . -147) 177981) ((-407 . -145) 177960) ((-962 . -1109) 177859) ((-240 . -898) 177791) ((-813 . -1109) 177701) ((-652 . -850) 177685) ((-479 . -602) 177664) ((-550 . -107) 177614) ((-1002 . -377) 177596) ((-1002 . -338) 177578) ((-97 . -1097) T) ((-962 . -23) 177389) ((-477 . -21) T) ((-477 . -25) T) ((-813 . -23) 177259) ((-1173 . -611) 177241) ((-59 . -19) 177225) ((-1173 . -612) 177147) ((-1169 . -724) T) ((-1122 . -724) T) ((-516 . -19) 177131) ((-496 . -19) 177115) ((-59 . -602) 177092) ((-1084 . -1097) T) ((-899 . -102) 177070) ((-852 . -724) T) ((-780 . -1097) T) ((-516 . -602) 177047) ((-496 . -602) 177024) ((-778 . -1097) T) ((-778 . -1062) 176991) ((-461 . -1097) T) ((-454 . -1097) T) ((-585 . -715) 176966) ((-647 . -1097) T) ((-1254 . -47) 176943) ((-1248 . -102) T) ((-1247 . -47) 176913) ((-1226 . -47) 176890) ((-1206 . -172) 176841) ((-1170 . -307) 176820) ((-1164 . -307) 176799) ((-1093 . -614) 176780) ((-1087 . -614) 176761) ((-1077 . -556) 176712) ((-1002 . -898) NIL) ((-1077 . -1216) 176663) ((-668 . -131) T) ((-625 . -1109) T) ((-1070 . -614) 176644) ((-1063 . -614) 176625) ((-1034 . -614) 176606) ((-1017 . -614) 176587) ((-697 . -644) 176537) ((-275 . -1097) T) ((-85 . -441) T) ((-85 . -395) T) ((-712 . -1054) 176507) ((-709 . -172) T) ((-50 . -1097) T) 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((-1226 . -882) 175661) ((-1084 . -715) 175510) ((-1059 . -646) 175497) ((-950 . -646) 175422) ((-780 . -715) 175251) ((-536 . -611) 175233) ((-536 . -612) 175214) ((-778 . -715) 175063) ((-1074 . -102) T) ((-381 . -25) T) ((-621 . -644) 175035) ((-381 . -21) T) ((-481 . -646) 174960) ((-461 . -715) 174931) ((-454 . -715) 174780) ((-985 . -102) T) ((-1226 . -1036) 174746) ((-1185 . -612) NIL) ((-1185 . -611) 174728) ((-735 . -102) T) ((-117 . -644) 174658) ((-603 . -614) 174640) ((-1139 . -1120) 174585) ((-1044 . -1205) 174514) ((-531 . -25) T) ((-899 . -309) 174452) ((-712 . -614) 174406) ((-679 . -93) T) ((-643 . -490) 174387) ((-141 . -102) T) ((-44 . -131) T) ((-674 . -93) T) ((-662 . -611) 174369) ((-343 . -1055) T) ((-289 . -1109) T) ((-643 . -611) 174322) ((-478 . -93) T) ((-355 . -611) 174304) ((-352 . -611) 174286) ((-344 . -611) 174268) ((-264 . -612) 174016) ((-264 . -611) 173998) ((-247 . -611) 173980) ((-247 . -612) 173841) ((-133 . -93) T) ((-138 . -93) T) ((-137 . -93) T) ((-1206 . -514) 173808) ((-1138 . -611) 173790) ((-1117 . -638) 173777) ((-817 . -855) T) ((-817 . -724) T) ((-600 . -288) 173754) ((-581 . -715) 173719) ((-479 . -612) NIL) ((-479 . -611) 173701) ((-518 . -715) 173646) ((-316 . -102) T) ((-313 . -102) T) ((-289 . -23) T) ((-152 . -131) T) ((-1117 . -1049) 173633) ((-908 . -611) 173615) ((-386 . -724) T) ((-870 . -1054) 173567) ((-908 . -612) 173549) ((-870 . -111) 173487) ((-712 . -1047) T) ((-710 . -1238) 173471) ((-692 . -349) NIL) ((-136 . -102) T) ((-114 . -102) T) ((-139 . -102) T) ((-519 . -611) 173403) ((-379 . -793) T) ((-223 . -1097) T) ((-379 . -790) T) ((-225 . -792) T) ((-225 . -789) T) ((-59 . -612) 173364) ((-59 . -611) 173276) ((-225 . -724) T) ((-516 . -612) 173237) ((-516 . -611) 173149) ((-497 . -611) 173081) ((-496 . -612) 173042) ((-496 . -611) 172954) ((-1077 . -363) 172905) ((-40 . -411) 172882) ((-77 . -1212) T) ((-869 . -907) NIL) ((-359 . -329) 172866) ((-359 . -363) T) ((-353 . -329) 172850) ((-353 . -363) T) ((-345 . -329) 172834) ((-345 . -363) T) ((-316 . -284) 172813) ((-108 . -363) T) ((-70 . -1212) T) ((-1226 . -338) 172765) ((-869 . -646) 172710) ((-1226 . -377) 172662) ((-962 . -131) 172517) ((-813 . -131) 172387) ((-956 . -649) 172371) ((-1084 . -172) 172282) ((-956 . -373) 172266) ((-1059 . -792) T) ((-1059 . -789) T) ((-870 . -614) 172164) ((-780 . -172) 172055) ((-778 . -172) 171966) ((-814 . -47) 171928) ((-1059 . -724) T) ((-327 . -489) 171912) ((-950 . -724) T) ((-454 . -172) 171823) ((-245 . -286) 171800) ((-1275 . -309) 171738) ((-1254 . -898) 171651) ((-1247 . -898) 171557) ((-481 . -724) T) ((-1246 . -1054) 171392) ((-1226 . -898) 171225) ((-1225 . -1054) 171033) ((-1206 . -290) 171012) ((-1182 . -1212) T) ((-1180 . -368) T) ((-1179 . -368) T) ((-1143 . -151) 170996) ((-1117 . -102) T) ((-1115 . -1097) T) ((-1077 . -23) T) ((-1077 . -1109) T) ((-1072 . -102) T) ((-925 . -953) T) ((-735 . -309) 170934) ((-75 . -1212) T) ((-30 . -953) T) ((-169 . -907) 170887) ((-662 . -382) 170859) ((-112 . -842) T) ((-1 . -611) 170841) ((-1001 . -409) 170813) ((-128 . -649) 170795) ((-50 . -618) 170779) ((-692 . -644) 170714) ((-594 . -898) 170627) ((-438 . -102) T) ((-128 . -373) 170609) ((-141 . -309) NIL) ((-870 . -1047) T) ((-831 . -848) 170588) ((-81 . -1212) T) ((-709 . -290) T) ((-40 . -1055) T) ((-581 . -172) T) ((-518 . -172) T) ((-511 . -611) 170570) ((-169 . -646) 170480) ((-507 . -611) 170462) ((-351 . -147) 170444) ((-351 . -145) T) ((-359 . -1109) T) ((-353 . -1109) T) ((-345 . -1109) T) ((-1002 . -307) T) ((-912 . -307) T) ((-870 . -243) T) ((-108 . -1109) T) ((-870 . -233) 170423) ((-1246 . -111) 170244) ((-1225 . -111) 170033) ((-245 . -1250) 170017) ((-564 . -846) T) ((-359 . -23) T) ((-354 . -349) T) ((-316 . -309) 170004) ((-313 . -309) 169945) ((-353 . -23) T) ((-319 . -131) T) ((-345 . -23) T) ((-1002 . -1020) T) ((-31 . -614) 169926) ((-108 . -23) T) ((-652 . -1049) 169910) ((-245 . -602) 169887) ((-652 . -638) 169857) ((-1248 . -38) 169749) ((-1235 . -907) 169728) ((-112 . -1097) T) ((-1033 . -102) T) ((-1235 . -646) 169653) ((-869 . -792) NIL) ((-853 . -646) 169627) ((-869 . -789) NIL) ((-814 . -884) NIL) ((-869 . -724) T) ((-1084 . -514) 169500) ((-780 . -514) 169447) ((-778 . -514) 169399) ((-571 . -646) 169386) ((-814 . -1036) 169214) ((-454 . -514) 169157) ((-388 . -389) T) ((-1246 . -614) 168970) ((-1225 . -614) 168718) ((-60 . -1212) T) ((-619 . -848) 168697) ((-500 . -659) T) ((-1143 . -974) 168666) ((-1022 . -644) 168603) ((-1001 . -452) T) ((-697 . -846) T) ((-510 . -790) T) ((-474 . -1054) 168438) ((-343 . -1097) T) ((-313 . -1148) NIL) ((-289 . -131) T) ((-394 . -1097) T) ((-868 . -1055) T) ((-692 . -370) 168405) ((-354 . -644) 168335) ((-223 . -618) 168312) ((-327 . -286) 168289) ((-474 . -111) 168110) ((-1246 . -1047) T) ((-1225 . -1047) T) ((-814 . -377) 168094) ((-169 . -724) T) ((-652 . -102) T) ((-1246 . -243) 168073) ((-1246 . -233) 168025) ((-1225 . -233) 167930) ((-1225 . -243) 167909) ((-1001 . -402) NIL) ((-668 . -637) 167857) ((-316 . -38) 167767) ((-313 . -38) 167696) ((-69 . -611) 167678) ((-319 . -493) 167644) ((-48 . -644) 167594) ((-1185 . -288) 167573) ((-1220 . -848) T) ((-1110 . -1109) 167483) ((-83 . -1212) T) ((-61 . -611) 167465) ((-479 . -288) 167444) ((-1277 . -1036) 167421) ((-1161 . -1097) T) ((-1110 . -23) 167291) ((-814 . -898) 167227) ((-1235 . -724) T) ((-1099 . -1212) T) ((-474 . -614) 167053) ((-1084 . -290) 166984) ((-964 . -1097) T) ((-891 . -102) T) ((-780 . -290) 166895) ((-327 . -19) 166879) ((-59 . -288) 166856) ((-778 . -290) 166787) ((-853 . -724) T) ((-117 . -846) NIL) ((-516 . -288) 166764) ((-327 . -602) 166741) ((-496 . -288) 166718) ((-454 . -290) 166649) ((-1033 . -309) 166500) ((-679 . -490) 166481) ((-571 . -724) T) ((-674 . -490) 166462) ((-679 . -611) 166412) ((-674 . -611) 166378) ((-660 . -611) 166360) ((-478 . -490) 166341) ((-478 . -611) 166307) ((-245 . -612) 166268) ((-245 . -490) 166245) ((-138 . -490) 166226) ((-137 . -490) 166207) ((-133 . -490) 166188) ((-245 . -611) 166080) ((-213 . -102) T) ((-138 . -611) 166046) ((-137 . -611) 166012) ((-133 . -611) 165978) ((-1144 . -34) T) ((-941 . -1212) T) ((-343 . -715) 165923) ((-668 . -25) T) ((-668 . -21) T) ((-1173 . -614) 165904) ((-474 . -1047) T) ((-633 . -417) 165869) ((-605 . -417) 165834) ((-1117 . -1148) T) ((-710 . -1049) 165657) ((-581 . -290) T) ((-518 . -290) T) ((-1247 . -307) 165636) ((-474 . -233) 165588) ((-474 . -243) 165567) ((-1226 . -307) 165546) ((-710 . -638) 165375) ((-1226 . -1020) NIL) ((-1077 . -131) T) ((-870 . -793) 165354) ((-144 . -102) T) ((-40 . -1097) T) ((-870 . -790) 165333) ((-642 . -1008) 165317) ((-580 . -1055) T) ((-564 . -1055) T) ((-495 . -1055) T) ((-407 . -452) T) ((-359 . -131) T) ((-316 . -400) 165301) ((-313 . -400) 165262) ((-353 . -131) T) ((-345 . -131) T) ((-1178 . -1097) T) ((-1117 . -38) 165249) ((-1091 . -611) 165216) ((-108 . -131) T) ((-952 . -1097) T) ((-919 . -1097) T) ((-769 . -1097) T) ((-670 . -1097) T) ((-699 . -147) T) ((-116 . -147) T) ((-1284 . -21) T) ((-1284 . -25) T) ((-1282 . -21) T) ((-1282 . -25) T) ((-662 . -1054) 165200) ((-531 . -848) T) ((-500 . -848) T) ((-355 . -1054) 165152) ((-352 . -1054) 165104) ((-344 . -1054) 165056) ((-251 . -1212) T) ((-250 . -1212) T) ((-264 . -1054) 164899) ((-247 . -1054) 164742) ((-662 . -111) 164721) ((-547 . -842) T) ((-355 . -111) 164659) ((-352 . -111) 164597) ((-344 . -111) 164535) ((-264 . -111) 164364) ((-247 . -111) 164193) ((-815 . -1216) 164172) ((-621 . -411) 164156) ((-44 . -21) T) ((-44 . -25) T) ((-813 . -637) 164062) ((-815 . -556) 164041) ((-251 . -1036) 163868) ((-250 . -1036) 163695) ((-126 . -119) 163679) ((-908 . -1054) 163644) ((-710 . -102) T) ((-697 . -1055) T) ((-536 . -616) 163547) ((-343 . -172) T) ((-88 . -611) 163529) ((-152 . -21) T) ((-152 . -25) T) ((-908 . -111) 163485) ((-40 . -715) 163430) ((-868 . -1097) T) ((-662 . -614) 163407) ((-643 . -614) 163388) ((-355 . -614) 163325) ((-352 . -614) 163262) ((-547 . -1097) T) ((-344 . -614) 163199) ((-327 . -612) 163160) ((-327 . -611) 163072) ((-264 . -614) 162825) ((-247 . -614) 162610) ((-1225 . -790) 162563) ((-1225 . -793) 162516) ((-251 . -377) 162485) ((-250 . -377) 162454) ((-652 . -38) 162424) ((-606 . -34) T) ((-482 . -1109) 162334) ((-475 . -34) T) ((-1110 . -131) 162204) ((-962 . -25) 162015) ((-908 . -614) 161965) ((-872 . -611) 161947) ((-962 . -21) 161902) ((-813 . -21) 161812) ((-813 . -25) 161663) ((-1218 . -368) T) ((-621 . -1055) T) ((-1175 . -556) 161642) ((-1169 . -47) 161619) ((-355 . -1047) T) ((-352 . -1047) T) ((-482 . -23) 161489) ((-344 . -1047) T) ((-264 . -1047) T) ((-247 . -1047) T) ((-1122 . -47) 161461) ((-117 . -1055) T) ((-1032 . -646) 161435) ((-956 . -34) T) ((-355 . -233) 161414) ((-355 . -243) T) ((-352 . -233) 161393) ((-352 . -243) T) ((-344 . -233) 161372) ((-344 . -243) T) ((-264 . -326) 161344) ((-247 . -326) 161301) ((-264 . -233) 161280) ((-1153 . -151) 161264) ((-251 . -898) 161196) ((-250 . -898) 161128) ((-1079 . -848) T) ((-414 . -1109) T) ((-1052 . -23) T) ((-908 . -1047) T) ((-322 . -646) 161110) ((-1022 . -846) T) ((-1206 . -1000) 161076) ((-1170 . -918) 161055) ((-1164 . -918) 161034) ((-1164 . -818) NIL) ((-997 . -1049) 160930) ((-908 . -243) T) ((-815 . -363) 160909) ((-385 . -23) T) ((-127 . -1097) 160887) ((-121 . -1097) 160865) ((-908 . -233) T) ((-128 . -34) T) ((-379 . -646) 160830) ((-997 . -638) 160778) ((-868 . -715) 160765) ((-1290 . -644) 160737) ((-1044 . -151) 160702) ((-40 . -172) T) ((-692 . -411) 160684) ((-710 . -309) 160671) ((-834 . -646) 160631) ((-825 . -646) 160605) ((-319 . -25) T) ((-319 . -21) T) ((-656 . -286) 160584) ((-580 . -1097) T) ((-564 . -1097) T) ((-495 . -1097) T) ((-245 . -288) 160561) ((-313 . -231) 160522) ((-1169 . -884) NIL) ((-55 . -1097) T) ((-1122 . -884) 160381) ((-129 . -848) T) ((-1169 . -1036) 160261) ((-1122 . -1036) 160144) ((-183 . -611) 160126) ((-852 . -1036) 160022) ((-780 . -286) 159949) ((-815 . -1109) T) ((-1032 . 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. -724) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1123 . -556) 146573) ((-354 . -290) T) ((-645 . -693) 146557) ((-379 . -1036) 146517) ((-294 . -1049) 146438) ((-1117 . -1055) T) ((-103 . -125) 146422) ((-294 . -638) 146364) ((-797 . -23) T) ((-1284 . -1279) 146340) ((-1262 . -286) 146317) ((-407 . -309) 146282) ((-1282 . -1279) 146261) ((-1248 . -1097) T) ((-868 . -611) 146243) ((-834 . -1036) 146212) ((-203 . -785) T) ((-202 . -785) T) ((-201 . -785) T) ((-200 . -785) T) ((-199 . -785) T) ((-198 . -785) T) ((-197 . -785) T) ((-196 . -785) T) ((-195 . -785) T) ((-194 . -785) T) ((-547 . -611) 146194) ((-495 . -1000) T) ((-274 . -837) T) ((-273 . -837) T) ((-272 . -837) T) ((-271 . -837) T) ((-48 . -290) T) ((-270 . -837) T) ((-269 . -837) T) ((-268 . -837) T) ((-193 . -785) T) ((-610 . -848) T) ((-652 . -411) 146178) ((-223 . -614) 146140) ((-110 . -848) T) ((-651 . -21) T) ((-651 . -25) T) ((-1285 . -38) 146110) ((-117 . -286) 146061) ((-1262 . -19) 146045) ((-1262 . -602) 146022) ((-1275 . -1097) T) ((-351 . -1049) 145967) ((-1074 . -1097) T) ((-985 . -1097) T) ((-961 . -131) T) ((-735 . -1097) T) ((-351 . -638) 145912) ((-733 . -131) T) ((-713 . -131) T) ((-511 . -791) T) ((-511 . -792) T) ((-453 . -131) T) ((-407 . -1148) 145890) ((-223 . -1047) T) ((-294 . -102) 145672) ((-141 . -1097) T) ((-697 . -1000) T) ((-91 . -1212) T) ((-127 . -611) 145604) ((-121 . -611) 145536) ((-1290 . -172) T) ((-1170 . -363) 145515) ((-1164 . -363) 145494) ((-316 . -1097) T) ((-418 . -131) T) ((-313 . -1097) T) ((-407 . -38) 145446) ((-1130 . -102) T) ((-1248 . -715) 145338) ((-652 . -1055) T) ((-1132 . -1257) T) ((-319 . -145) 145317) ((-319 . -147) 145296) ((-136 . -1097) T) ((-139 . -1097) T) ((-114 . -1097) T) ((-856 . -102) T) ((-580 . -611) 145278) ((-564 . -612) 145177) ((-564 . -611) 145159) ((-495 . -611) 145141) ((-495 . -612) 145086) ((-485 . -23) T) ((-482 . -848) 145037) ((-487 . -637) 145019) ((-963 . -611) 145001) ((-217 . 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. -1049) 141312) ((-474 . -47) 141282) ((-134 . -102) T) ((-40 . -233) 141254) ((-40 . -243) T) ((-116 . -102) T) ((-594 . -556) 141233) ((-339 . -638) 141217) ((-692 . -612) 141125) ((-316 . -514) 141091) ((-174 . -638) 141023) ((-313 . -514) 140915) ((-1246 . -1036) 140899) ((-1225 . -1036) 140685) ((-997 . -411) 140669) ((-427 . -23) T) ((-1117 . -172) T) ((-1248 . -290) T) ((-652 . -715) 140639) ((-144 . -1097) T) ((-48 . -1000) T) ((-407 . -231) 140623) ((-295 . -235) 140573) ((-869 . -918) T) ((-869 . -818) NIL) ((-868 . -614) 140545) ((-862 . -848) T) ((-1225 . -338) 140515) ((-1225 . -377) 140485) ((-222 . -1118) 140469) ((-1262 . -288) 140446) ((-1206 . -646) 140371) ((-1001 . -644) 140301) ((-961 . -21) T) ((-961 . -25) T) ((-733 . -21) T) ((-733 . -25) T) ((-713 . -21) T) ((-713 . -25) T) ((-709 . -646) 140266) ((-453 . -21) T) ((-453 . -25) T) ((-339 . -102) T) ((-174 . -102) T) ((-997 . -1055) T) ((-868 . -1047) T) ((-772 . -102) T) ((-1247 . -363) 140245) ((-1246 . -898) 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-235) 137864) ((-1084 . -907) 137843) ((-116 . -38) 137830) ((-209 . -798) T) ((-208 . -798) T) ((-207 . -798) T) ((-206 . -798) T) ((-870 . -1020) 137808) ((-1275 . -489) 137792) ((-780 . -907) 137771) ((-778 . -907) 137750) ((-1185 . -1212) T) ((-454 . -907) 137729) ((-735 . -489) 137713) ((-1084 . -646) 137638) ((-697 . -614) 137573) ((-780 . -646) 137498) ((-621 . -1054) 137485) ((-479 . -1212) T) ((-343 . -368) T) ((-141 . -489) 137467) ((-778 . -646) 137392) ((-1138 . -1212) T) ((-549 . -848) T) ((-461 . -646) 137363) ((-264 . -884) 137222) ((-247 . -884) NIL) ((-117 . -1054) 137167) ((-454 . -646) 137092) ((-662 . -1036) 137069) ((-621 . -111) 137054) ((-390 . -1049) 137038) ((-355 . -1036) 137022) ((-352 . -1036) 137006) ((-344 . -1036) 136990) ((-264 . -1036) 136834) ((-247 . -1036) 136710) ((-117 . -111) 136639) ((-59 . -1212) T) ((-390 . -638) 136623) ((-619 . -1049) 136607) ((-519 . -1212) T) ((-516 . -1212) T) ((-497 . -1212) T) ((-496 . -1212) T) ((-437 . -611) 136589) 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-898) 135364) ((-247 . -898) 135341) ((-117 . -1047) T) ((-814 . -1109) T) ((-1084 . -724) T) ((-621 . -233) 135320) ((-619 . -102) T) ((-780 . -724) T) ((-778 . -724) T) ((-413 . -1109) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1217 . -848) T) ((-454 . -724) T) ((-814 . -23) T) ((-729 . -25) T) ((-729 . -21) T) ((-1074 . -286) 135299) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -765) 135281) ((-692 . -1054) 135231) ((-1254 . -131) T) ((-1247 . -131) T) ((-1226 . -131) T) ((-1171 . -25) T) ((-1139 . -411) 135215) ((-633 . -367) 135147) ((-605 . -367) 135079) ((-1153 . -1146) 135063) ((-103 . -1097) 135041) ((-1171 . -21) T) ((-1170 . -21) T) ((-863 . -611) 135023) ((-997 . -715) 134971) ((-223 . -646) 134938) ((-692 . -111) 134872) ((-50 . -724) T) ((-1170 . -25) T) ((-351 . -349) T) ((-1164 . -21) T) ((-1077 . -452) 134823) ((-1164 . -25) T) ((-710 . -514) 134770) ((-581 . -724) T) ((-518 . -724) T) ((-1123 . -21) T) ((-1123 . -25) T) ((-595 . -131) T) ((-294 . 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. -286) 132157) ((-1163 . -1080) T) ((-992 . -1080) T) ((-814 . -131) T) ((-117 . -793) NIL) ((-117 . -790) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1109) 132067) ((-250 . -1109) 131977) ((-1022 . -1047) T) ((-1001 . -1055) T) ((-48 . -614) 131910) ((-343 . -646) 131855) ((-619 . -38) 131839) ((-1275 . -611) 131801) ((-1275 . -612) 131762) ((-1074 . -611) 131744) ((-1022 . -243) T) ((-354 . -1047) T) ((-813 . -1269) 131714) ((-251 . -23) T) ((-250 . -23) T) ((-985 . -611) 131696) ((-735 . -612) 131657) ((-735 . -611) 131639) ((-797 . -848) 131618) ((-1156 . -151) 131565) ((-997 . -514) 131477) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 131458) ((-1002 . -25) T) ((-141 . -611) 131440) ((-141 . -612) 131399) ((-908 . -307) T) ((-1002 . -21) T) ((-969 . -25) T) ((-912 . -21) T) ((-912 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-841 . -411) 131383) ((-48 . -1047) T) ((-1284 . -1276) 131367) ((-1282 . -1276) 131351) ((-1033 . -602) 131326) ((-316 . 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-848) 128983) ((-1044 . -1097) T) ((-815 . -452) 128962) ((-152 . -1049) 128946) ((-1044 . -1068) 128875) ((-1025 . -974) 128844) ((-817 . -1109) T) ((-1001 . -715) 128789) ((-152 . -638) 128773) ((-386 . -1109) T) ((-476 . -974) 128742) ((-463 . -974) 128711) ((-110 . -151) 128693) ((-73 . -611) 128675) ((-891 . -611) 128657) ((-1077 . -722) 128636) ((-1290 . -1047) T) ((-814 . -637) 128584) ((-294 . -1055) 128526) ((-169 . -1216) 128431) ((-225 . -1109) T) ((-324 . -23) T) ((-1164 . -990) 128383) ((-841 . -1097) T) ((-1248 . -1054) 128288) ((-1123 . -738) 128267) ((-1246 . -918) 128246) ((-1225 . -918) 128225) ((-868 . -724) T) ((-169 . -556) 128136) ((-580 . -646) 128123) ((-564 . -646) 128110) ((-407 . -1097) T) ((-263 . -1097) T) ((-213 . -611) 128092) ((-495 . -646) 128057) ((-225 . -23) T) ((-1225 . -818) 128010) ((-1284 . -102) T) ((-354 . -1281) 127987) ((-1282 . -102) T) ((-1248 . -111) 127879) ((-813 . -1049) 127776) ((-813 . -638) 127718) ((-144 . -611) 127700) ((-991 . 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115251) ((-174 . -715) 115183) ((-407 . -286) 115141) ((-870 . -556) T) ((-108 . -400) 115123) ((-84 . -384) T) ((-84 . -395) T) ((-699 . -172) T) ((-615 . -611) 115105) ((-99 . -724) T) ((-482 . -102) 114895) ((-99 . -473) T) ((-116 . -172) T) ((-1284 . -644) 114854) ((-1282 . -644) 114813) ((-1110 . -38) 114783) ((-169 . -637) 114731) ((-1052 . -102) T) ((-997 . -614) 114621) ((-869 . -25) T) ((-813 . -238) 114600) ((-869 . -21) T) ((-816 . -102) T) ((-44 . -644) 114543) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 114521) ((-127 . -1212) T) ((-121 . -1212) T) ((-815 . -1049) 114472) ((-815 . -638) 114414) ((-1032 . -131) T) ((-668 . -367) 114398) ((-152 . -644) 114357) ((-997 . -1047) T) ((-1235 . -637) 114305) ((-1101 . -611) 114287) ((-1001 . -611) 114269) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1097) T) ((-1001 . -612) 114253) ((-997 . -243) 114232) ((-997 . -233) 114211) ((-1290 . -724) T) ((-1254 . 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112784) ((-1235 . -25) T) ((-1235 . -21) T) ((-853 . -25) T) ((-44 . -367) 112768) ((-853 . -21) T) ((-729 . -452) 112719) ((-1285 . -611) 112701) ((-1274 . -1049) 112671) ((-1052 . -309) 112609) ((-669 . -1080) T) ((-604 . -1080) T) ((-390 . -1097) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1080) T) ((-161 . -1080) T) ((-156 . -1080) T) ((-154 . -1080) T) ((-1274 . -638) 112579) ((-619 . -1097) T) ((-697 . -884) 112561) ((-1262 . -1212) T) ((-227 . -309) 112499) ((-144 . -368) T) ((-1044 . -612) 112441) ((-1044 . -611) 112384) ((-313 . -907) NIL) ((-1220 . -842) T) ((-697 . -1036) 112329) ((-709 . -918) T) ((-474 . -1216) 112308) ((-1170 . -452) 112287) ((-1164 . -452) 112266) ((-330 . -102) T) ((-870 . -1109) T) ((-319 . -644) 112148) ((-316 . -646) 111969) ((-313 . -646) 111898) ((-474 . -556) 111849) ((-339 . -514) 111815) ((-550 . -151) 111765) ((-40 . -307) T) ((-841 . -611) 111747) ((-699 . -290) T) ((-870 . -23) T) ((-379 . -493) T) ((-1077 . -231) 111717) ((-512 . -102) T) 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110500) ((-1254 . -95) 110466) ((-633 . -611) 110435) ((-605 . -611) 110404) ((-225 . -848) T) ((-1247 . -95) 110370) ((-1247 . -35) 110336) ((-1246 . -1109) T) ((-1117 . -646) 110323) ((-1226 . -95) 110289) ((-1225 . -1109) T) ((-592 . -151) 110271) ((-1077 . -349) 110250) ((-174 . -290) T) ((-117 . -377) 110227) ((-117 . -338) 110204) ((-1226 . -35) 110170) ((-868 . -307) T) ((-313 . -792) NIL) ((-313 . -789) NIL) ((-316 . -724) 110019) ((-313 . -724) T) ((-474 . -363) 109998) ((-359 . -349) 109977) ((-353 . -349) 109956) ((-345 . -349) 109935) ((-316 . -473) 109914) ((-1246 . -23) T) ((-1225 . -23) T) ((-716 . -1109) T) ((-712 . -131) T) ((-651 . -102) T) ((-477 . -715) 109879) ((-45 . -282) 109829) ((-105 . -1097) T) ((-68 . -611) 109811) ((-968 . -102) T) ((-862 . -102) T) ((-621 . -898) 109770) ((-1286 . -1097) T) ((-381 . -1097) T) ((-82 . -1212) T) ((-1211 . -1097) T) ((-1059 . -848) T) ((-117 . -898) NIL) ((-780 . -918) 109749) ((-711 . -848) T) ((-531 . -1097) T) ((-500 . 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. -1109) T) ((-1206 . -131) T) ((-1022 . -918) T) ((-1001 . -724) T) ((-841 . -646) 90474) ((-710 . -884) NIL) ((-595 . -1049) 90447) ((-581 . -1109) T) ((-518 . -1109) T) ((-594 . -1049) 90330) ((-1164 . -400) 90282) ((-1002 . -309) NIL) ((-813 . -489) 90266) ((-595 . -638) 90239) ((-354 . -918) T) ((-594 . -638) 90136) ((-1153 . -34) T) ((-407 . -646) 90088) ((-50 . -23) T) ((-709 . -131) T) ((-710 . -1036) 89968) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 89939) ((-1137 . -1097) T) ((-1277 . -1276) 89923) ((-699 . -793) T) ((-699 . -790) T) ((-1117 . -307) T) ((-379 . -147) T) ((-280 . -611) 89905) ((-1225 . -990) 89875) ((-48 . -918) T) ((-673 . -489) 89859) ((-251 . -1269) 89829) ((-250 . -1269) 89799) ((-1173 . -848) T) ((-1110 . -172) 89778) ((-1117 . -1020) T) ((-1044 . -34) T) ((-834 . -147) 89757) ((-834 . -145) 89736) ((-735 . -107) 89720) ((-610 . -132) T) ((-482 . -1097) 89510) ((-1175 . -1055) T) ((-869 . -452) T) ((-85 . -1212) T) ((-240 . -38) 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. -23) T) ((-116 . -646) 80504) ((-474 . -145) 80483) ((-418 . -411) 80467) ((-474 . -147) 80446) ((-110 . -489) 80428) ((-311 . -614) 80409) ((-2 . -611) 80391) ((-186 . -102) T) ((-1155 . -19) 80373) ((-1155 . -602) 80348) ((-656 . -21) T) ((-656 . -25) T) ((-592 . -1141) T) ((-1110 . -286) 80325) ((-336 . -25) T) ((-336 . -21) T) ((-240 . -644) 80075) ((-495 . -363) T) ((-1277 . -38) 80045) ((-1169 . -1049) 79868) ((-1139 . -1212) T) ((-1122 . -1049) 79711) ((-852 . -1049) 79695) ((-630 . -602) 79670) ((-1169 . -638) 79499) ((-1122 . -638) 79348) ((-852 . -638) 79318) ((-1284 . -1054) 79302) ((-1282 . -1054) 79286) ((-549 . -1097) T) ((-1084 . -25) T) ((-1084 . -21) T) ((-531 . -790) T) ((-531 . -793) T) ((-117 . -1216) T) ((-961 . -1055) T) ((-621 . -556) T) ((-780 . -25) T) ((-780 . -21) T) ((-778 . -21) T) ((-778 . -25) T) ((-733 . -1055) T) ((-713 . -1055) T) ((-668 . -1054) 79270) ((-517 . -1080) T) ((-461 . -25) T) ((-117 . -556) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 65327070..efc8370c 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3452782367) +(30 . 3452796866) (4413 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -478,659 +478,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |height| |refine| |localAbs| |tableau| - |internalZeroSetSplit| |ord| |paren| |gderiv| |transform| |s20adf| - |list?| |leftUnit| |pseudoRemainder| |lift| |associatorDependence| - |components| |clip| |ScanFloatIgnoreSpacesIfCan| |parseString| - |convert| |principalIdeal| |singularitiesOf| |setOrder| |SFunction| - |iFTable| |reduce| |logGamma| |drawComplexVectorField| |euler| - |coth2tanh| |acotIfCan| |branchPoint?| |getZechTable| |elColumn2!| - |mathieu12| |move| |coshIfCan| |antisymmetric?| |connect| - |reducedQPowers| |lllip| |cylindrical| |submod| |flagFactor| - |semiIndiceSubResultantEuclidean| |predicates| |LazardQuotient| - |iiasin| |solve1| |moduleSum| |reverseLex| |rightScalarTimes!| - |symbol| |expandLog| |associative?| |OMreadStr| |sturmSequence| - |rischDEsys| |front| |basisOfRightAnnihilator| |f01bsf| - |normalizedAssociate| |expression| |tRange| - |tryFunctionalDecomposition| |viewpoint| |coefChoose| |algebraic?| - |primitiveElement| |selectIntegrationRoutines| |bumptab| |digit| - |integer| |patternMatchTimes| |domainOf| |iicsch| |FormatArabic| - |headReduce| |f02aff| |showTheRoutinesTable| |UpTriBddDenomInv| - |lazyPrem| |localUnquote| |constantLeft| |getMeasure| |ignore?| |abs| - |B1solve| |Si| |create3Space| |complexSolve| |complexRoots| - |unitCanonical| |outputArgs| |conjugate| |badValues| |revert| - |cyclic?| |rightRankPolynomial| |normal01| |middle| |doubleResultant| - |variable?| |minimumDegree| |rationalFunction| |nextPrimitivePoly| - |useSingleFactorBound| |declare| |implies| |f04atf| |addPoint| - |iExquo| |showAllElements| |c06eaf| |printingInfo?| - |differentialVariables| |s21bcf| |s17acf| |rdHack1| |split| - |initiallyReduce| |tail| |OMopenString| |port| - |removeRedundantFactorsInPols| |quotient| |aQuartic| - |powerAssociative?| |expandTrigProducts| |curry| |complexEigenvalues| - |drawToScale| |order| |push!| ** |rroot| |thenBranch| |buildSyntax| - |validExponential| |mightHaveRoots| |byte| |lowerCase| - |solveLinearPolynomialEquationByFractions| |difference| |e02def| - |denomLODE| |root?| |t| |outputList| |cycleTail| |label| |maxPoints| - |rules| |hostPlatform| |error| |completeEval| |shanksDiscLogAlgorithm| - |f01qef| |OMgetEndBVar| |lllp| |leftRank| |dequeue!| - |fortranDoubleComplex| |acscIfCan| |principalAncestors| |prindINFO| - |assert| |unknown| |s20acf| |rotate| |exists?| |setprevious!| - |totalLex| |hessian| |prime?| |int| |leader| |modulus| |makeCos| - |inverseColeman| |extractBottom!| |sumOfSquares| - |coercePreimagesImages| |oddlambert| |extractTop!| |largest| |orbit| - |idealiser| |innerEigenvectors| |besselI| |adaptive?| |imports| - |dmpToHdmp| |bezoutResultant| |wronskianMatrix| |leftTrace| - |permutationRepresentation| |outputAsScript| |removeZero| |OMgetApp| - |inHallBasis?| |roughUnitIdeal?| |bits| |makingStats?| - |leftTraceMatrix| |bipolar| |leastMonomial| |multiplyCoefficients| - |getSyntaxFormsFromFile| |determinant| |setrest!| |iiperm| |smith| - |generalizedContinuumHypothesisAssumed| |PollardSmallFactor| - |viewPhiDefault| |li| |children| |constructor| |lex| |hasPredicate?| - |palgextint| |rightExactQuotient| |genericRightTrace| |stFunc2| |max| - |gbasis| |leftPower| |is?| |extensionDegree| |repSq| |option| - |compdegd| |raisePolynomial| |const| |qinterval| |blue| - |subtractIfCan| |useSingleFactorBound?| |padicFraction| - |semiLastSubResultantEuclidean| |printTypes| |shiftLeft| |graphCurves| - |showTheFTable| UTS2UP |getMultiplicationMatrix| |expressIdealMember| - |cycleRagits| |sh| |clearTable!| |bfKeys| |factorByRecursion| |e04gcf| - |rk4qc| |doubleComplex?| |bezoutDiscriminant| |alternatingGroup| - |goodnessOfFit| |checkPrecision| |leftQuotient| |ParCondList| - |exactQuotient| |float?| |bumptab1| |balancedBinaryTree| |chvar| - |tValues| |constant?| |rightTrim| |minGbasis| |setFormula!| - |tanh2trigh| |zCoord| |coleman| |solveid| |Is| |isTimes| |realSolve| - |leftTrim| |parents| |quadratic| |integralDerivationMatrix| - |complexNormalize| |alternative?| |perfectNthPower?| |argscript| - |increasePrecision| |yCoord| |exprHasLogarithmicWeights| |ddFact| - |updateStatus!| |printHeader| |permutation| |over| |bivariate?| - |strongGenerators| |tan2trig| |outputFixed| |just| |OMputEndAttr| - |printInfo| |reduced?| |numerators| |removeConstantTerm| - |LagrangeInterpolation| |lifting1| |commonDenominator| |cotIfCan| - |test| |OMwrite| |d01gaf| |e02bcf| |rootRadius| - |semiDiscriminantEuclidean| |cyclotomicFactorization| |infieldint| - |c02aff| |nextNormalPrimitivePoly| |enterPointData| |hclf| |solve| - |leftDiscriminant| |minimumExponent| |fillPascalTriangle| |d01aqf| - |changeName| |e01sff| |generalizedInverse| |listOfLists| |fprindINFO| - |connectTo| |createNormalElement| |returnTypeOf| |nonLinearPart| - |listexp| |showTypeInOutput| |geometric| |expIfCan| |cCosh| |pack!| - |e02agf| |setCondition!| |generate| |close| |eq| |f2st| |eigenvector| - |factorSquareFreePolynomial| |primes| |kind| |pile| |real?| |before?| - |diagonals| |iter| |coerceP| |contains?| |setelt!| |prefix| - |setClipValue| |pushNewContour| |number?| |anfactor| |incrementBy| - |op| |cycles| |getGraph| |pattern| |display| |flatten| |option?| - |Lazard2| |cosSinInfo| |host| |dimensions| |clipPointsDefault| - |gcdcofactprim| |crest| |dmpToP| |expand| |chebyshevT| |medialSet| - |df2ef| |increase| |partialDenominators| |leftOne| |filterWhile| - |unexpand| |atrapezoidal| |hermiteH| |var1StepsDefault| - |infieldIntegrate| |ldf2vmf| |fglmIfCan| |cyclotomic| |filterUntil| - |writeLine!| |primintegrate| |checkRur| |thetaCoord| - |nativeModuleExtension| |factor1| |vertConcat| |message| |select| - |intensity| |outlineRender| |coerceL| |insertTop!| |s13acf| - |solveInField| |input| |coerceS| |definingEquations| - |numericalIntegration| |readBytes!| |compiledFunction| |symbolTable| - |rischDE| |noLinearFactor?| |iisin| |union| |reductum| - |changeNameToObjf| |outputFloating| |library| |setProperty!| |exp| - |divergence| |resultantReduit| |truncate| |leadingIdeal| |f04adf| - |algintegrate| |getExplanations| |groebSolve| |vedf2vef| |back| - |noncommutativeJordanAlgebra?| |zeroDimPrime?| |lfintegrate| |LiePoly| - |quasiComponent| |product| |isNot| |changeBase| |newTypeLists| - |OMconnectTCP| |pop!| |outerProduct| |modularGcdPrimitive| |f02axf| - |indicialEquations| |collect| |cons| |backOldPos| |cSec| |makeRecord| - |set| |extractSplittingLeaf| |superscript| |sorted?| |curveColor| - |antisymmetricTensors| |modularGcd| |multisect| |univariatePolynomial| - |monomials| |qualifier| |swap!| |dfRange| |rCoord| |inverseLaplace| - |leftCharacteristicPolynomial| |drawStyle| |digamma| |nthRoot| - |elements| |palgRDE0| |OMlistSymbols| |univariatePolynomials| |expPot| - |quote| |qPot| |mat| |csc2sin| |expextendedint| |skewSFunction| - |point?| |curryRight| |bsolve| |stop| |exp1| |scalarTypeOf| - |reduction| |copies| |position!| |rspace| |qfactor| |gramschmidt| - |ocf2ocdf| |f02aef| |heap| |second| |denominators| |OMgetAttr| - |isPlus| |primeFactor| |subResultantGcd| |btwFact| |s18aff| |third| - |viewSizeDefault| |escape| |f01mcf| |subPolSet?| |signature| - |compound?| |s17ajf| |isEquiv| |probablyZeroDim?| |OMsupportsCD?| - |algebraicSort| |removeIrreducibleRedundantFactors| |iicoth| - |reduceByQuasiMonic| |light| |queue| |superHeight| |bottom!| |maxrank| - |ref| |toScale| |removeSquaresIfCan| |rootPoly| |expt| - |functionIsOscillatory| |lhs| |nonSingularModel| |radicalRoots| - |goodPoint| |updatF| |lfextlimint| |toseSquareFreePart| - |generalPosition| |optimize| |lifting| |rhs| |scripted?| |iisech| - |discriminant| |node?| |relerror| |f02ajf| |OMmakeConn| |tanIfCan| - |void| |factorOfDegree| |multiEuclidean| |getProperties| |makeSin| - |reducedContinuedFraction| |tracePowMod| |makeFR| |systemCommand| - |toseInvertible?| |removeCoshSq| |makeop| |idealiserMatrix| |kmax| - |bit?| |recur| |resize| |associatedEquations| |maxPoints3D| - |OMgetVariable| |infLex?| |script| |iflist2Result| |brillhartTrials| - |inputOutputBinaryFile| |zeroDim?| |viewZoomDefault| |intcompBasis| - |partitions| |monomialIntegrate| |viewWriteAvailable| |extractPoint| - |symFunc| |nthExponent| |sumSquares| |OMputEndBVar| - |viewDeltaYDefault| |green| |mathieu22| |linearDependence| |f01rdf| - |OMgetEndError| |lexico| |normal| |lazy?| |linearMatrix| |exprToXXP| - |part?| |byteBuffer| |explimitedint| |SturmHabichtMultiple| - |monicDecomposeIfCan| |nullary| |tex| |OMsend| |key| |ode| - |oddInfiniteProduct| |scan| |exprToUPS| |mr| |hexDigit?| |baseRDE| - |weight| |numericalOptimization| |elem?| |hspace| |setColumn!| - |tablePow| |diagonalProduct| |integralRepresents| - |selectNonFiniteRoutines| |stoseInvertible?sqfreg| |diagonal| |delta| - |filename| |mainSquareFreePart| |sqfrFactor| |depth| |OMgetError| - |showTheSymbolTable| |rightDiscriminant| |decrease| |cond| |makeMulti| - |fullDisplay| |removeDuplicates!| |compBound| |setAttributeButtonStep| - |pole?| |poisson| |matrixDimensions| |getGoodPrime| |lookup| - |splitNodeOf!| |parse| |nullary?| |palgLODE0| |incrementKthElement| - |exprHasAlgebraicWeight| |factorsOfCyclicGroupSize| |commutative?| - |numberOfComputedEntries| |pointColorDefault| |updatD| |elliptic| - |legendre| |s19adf| |iCompose| |OMputVariable| |hasTopPredicate?| - |cothIfCan| |tableForDiscreteLogarithm| |bracket| |factorFraction| - |binomThmExpt| |imagj| |presub| |ParCond| |round| |substring?| |iiabs| - |genericRightNorm| |rewriteSetWithReduction| |sample| |d01gbf| - |squareFree| |LyndonWordsList| |perspective| |graphs| |prevPrime| - |univariate?| |regularRepresentation| |sylvesterMatrix| - |nextSubsetGray| |lambda| |startTableInvSet!| |trailingCoefficient| - |suffix?| |uncouplingMatrices| |call| |imagk| |htrigs| |ffactor| - |exportedOperators| |solveLinear| |pureLex| |moreAlgebraic?| |super| - |lepol| |generalizedContinuumHypothesisAssumed?| |Beta| |stirling1| - |fortranInteger| |lo| |subresultantSequence| |vspace| - |infiniteProduct| EQ |OMUnknownSymbol?| |mapCoef| |rightPower| - |edf2ef| |setright!| |moduloP| |limit| |indiceSubResultantEuclidean| - |removeSinhSq| |prinb| |modTree| |resultant| |lfextendedint| - |deleteRoutine!| |polygon?| |mapExponents| |createNormalPrimitivePoly| - |chiSquare1| |printInfo!| |iiasech| |cCoth| |quartic| |arg1| - |leftNorm| |f04axf| |redPo| |unit?| |jordanAdmissible?| |binaryTree| - |minIndex| |rk4a| |arg2| |aspFilename| |monicModulo| |e01bgf| |e02gaf| - |index| |euclideanSize| |lcm| |safetyMargin| |cCos| - |reciprocalPolynomial| |multinomial| |nullity| |iibinom| |polygamma| - |genericLeftMinimalPolynomial| |nextNormalPoly| |genericLeftNorm| - |algebraicOf| |conditions| |bezoutMatrix| |irreducible?| - |identityMatrix| |composite| |append| |coordinates| |optional?| - |scaleRoots| |trapezoidalo| |integralCoordinates| |match| |delete| - |rightUnits| |delay| |semiResultantEuclideannaif| |cfirst| |pair| - |s17dgf| |gcd| |oddintegers| |newSubProgram| |expandPower| |isOp| - |value| |result| |reverse!| |firstUncouplingMatrix| |makeVariable| - |nextPartition| |OMputBVar| |false| |rightUnit| |cardinality| - |localReal?| |rootProduct| |lastSubResultantEuclidean| |adaptive| - |makeSUP| |laplace| |FormatRoman| |coefficient| |associates?| |iifact| - |sdf2lst| |reset| |stiffnessAndStabilityFactor| |sech2cosh| - |extractIndex| |alphabetic?| |removeRedundantFactors| |direction| - |generalizedEigenvector| |multMonom| |basisOfCommutingElements| - |ratpart| |s17adf| |prod| |makeViewport2D| |viewPosDefault| |every?| - |write| |nthFactor| |mainCoefficients| |SturmHabichtCoefficients| - |makeEq| |#| |groebner| |maximumExponent| |setPredicates| |tree| - |save| |numberOfCycles| |internalDecompose| |exponents| |discreteLog| - |distance| |e04jaf| |cot2trig| |findBinding| |setleft!| |dec| - |stoseInvertibleSetsqfreg| |iiasinh| |figureUnits| |mindeg| |contract| - |lighting| |LowTriBddDenomInv| |rootSplit| |karatsubaOnce| - |jacobiIdentity?| |setlast!| |s21baf| |d02bbf| |sincos| |OMgetBVar| - |pushuconst| |internalSubQuasiComponent?| |xn| |wholeRadix| |colorDef| - |symmetricSquare| |rightRemainder| |permutations| |startPolynomial| - |genericPosition| |contractSolve| |rationalPower| |precision| |f04mcf| - |mulmod| |patternVariable| |partialNumerators| |clearTheFTable| - |ScanFloatIgnoreSpaces| |stoseInvertible?reg| |s18def| |addBadValue| - |evaluate| |box| |invmod| |mapmult| |subMatrix| |generator| - |polyRicDE| |clipSurface| |e02bbf| |ode2| |comment| |hostByteOrder| - |fortranLogical| |nlde| |OMencodingBinary| |log10| |asimpson| |imagK| - |socf2socdf| |unitsColorDefault| |OMgetObject| |recolor| |s19aaf| - |radicalSolve| |bitand| |degreeSubResultant| |taylorRep| |ip4Address| - |quoByVar| |level| |symmetricProduct| |stoseInvertibleSetreg| - |separateDegrees| |bitior| |f01rcf| |f02adf| |leviCivitaSymbol| - |firstDenom| |norm| |d03eef| |OMputApp| |supDimElseRittWu?| - |polynomialZeros| |coth2trigh| |leftMult| |currentCategoryFrame| - |lowerCase!| |s13adf| |laurentIfCan| |ranges| |yCoordinates| - |matrixGcd| |basicSet| |c06gqf| F |genericLeftDiscriminant| |separant| - |s14baf| |OMgetBind| |sort!| |algebraicVariables| |open| |harmonic| - |jacobian| |matrix| |numer| |preprocess| |particularSolution| |search| - |setAdaptive| |semiResultantEuclidean2| |normalizeIfCan| - |resetBadValues| |integralBasisAtInfinity| |s17aff| |denom| |fortran| - |cyclicEqual?| |divisor| |null| |drawComplex| |OMputSymbol| - |headReduced?| |tubePointsDefault| |rootBound| |remove!| |cot2tan| - |hcrf| |not| |balancedFactorisation| |e01baf| |e04ycf| - |coerceListOfPairs| |createMultiplicationTable| |OMputFloat| |and| - |clipWithRanges| |viewport3D| |iiacsch| |complexElementary| - |operations| |areEquivalent?| |sylvesterSequence| |airyBi| |f02bbf| - |or| |fracPart| |categories| |acschIfCan| |lieAdmissible?| |curryLeft| - |any| |eyeDistance| |rangeIsFinite| |cyclicParents| - |LyndonCoordinates| |xor| |diff| |reseed| - |functionIsContinuousAtEndPoints| |bernoulliB| |createGenericMatrix| - |invertIfCan| |viewport2D| |pointLists| |case| |fullPartialFraction| - |e02dcf| |OMbindTCP| |nor| |extendedint| |enqueue!| |Zero| - |bandedJacobian| |fortranLinkerArgs| |mapdiv| |monomial?| |shift| - |dominantTerm| |chainSubResultants| |trigs| |subHeight| |One| - |var1Steps| |radicalEigenvector| |sumOfDivisors| |stopTableInvSet!| - |coerce| |algSplitSimple| Y |conjug| |nextColeman| - |setScreenResolution| |complexIntegrate| |nthRootIfCan| - |createPrimitiveNormalPoly| |listConjugateBases| |construct| - |palglimint0| |toseLastSubResultant| |invertibleSet| |printStats!| - |getStream| |degreeSubResultantEuclidean| |normalizedDivide| - |rightQuotient| |nthCoef| |readByte!| |cyclicGroup| |extractIfCan| - |s21bdf| |gcdPolynomial| |addMatch| |tan2cot| |rk4f| |invmultisect| - |datalist| |belong?| |d02cjf| |primPartElseUnitCanonical!| |fibonacci| - |showScalarValues| |top| |computePowers| |e01sbf| |iiatan| - |numberOfPrimitivePoly| |inc| |OMgetAtp| |numFunEvals3D| - |numberOfChildren| |reopen!| |airyAi| |numericIfCan| |romberg| - |e02daf| |leaf?| |showSummary| |definingInequation| |critM| - |OMputError| |seriesSolve| |derivationCoordinates| |sort| - |genericLeftTraceForm| |reducedDiscriminant| |leftScalarTimes!| - |c05adf| |getButtonValue| |obj| |iilog| |cLog| |fixedPoints| - |linearAssociatedExp| |intChoose| |continue| |clipParametric| - |unaryFunction| |s18aef| |outputAsTex| |laguerre| |cartesian| |df2fi| - |double?| |cAtan| |selectAndPolynomials| |cache| |showAttributes| - |pmintegrate| |Ci| |limitPlus| |whileLoop| |realEigenvectors| - |rotatey| |rank| |rightZero| |getMatch| |satisfy?| |stFunc1| - |OMgetEndBind| |mathieu24| |list| |accuracyIF| |complexEigenvectors| - |complexNumericIfCan| |nextsousResultant2| |randomLC| |makeSketch| - |exprToGenUPS| |alphanumeric?| |d01alf| |Aleph| |digit?| |random| - |car| |sub| |completeEchelonBasis| |clearFortranOutputStack| - |resultantnaif| |charthRoot| |laurentRep| |setnext!| |extractClosed| - |jordanAlgebra?| |stoseSquareFreePart| |cdr| |iomode| - |monicRightFactorIfCan| |has?| |toroidal| |chebyshevU| |setEmpty!| - |intersect| |patternMatch| |mainForm| |kroneckerDelta| |palgextint0| - |setDifference| |subst| |evaluateInverse| |nthr| |name| |select!| - |repeating?| |dioSolve| |pmComplexintegrate| |infix| |frst| - |fixedDivisor| |fractRagits| |generalInfiniteProduct| - |setIntersection| |createZechTable| |subTriSet?| |body| |frobenius| - |linearDependenceOverZ| |edf2df| |nilFactor| - |resultantReduitEuclidean| |length| |OMreadFile| |shellSort| |f04maf| - |setUnion| |elseBranch| |separate| |selectODEIVPRoutines| - |mainContent| |overlap| |remove| |scripts| |mainMonomials| |plotPolar| - |tanh2coth| |radPoly| |leftFactorIfCan| |apply| |fixPredicate| - |endOfFile?| |cosIfCan| |showRegion| |lists| |uniform| - |rationalPoint?| |alphanumeric| |modifyPointData| |subSet| |qqq| - |finiteBound| |po| |setPosition| |integers| |integralLastSubResultant| - |last| |formula| |henselFact| |c06fuf| |setMaxPoints| |even?| - |headRemainder| |size| |splitConstant| |e02aef| |charpol| |rootOf| - |trunc| |assoc| |close!| |eof?| |output| |explicitlyFinite?| |csubst| - |nonQsign| |isOr| |setref| |objects| |explicitlyEmpty?| |positive?| - |freeOf?| |scalarMatrix| |showFortranOutputStack| |factorSquareFree| - |d01anf| |monomRDEsys| |mapUp!| |UnVectorise| |base| |newReduc| - |enumerate| |listBranches| |qelt| |getIdentifier| |makeUnit| - |rootDirectory| |cSin| |e04fdf| |first| |bipolarCylindrical| |isAnd| - |binary| |purelyTranscendental?| |s17dhf| |qsetelt| |rightRecip| - |OMgetString| |overset?| |nrows| |copyInto!| |simplifyExp| |rest| - |f04qaf| |crushedSet| |polarCoordinates| |finite?| |pomopo!| |xRange| - |iisqrt2| |leftLcm| |ncols| |countRealRoots| |writable?| |concat!| - |substitute| |aQuadratic| |viewWriteDefault| |isOpen?| - |continuedFraction| |cAcosh| |yRange| |quotientByP| |debug3D| - |selectsecond| |dictionary| |quasiMonicPolynomials| |removeDuplicates| - |OMgetEndApp| |subCase?| |nextPrimitiveNormalPoly| |drawCurves| |row| - |zRange| |radicalSimplify| |leftDivide| |RemainderList| |c06fpf| - |monic?| |edf2fi| |tab| |euclideanGroebner| |laplacian| |iisec| |next| - |map!| |irreducibleRepresentation| |fortranCompilerName| |generic?| BY - |denominator| |dot| |corrPoly| |d01apf| |nodes| |showClipRegion| - |cschIfCan| |qsetelt!| |makeResult| |rewriteIdealWithRemainder| - |leaves| |contours| |callForm?| |myDegree| |signAround| - |symmetricDifference| |errorInfo| |RittWuCompare| |resetVariableOrder| - |cyclicSubmodule| |wrregime| |taylorIfCan| |rightMinimalPolynomial| - |e01saf| |s17dlf| |nodeOf?| |legendreP| |divideIfCan| - |createLowComplexityTable| |applyQuote| |hitherPlane| |factors| - |bivariatePolynomials| |iiexp| |printCode| |subResultantsChain| - |lexGroebner| |semiSubResultantGcdEuclidean2| |pdct| |commaSeparate| - |cyclic| |nthExpon| |setImagSteps| |kovacic| |realElementary| - |replace| |pquo| |userOrdered?| |minPoly| |internalSubPolSet?| - |createPrimitiveElement| |point| |monicLeftDivide| |isList| - |retractable?| |bounds| |terms| |multiset| |defineProperty| |previous| - |gensym| |removeRoughlyRedundantFactorsInPols| |LyndonBasis| |linears| - |flexible?| |acsch| |ellipticCylindrical| |invertible?| |d01asf| - |ruleset| |critBonD| |factorset| |jacobi| |insertionSort!| |conical| - |deref| |nextsubResultant2| NOT |fill!| |clipBoolean| |c06gcf| - |extendedIntegrate| |exponent| |bigEndian| |HenselLift| |imagJ| - |OMputEndObject| |acosIfCan| OR |series| |nil?| |appendPoint| |any?| - |OMreceive| |toseInvertibleSet| |expintfldpoly| |pushucoef| |dark| - |viewDeltaXDefault| |acothIfCan| AND |computeBasis| |zeroMatrix| - |addMatchRestricted| |suchThat| |computeCycleEntry| |entries| |f01qdf| - |mathieu23| |firstNumer| |subresultantVector| |tanQ| |inspect| - |rightFactorCandidate| |numberOfHues| |mapExpon| |bandedHessian| - |prefix?| |integerBound| |arguments| |singleFactorBound| |sPol| - |merge| |quasiRegular?| |qroot| |initials| |setProperties!| |epilogue| - |birth| |points| |mkcomm| |f01qcf| |boundOfCauchy| |incr| |exQuo| - |PDESolve| |vark| |min| |characteristic| |readIfCan!| |OMputBind| - 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|diophantineSystem| |wordsForStrongGenerators| |bat1| |stopTable!| - |fmecg| |iroot| |ODESolve| |integralMatrix| ~ |generators| - |antiCommutator| |showArrayValues| <= |factorPolynomial| - |tanintegrate| |d01fcf| |charClass| |s17agf| |cCot| |withPredicates| - |nextPrime| |returnType!| |iicot| |meshPar2Var| >= |hermite| |parts| - |homogeneous?| |e04ucf| |gcdPrimitive| |acoshIfCan| - |createIrreduciblePoly| |e01sef| |morphism| |brillhartIrreducible?| - |iiasec| |zeroOf| |sinh2csch| |outputMeasure| |addPointLast| |setRow!| - |squareFreePolynomial| |zero?| |mainKernel| |someBasis| - |factorGroebnerBasis| |status| |constantKernel| |/\\| |sign| - |cycleSplit!| |varList| GE |cExp| |zag| |spherical| |scopes| - |leadingBasisTerm| |symmetricRemainder| |cAsin| |OMgetEndAtp| |\\/| - |empty| |halfExtendedSubResultantGcd1| + |cosh2sech| GT |maxColIndex| - |setPrologue!| |iiacsc| |fortranCarriageReturn| |constantOpIfCan| - |rationalApproximation| |distFact| |factorAndSplit| - |numberOfOperations| |s18acf| - |transcendent?| LE |c05pbf| - |removeSuperfluousCases| |pushFortranOutputStack| |lyndon| - |removeCosSq| |f02fjf| |besselK| |axes| / |rur| |internal?| LT - |e01bff| |squareMatrix| |popFortranOutputStack| |s18adf| |getOperands| - |cCsc| |squareFreeFactors| |isConnected?| |readable?| - |characteristicPolynomial| |denomRicDE| |postfix| |binarySearchTree| - |insertMatch| |iiGamma| |readInt8!| |minPol| |outputAsFortran| - |compile| |cubic| |column| |symbolIfCan| - |halfExtendedSubResultantGcd2| |generic| |multiple?| |retract| - |pushup| |symbol?| |plot| |ridHack1| |leadingExponent| - |commutativeEquality| |cyclicEntries| |upperCase?| |groebnerFactorize| - |setRealSteps| |hasSolution?| |infinityNorm| |pToHdmp| |var2Steps| - |OMReadError?| |rightTraceMatrix| |halfExtendedResultant1| |remainder| - |e02adf| |shiftRight| |limitedint| |wholeRagits| |property| - |leftFactor| |schema| |factorSquareFreeByRecursion| |maxRowIndex| - |arity| |polar| |simplifyPower| |findConstructor| |lazyIntegrate| - |quasiMonic?| |ode1| |sin?| |roman| |exprex| - |initializeGroupForWordProblem| |paraboloidal| |complexZeros| - |printStatement| |alphabetic| |setvalue!| |numerator| |tensorProduct| - |palgint0| |internalIntegrate| |repeatUntilLoop| |odd?| |applyRules| - |mindegTerm| |permutationGroup| |SturmHabicht| |f07aef| - |monicRightDivide| |units| |dimensionOfIrreducibleRepresentation| - |semicolonSeparate| |f2df| |mapUnivariate| |associator| |setStatus| - |changeMeasure| |totalGroebner| |isTerm| |alternating| |groebgen| - |removeRedundantFactorsInContents| |iitanh| |subResultantChain| - |changeThreshhold| |exactQuotient!| |curve| |basisOfNucleus| - |squareFreeLexTriangular| |primitivePart!| |recip| - |functionIsFracPolynomial?| |selectPolynomials| |basisOfLeftNucloid| - |parabolic| |decimal| |quadraticNorm| |exteriorDifferential| - |processTemplate| |atanIfCan| |collectQuasiMonic| |reverse| |plus| - |ricDsolve| |internalInfRittWu?| |clearCache| |BumInSepFFE| |cSinh| - |transcendentalDecompose| |lintgcd| |meshFun2Var| |d01bbf| - |zeroSetSplitIntoTriangularSystems| |absolutelyIrreducible?| |c06ecf| - 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|module| |changeWeightLevel| |rightExtendedGcd| |failed| |interval| - |weakBiRank| |sizeMultiplication| |read!| |monom| |eval| |cAsinh| - |check| |dom| |lazyPquo| |rightRank| |cycle| |intermediateResultsIF| - |startTableGcd!| |s15aef| |secIfCan| |OMgetSymbol| |complexForm| - |rule| |rischNormalize| |inRadical?| |radicalOfLeftTraceForm| - |divideIfCan!| |abelianGroup| |members| |upperCase| |radix| - |transcendenceDegree| |distribute| |lazyVariations| |palgintegrate| - |e04dgf| |positiveSolve| |linearlyDependent?| |sinIfCan| - |setScreenResolution3D| |primitivePart| |unvectorise| |common| - |leftExtendedGcd| |leftUnits| |mdeg| |biRank| |innerSolve| |find| - |bubbleSort!| |split!| |iisinh| |OMputObject| |external?| |prem| - |e01bef| |f02agf| |cAcsch| |ceiling| |hue| |overlabel| - |multiplyExponents| |semiDegreeSubResultantEuclidean| |readLineIfCan!| - |cyclotomicDecomposition| |notelem| |mainExpression| |fTable| - |linearlyDependentOverZ?| |saturate| |plus!| |title| - |nextIrreduciblePoly| |ideal| |definingPolynomial| |cup| |build| - |clearDenominator| |expr| |plenaryPower| |rightGcd| |flexibleArray| - |exptMod| |normalElement| |mvar| |logical?| |atom?| |interactiveEnv| - |getDatabase| |reflect| |overbar| |possiblyInfinite?| |mirror| - |quatern| |symbolTableOf| |OMserve| |usingTable?| |removeSinSq| - |rangePascalTriangle| |inf| |curveColorPalette| |operator| - |completeSmith| |addiag| |binomial| |stFuncN| |e| |coerceImages| - |fortranCharacter| |latex| |lyndon?| |trivialIdeal?| |f01ref| - |zeroVector| |readUInt32!| |LiePolyIfCan| |createRandomElement| - |csch2sinh| |measure2Result| |bumprow| |setProperty| |putColorInfo| - |f02awf| |variable| |power!| |true| |operators| |negative?| - |trace2PowMod| |s17def| |linear| |iterationVar| |elRow1!| - |eigenvalues| |pascalTriangle| |s19abf| |iterators| |writeBytes!| - |imagi| |head| |moebius| |d03faf| |nothing| |lazyGintegrate| - |initiallyReduced?| |redPol| |integerIfCan| |inverseIntegralMatrix| - |deepestTail| |outputGeneral| |splitDenominator| |palgRDE| - |prefixRagits| |polynomial| |f04arf| |startStats!| |getlo| - |doubleFloatFormat| |readUInt16!| |findCycle| |init| |null?| - |createThreeSpace| |s17ahf| |mainVariables| |mergeFactors| - |factorList| |OMgetInteger| |basisOfCenter| |readUInt8!| |hexDigit| - |d02gaf| |musserTrials| |lineColorDefault| - |setLegalFortranSourceExtensions| |OMencodingSGML| - |createPrimitivePoly| |nthFractionalTerm| |completeHermite| |d02bhf| - |stosePrepareSubResAlgo| |meshPar1Var| |extract!| |pdf2df| |imagI| - |BasicMethod| |dihedralGroup| |keys| |ratPoly| |swap| |fortranDouble| - |maxdeg| |powmod| |cycleLength| |distdfact| |primextendedint| - |constantOperator| |lazyPremWithDefault| |properties| |changeVar| - |scanOneDimSubspaces| |wreath| |f04asf| |c06frf| |width| |s14abf| - |decompose| |sqfree| |sturmVariationsOf| |deleteProperty!| - |complexExpand| |argument| |translate| |mainPrimitivePart| |elliptic?| - |maxIndex| |minordet| |operation| |primitive?| |logIfCan| |f01brf| - |merge!| |rename!| |isAbsolutelyIrreducible?| |setErrorBound| - |lazyPseudoDivide| |hMonic| |iprint| |dihedral| |dAndcExp| |badNum| - |pseudoDivide| |orthonormalBasis| |eigenvectors| - |nextLatticePermutation| |entry?| |constDsolve| |rootsOf| |expint| - |solveLinearlyOverQ| |rewriteIdealWithHeadRemainder| |sayLength| - |algDsolve| |GospersMethod| |readLine!| |restorePrecision| - |evenInfiniteProduct| |normalizeAtInfinity| |integralAtInfinity?| - |createMultiplicationMatrix| |lowerPolynomial| - |useEisensteinCriterion?| |exponential1| |antiCommutative?| - |internalLastSubResultant| |SturmHabichtSequence| |more?| |mix| - |twoFactor| |infinite?| |loopPoints| |iiacosh| |slash| |tubePoints| - |useEisensteinCriterion| |constantRight| |roughBasicSet| - |genericLeftTrace| |dimension| |OMputAttr| |expenseOfEvaluation| - |youngGroup| |triangularSystems| |primlimitedint| |rightDivide| - |schwerpunkt| |ReduceOrder| |simpleBounds?| |cAcot| |symmetricGroup| - |optional| |OMsetEncoding| |finiteBasis| |setchildren!| |writeInt8!| - |minRowIndex| |pr2dmp| |stoseLastSubResultant| |computeInt| |meatAxe| - |representationType| |autoReduced?| |oblateSpheroidal| |s13aaf| - 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SEGMENT |fortranLiteral| |cPower| |nil| |listOfMonoms| |graphState| - |leftAlternative?| |s19acf| |trueEqual| |less?| - |numberOfIrreduciblePoly| |setButtonValue| |xCoord| |d01amf| - |setAdaptive3D| |palginfieldint| |complexNumeric| |curve?| - |factorSFBRlcUnit| |viewDefaults| |unit| |iicos| |bombieriNorm| - |cycleElt| |signatureAst| |cAcsc| |parametric?| |center| |principal?| - |lambert| |numberOfVariables| |replaceKthElement| |typeList| - |lyndonIfCan| |approximate| |putGraph| |kernels| |insertBottom!| - |Hausdorff| |testModulus| |primeFrobenius| |e02dff| |complex| - |endSubProgram| |isExpt| |log| |normFactors| |polygon| |univariate| - |ramifiedAtInfinity?| |cSech| |addmod| |subscript| |integralBasis| - |minPoints3D| |node| |Frobenius| |univariatePolynomialsGcds| - |modifyPoint| F2FG |shufflein| |simpson| |mergeDifference| |asinIfCan| - |reduceLODE| |generalLambert| |lfinfieldint| |weighted| |erf| - |rightRegularRepresentation| |conditionP| |unitVector| |c06ebf| - |simplify| |duplicates?| |OMgetEndObject| |factor| |failed?| - |clearTheSymbolTable| |sncndn| |prepareSubResAlgo| |constantIfCan| - |setEpilogue!| |create| |concat| |setStatus!| |readInt16!| |linGenPos| - |sqrt| |dmp2rfi| |besselY| |inverseIntegralMatrixAtInfinity| - |singRicDE| |matrixConcat3D| |trapezoidal| |symmetricPower| |dilog| - |viewThetaDefault| |minrank| |upDateBranches| |possiblyNewVariety?| - |real| |initTable!| |hasHi| |polyRDE| |pow| |transpose| |setValue!| - |factorials| |branchPointAtInfinity?| |rombergo| - |resultantEuclideannaif| |sin| |imag| |systemSizeIF| |subspace| - |mantissa| |controlPanel| |directProduct| |top!| |setOfMinN| - |lflimitedint| |limitedIntegrate| |monomRDE| |normalise| |ListOfTerms| - |cos| |isImplies| |quickSort| |collectUnder| |size?| - |seriesToOutputForm| |associatedSystem| |singular?| |setFieldInfo| - |elRow2!| |wholePart| |tan| |squareTop| |LyndonWordsList1| - |rowEchelonLocal| |hyperelliptic| |outputSpacing| |getCurve| - |approxSqrt| |consnewpol| |rowEchLocal| |OMsupportsSymbol?| |brace| - |cot| |d01akf| |besselJ| |empty?| |leftMinimalPolynomial| |varselect| - |logpart| |listYoungTableaus| |extendIfCan| |adaptive3D?| |destruct| - |sec| |explicitEntries?| |OMgetFloat| |rdregime| |getRef| |source| - |objectOf| |unknownEndian| |countRealRootsMultiple| |optpair| - |getOrder| |central?| |csc| |getConstant| |minPoints| |unmakeSUP| - |getCode| |combineFeatureCompatibility| |sortConstraints| - |useNagFunctions| |cAcoth| |opeval| |laguerreL| |asin| |category| - |power| |bringDown| |critT| |ptFunc| |optAttributes| |bitCoef| - |c06ekf| |commutator| |writeByte!| |equation| |inconsistent?| |acos| - |domain| |getProperty| |prinpolINFO| |characteristicSet| - |stoseIntegralLastSubResultant| |irreducibleFactor| |primlimintfrac| - |e02ddf| |generalSqFr| |compactFraction| |monomial| |prepareDecompose| - |atan| |mkIntegral| |entry| |mainValue| |package| |beauzamyBound| - |e02akf| |weierstrass| |polyred| |asinhIfCan| |tanAn| |show| - |selectFiniteRoutines| |coordinate| |multivariate| |acot| - |convergents| |Vectorise| |f07adf| |resultantEuclidean| |target| - |basisOfLeftAnnihilator| |cTanh| |baseRDEsys| |traverse| - 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|lazyPseudoRemainder| |showAll?| |csch| |puiseux| |univariateSolve| - |OMunhandledSymbol| |red| |midpoints| |range| |problemPoints| - |rubiksGroup| |rk4| |interpolate| |adjoint| |asinh| |copy| - |invertibleElseSplit?| |positiveRemainder| |linSolve| |parent| - |minimize| |ScanArabic| |cyclicCopy| |compose| |relativeApprox| |inv| - |triangulate| |acosh| |d03edf| |OMputEndApp| - |stoseInternalLastSubResultant| |lowerCase?| |digits| |tubeRadius| - |update| |ground?| |asecIfCan| |stronglyReduce| |OMputAtp| |partition| - |atanh| |padicallyExpand| |polCase| |makeprod| - |selectSumOfSquaresRoutines| |constantToUnaryFunction| |ground| - |pushdterm| |numberOfMonomials| |f02xef| |purelyAlgebraic?| - |OMputInteger| |acoth| |autoCoerce| |OMgetEndAttr| |normalize| - |OMputString| |droot| |equality| |dequeue| |identitySquareMatrix| - |minimalPolynomial| |minus!| |torsion?| |leadingMonomial| |asech| - |shrinkable| |one?| |errorKind| |f02aaf| |leftRankPolynomial| - |completeHensel| |fractRadix| |leadingSupport| LODO2FUN |c06gbf| - |leadingCoefficient| |trigs2explogs| |rightFactorIfCan| |quasiRegular| - |numberOfDivisors| |setLength!| |push| |universe| |mpsode| - |generateIrredPoly| |interReduce| |multiple| |primitiveMonomials| - |sinhIfCan| |graeffe| |binaryFunction| |measure| |position| - |semiResultantReduitEuclidean| |totolex| |normalForm| |dualSignature| - |shiftRoots| |interpretString| |recoverAfterFail| |composites| |say| - |showTheIFTable| |stripCommentsAndBlanks| |numberOfFactors| |padecf| - |euclideanNormalForm| |perfectSqrt| |e02ahf| |testDim| |indices| - |match?| |child| |critB| |powerSum| |cCsch| |in?| |perfectSquare?| - |makeCrit| |octon| |componentUpperBound| |randnum| |bernoulli| - |sizeLess?| |psolve| |summation| |decomposeFunc| - |generalizedEigenvectors| |basisOfMiddleNucleus| |e01bhf| - |internalIntegrate0| |bitLength| |shallowExpand| |froot| |ScanRoman| - |selectfirst| |sequence| |quoted?| |quasiAlgebraicSet| |asechIfCan| - |makeYoungTableau| |content| |setTex!| |directSum| |indicialEquation| - |debug| |hash| |rational| |Gamma| |pseudoQuotient| |OMParseError?| - |divisorCascade| |unitNormal| |Ei| |lieAlgebra?| |midpoint| |count| D - |double| |component| |polyPart| |Lazard| |leadingIndex| |rootSimp| - |vconcat| |graphStates| |Nul| |tanSum| |totalDegree| |bothWays| - |outputForm| |reindex| |setfirst!| |removeSuperfluousQuasiComponents| - |externalList| |packageCall| |palgint| |sechIfCan| |OMputEndBind| - |movedPoints| |hasoln| |stoseInvertible?| |approximants| - |leftRegularRepresentation| |solid?| |eulerPhi| |radicalEigenvectors| - |integral?| |c06gsf| |whitePoint| |pade| |separateFactors| |f02akf| - |mapBivariate| |wordInGenerators| |getVariableOrder| |moebiusMu| - |phiCoord| |ksec| |UP2ifCan| |f01maf| |getBadValues| |rightOne| - |explogs2trigs| |setProperties| |fortranComplex| |lquo| - |solveLinearPolynomialEquation| |mainMonomial| |multiEuclideanTree| - |closed?| |zerosOf| |primPartElseUnitCanonical| - |exprHasWeightCosWXorSinWX| |realRoots| |d01ajf| |zero| - |splitSquarefree| |deepExpand| |goto| |integrate| |s17dcf| - |showIntensityFunctions| |declare!| |inputBinaryFile| |virtualDegree| - |readInt32!| |certainlySubVariety?| |capacity| |subQuasiComponent?| - |f07fdf| |pastel| |predicate| |mainVariable?| |taylorQuoByVar| - |cyclePartition| |simpsono| |And| |leftRecip| - |subResultantGcdEuclidean| |e04mbf| |redpps| |symmetric?| - |lazyResidueClass| |iidprod| |currentSubProgram| |complementaryBasis| - |Or| |subNodeOf?| |prime| |leftRemainder| |lprop| |fractionFreeGauss!| - |deepCopy| |reify| |makeTerm| |write!| |Not| |index?| |argumentListOf| - |integralMatrixAtInfinity| |karatsubaDivide| |bitTruth| - |leadingCoefficientRicDE| |irreducibleFactors| |iipow| - |numberOfComponents| |setMaxPoints3D| |nary?| |reducedForm| - |linearAssociatedOrder| |complexLimit| |vectorise| |allRootsOf| |bat| - |lastSubResultantElseSplit| |decreasePrecision| |OMopenFile| - |unprotectedRemoveRedundantFactors| |rotate!| |realZeros| |inverse| - |highCommonTerms| |rationalPoints| |antiAssociative?| |currentScope| - |parabolicCylindrical| |extension| |oneDimensionalArray| - |pointSizeDefault| |segment| |e02bdf| |eisensteinIrreducible?| - |halfExtendedResultant2| |sumOfKthPowerDivisors| |colorFunction| - |color| |mainVariable| |primaryDecomp| |s17aef| |totalDifferential| - |iiacos| |extendedResultant| |returns| |parameters| |trim| - |internalAugment| |maxint| |coHeight| |pointColorPalette| |nsqfree| - |simplifyLog| |id| |normInvertible?| |specialTrigs| |npcoef| |seed| - |rootPower| |selectPDERoutines| |physicalLength| |OMconnInDevice| - |zeroSetSplit| |mathieu11| |typeLists| |imagE| |doubleDisc| - |stirling2| |wordInStrongGenerators| |redmat| |isMult| |clikeUniv| - |table| |quadraticForm| |bivariateSLPEBR| |represents| |pair?| - |integral| |character?| UP2UTS |zeroSquareMatrix| |new| |cscIfCan| - |pol| |monicCompleteDecompose| |identification| |maxrow| |high| - |leadingTerm| |zeroDimensional?| |loadNativeModule| |ramified?| - |insert| |rowEchelon| |isobaric?| |numFunEvals| |insertRoot!| |diag| - |littleEndian| |eq?| |lazyPseudoQuotient| |normDeriv2| - |indicialEquationAtInfinity| |cAcos| |extractProperty| |fintegrate| - |hdmpToP| |lazyIrreducibleFactors| |genericRightDiscriminant| - |options| |e04naf| |eigenMatrix| |ratDsolve| |atanhIfCan| |gcdprim| - |eulerE| |unrankImproperPartitions0| |basis| |solveRetract| |pi| - |listLoops| |rewriteIdealWithQuasiMonicGenerators| |yellow| - |pleskenSplit| |chiSquare| |resetAttributeButtons| |comparison| |ipow| - |palglimint| |infinity| |triangSolve| |nand| |retractIfCan| - |torsionIfCan| |rightTrace| |f04mbf| |modularFactor| - |discriminantEuclidean| |routines| |splitLinear| |nullSpace| |string| - |algint| |var2StepsDefault| |makeGraphImage| |repeating| |pToDmp| - |triangular?| |tab1| |totalfract| |unary?| |equiv| - |expenseOfEvaluationIF| |lfunc| |rootOfIrreduciblePoly| |sum| |ptree| - |factorial| |resetNew| |kernel| |supRittWu?| |prologue| |sequences| - |rst| |isPower| |mapUnivariateIfCan| |primintfldpoly| |draw| |s21bbf| - |reducedSystem| |squareFreePart| |mapGen| |complete| |ratDenom| - |OMputEndAtp| |physicalLength!| |coord| |expintegrate| - |prolateSpheroidal| |augment| |left| |topFortranOutputStack| - |leastAffineMultiple| |mainCharacterization| |fi2df| |s18dcf| |f04jgf| - |exponentialOrder| |horizConcat| |reduceBasisAtInfinity| |right| - |rootKerSimp| |enterInCache| |isQuotient| |listRepresentation| |cTan| - |OMUnknownCD?| |symmetricTensors| |bfEntry| |genericRightTraceForm| - |linear?| |lp| |characteristicSerie| |edf2efi| |aLinear| - |singularAtInfinity?| |scale| |makeObject| |orbits| |lazyEvaluate| - |selectOrPolynomials| |squareFreePrim| |map| - |selectMultiDimensionalRoutines| |s17akf| |structuralConstants| - |presuper| |powern| |branchIfCan| |uniform01| - |selectOptimizationRoutines| |cos2sec| |elt| |arrayStack| |An| - |rewriteSetByReducingWithParticularGenerators| |magnitude| - |currentEnv| |stopTableGcd!| |roughSubIdeal?| |divide| |open?| |coef| - |numberOfNormalPoly| |block| |duplicates| |getOperator| |critpOrder| - |gcdcofact| |extendedSubResultantGcd| |bag| |df2st| |iisqrt3| - |fortranLiteralLine| |OMcloseConn| |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 + |Record| |Union| |critM| |loopPoints| |commutativeEquality| |s17dcf| + |nullity| |shallowCopy| |appendPoint| |selectFiniteRoutines| |iiacosh| + |showIntensityFunctions| |OMputError| |expr| |cyclicEntries| |iibinom| + |traceMatrix| |any?| |coordinate| |cyclotomicFactorization| + |seriesSolve| |slash| |upperCase?| |inputBinaryFile| |f07fef| + |polygamma| |convergents| |OMreceive| |infieldint| |tubePoints| + |derivationCoordinates| |groebnerFactorize| |virtualDegree| + |genericLeftMinimalPolynomial| |numberOfImproperPartitions| + |Vectorise| |toseInvertibleSet| |c02aff| |useEisensteinCriterion| + |genericLeftTraceForm| |setRealSteps| |readInt32!| |expintfldpoly| + |f07adf| |nextNormalPrimitivePoly| |hasSolution?| |constantRight| + |reducedDiscriminant| |certainlySubVariety?| |variable| + |rightDiscriminant| |limitedint| |zRange| |pushucoef| + |resultantEuclidean| |enterPointData| |symbol| |capacity| + |leftScalarTimes!| |roughBasicSet| |infinityNorm| |iterators| + |decrease| |map!| |wholeRagits| |basisOfLeftAnnihilator| |dark| |hclf| + |expression| |genericLeftTrace| |c05adf| |pToHdmp| + |subQuasiComponent?| |qsetelt!| |makeMulti| |leftFactor| |cTanh| + |viewDeltaXDefault| |solve| |integer| |var2Steps| |f07fdf| + |fullDisplay| |schema| |acothIfCan| |baseRDEsys| |leftDiscriminant| + |outputGeneral| |s17aff| |OMReadError?| |pastel| |removeDuplicates!| + |factorSquareFreeByRecursion| |computeBasis| |traverse| + |minimumExponent| |cyclicEqual?| |splitDenominator| |rightTraceMatrix| + |mainVariable?| |compBound| |maxRowIndex| |zeroMatrix| + |unrankImproperPartitions1| |fillPascalTriangle| |divisor| |palgRDE| + |taylorQuoByVar| |halfExtendedResultant1| |point| + |setAttributeButtonStep| |arity| |drawComplex| |d01aqf| |port| + |prefixRagits| |cyclePartition| |remainder| |polar| |pole?| |acsch| + |dictionary| |viewThetaDefault| ** |changeName| |f04arf| |OMputSymbol| + |e02adf| |simpsono| |simplifyPower| |poisson| |minrank| + |quasiMonicPolynomials| |e01sff| |t| |startStats!| |headReduced?| + |leftRecip| |shiftRight| |series| |findConstructor| |matrixDimensions| + |OMgetEndApp| |upDateBranches| |generalizedInverse| |getlo| + |tubePointsDefault| |label| |error| |getGoodPrime| |lazyIntegrate| + |possiblyNewVariety?| |subCase?| |listOfLists| |rootBound| + |doubleFloatFormat| |makeCrit| |ODESolve| |nextPrimitiveNormalPoly| + |lookup| |quasiMonic?| |assert| |initTable!| |integralMatrix| + |fprindINFO| |readUInt16!| |remove!| |octon| |prefix?| |splitNodeOf!| + |ode1| |hasHi| |drawCurves| |connectTo| |findCycle| |cot2tan| + |generators| |componentUpperBound| |nullary?| |min| |sin?| |gderiv| + |polyRDE| |row| |createNormalElement| |hcrf| |null?| |antiCommutator| + |randnum| |palgLODE0| |transform| |roman| |pow| |radicalSimplify| + |mapUnivariateIfCan| |returnTypeOf| |balancedFactorisation| + |createThreeSpace| |bernoulli| |showArrayValues| |exprex| |s20adf| + |incrementKthElement| |leftDivide| |transpose| |primintfldpoly| + |nonLinearPart| |e01baf| |s17ahf| |sizeLess?| |factorPolynomial| + |exprHasAlgebraicWeight| |initializeGroupForWordProblem| |list?| + |setValue!| |RemainderList| |s21bbf| |constructor| |listexp| |e04ycf| + |mainVariables| |tanintegrate| |psolve| |paraboloidal| + |factorsOfCyclicGroupSize| |leftUnit| |factorials| |c06fpf| + |reducedSystem| |showTypeInOutput| |summation| |mergeFactors| + |coerceListOfPairs| |d01fcf| |infix?| |option| |complexZeros| + |commutative?| |pseudoRemainder| |branchPointAtInfinity?| |monic?| + |squareFreePart| |charClass| |geometric| |createMultiplicationTable| + |factorList| |mask| |decomposeFunc| |printStatement| + |associatorDependence| |numberOfComputedEntries| |edf2fi| |rombergo| + |mapGen| |expIfCan| |OMputFloat| |OMgetInteger| + |generalizedEigenvectors| |s17agf| |alphabetic| |components| + |pointColorDefault| |condition| |resultantEuclideannaif| |tab| + |complete| |cCosh| |tRange| |basisOfCenter| |clipWithRanges| + |basisOfMiddleNucleus| |cCot| |clip| |updatD| |setvalue!| + |systemSizeIF| |euclideanGroebner| |ratDenom| |constant| + |tryFunctionalDecomposition| |pack!| |rightTrim| |readUInt8!| + |viewport3D| |e01bhf| |withPredicates| |elliptic| + |ScanFloatIgnoreSpacesIfCan| |numerator| |laplacian| |subspace| + |OMputEndAtp| |e02agf| |leftTrim| |hexDigit| |iiacsch| + |internalIntegrate0| |nextPrime| |parseString| |legendre| + |tensorProduct| |iisec| |controlPanel| |physicalLength!| + |setCondition!| |d02gaf| |complexElementary| |bitLength| |returnType!| + |showTheRoutinesTable| |palgint0| |s19adf| |principalIdeal| |top!| + |irreducibleRepresentation| |coord| |f2st| |musserTrials| + |areEquivalent?| |iicot| |shallowExpand| |singularitiesOf| + |internalIntegrate| |iCompose| |fortranCompilerName| |setOfMinN| + |comment| |expintegrate| |eigenvector| |sylvesterSequence| + |lineColorDefault| |meshPar2Var| |froot| |repeatUntilLoop| + |OMputVariable| |setOrder| |lflimitedint| |generic?| + |prolateSpheroidal| |factorSquareFreePolynomial| + |setLegalFortranSourceExtensions| |airyBi| |ScanRoman| |hermite| + |SFunction| |hasTopPredicate?| |odd?| |limitedIntegrate| |denominator| + |augment| |primes| |f02bbf| |OMencodingSGML| |homogeneous?| + |selectfirst| |close| |applyRules| |iFTable| |cothIfCan| |monomRDE| + |dot| |topFortranOutputStack| |kind| |pile| |createPrimitivePoly| + |fracPart| |sequence| |e04ucf| |logGamma| |tableForDiscreteLogarithm| + |mindegTerm| |corrPoly| |normalise| |leastAffineMultiple| |varList| + |real?| |op| |nthFractionalTerm| |acschIfCan| |quoted?| |gcdPrimitive| + |display| |drawComplexVectorField| |bracket| |permutationGroup| + |d01apf| |ListOfTerms| |mainCharacterization| |before?| + |lieAdmissible?| |completeHermite| |acoshIfCan| |quasiAlgebraicSet| + |pattern| |euler| |factorFraction| |SturmHabicht| |isImplies| |nodes| + |fi2df| |diagonals| |curryLeft| |d02bhf| |createIrreduciblePoly| + |asechIfCan| |binomThmExpt| |f07aef| |coth2tanh| |quickSort| + |showClipRegion| |s18dcf| |coerceP| |mantissa| + |stosePrepareSubResAlgo| |eyeDistance| |e01sef| |makeYoungTableau| + |imagj| |monicRightDivide| |acotIfCan| |collectUnder| |cschIfCan| + |f04jgf| |contains?| |rangeIsFinite| |meshPar1Var| |morphism| + |content| |branchPoint?| |compile| + |dimensionOfIrreducibleRepresentation| |presub| |size?| |makeResult| + |exponentialOrder| |extract!| |setelt!| |brillhartIrreducible?| + |cyclicParents| |retract| |setTex!| |input| |message| |getZechTable| + |semicolonSeparate| |ParCond| |seriesToOutputForm| + |rewriteIdealWithRemainder| |horizConcat| |setClipValue| |pdf2df| + |LyndonCoordinates| |union| |iiasec| |directSum| |library| |f2df| + |elColumn2!| |round| |associatedSystem| |contours| + |reduceBasisAtInfinity| |pushNewContour| |diff| |imagI| |zeroOf| + |indicialEquation| |iiabs| |mapUnivariate| |mathieu12| |callForm?| + |singular?| |rootKerSimp| |number?| |BasicMethod| |reseed| |rational| + |sinh2csch| |genericRightNorm| |associator| |move| |setFieldInfo| + |myDegree| |enterInCache| |anfactor| |functionIsContinuousAtEndPoints| + |dihedralGroup| |outputMeasure| |Gamma| |coshIfCan| |setStatus| + |rewriteSetWithReduction| |signAround| |elRow2!| |listRepresentation| + |cycles| |ratPoly| |bernoulliB| |addPointLast| |pseudoQuotient| |set| + |antisymmetric?| |changeMeasure| |sample| |wholePart| + |symmetricDifference| |cTan| |cons| |getGraph| |swap| + |createGenericMatrix| |setRow!| |OMParseError?| |d01gbf| + |totalGroebner| |connect| |squareTop| |errorInfo| |OMUnknownCD?| + |FormatArabic| |option?| |fortranDouble| |invertIfCan| + |divisorCascade| |squareFreePolynomial| |reducedQPowers| |isTerm| + |squareFree| |LyndonWordsList1| |RittWuCompare| |symmetricTensors| + |headReduce| |plus| |Lazard2| |viewport2D| |maxdeg| |unitNormal| + |zero?| |alternating| |LyndonWordsList| |lllip| |rowEchelonLocal| + |resetVariableOrder| |bfEntry| |cosSinInfo| |pointLists| |powmod| + |mainKernel| |Ei| |cylindrical| |groebgen| |perspective| + |hyperelliptic| |cyclicSubmodule| |genericRightTraceForm| |host| + |rank| |fullPartialFraction| |cycleLength| |lieAlgebra?| |someBasis| + |submod| |removeRedundantFactorsInContents| |graphs| |outputSpacing| + |wrregime| |linear?| |dimensions| |distdfact| |e02dcf| + |factorGroebnerBasis| |midpoint| |iitanh| |selectIntegrationRoutines| + |flagFactor| |prevPrime| |getCurve| |taylorIfCan| + |characteristicSerie| |clipPointsDefault| |times| |primextendedint| + |OMbindTCP| |component| |constantKernel| |initial| + |semiIndiceSubResultantEuclidean| |bumptab| |univariate?| + |subResultantChain| |rightMinimalPolynomial| |approxSqrt| |edf2efi| + |gcdcofactprim| |constantOperator| |nor| |polyPart| |sign| + |regularRepresentation| |predicates| |changeThreshhold| |consnewpol| + |e01saf| |aLinear| |crest| |extendedint| |lazyPremWithDefault| + |Lazard| |cycleSplit!| |sylvesterMatrix| |LazardQuotient| + |exactQuotient!| |rowEchLocal| |s17dlf| |digit?| |singularAtInfinity?| + |leadingIndex| |dmpToP| |changeVar| |enqueue!| |cExp| |optimize| + |iiasin| |nextSubsetGray| |curve| |OMsupportsSymbol?| |nodeOf?| + |scale| |monom| |chebyshevT| |bandedJacobian| |scanOneDimSubspaces| + |rootSimp| |zag| |basisOfNucleus| |solve1| |startTableInvSet!| + |d01akf| |legendreP| |orbits| |lists| |rule| |medialSet| |wreath| + |fortranLinkerArgs| |spherical| |vconcat| |node| |digit| + |trailingCoefficient| |squareFreeLexTriangular| |besselJ| + |divideIfCan| |lazyEvaluate| |f04asf| |mapdiv| |scopes| |graphStates| + |patternMatchTimes| |uncouplingMatrices| |primitivePart!| + |createLowComplexityTable| |empty?| |selectOrPolynomials| |e04gcf| + |UpTriBddDenomInv| |common| |c06frf| |monomial?| |leadingBasisTerm| + |Nul| |imagk| |recip| |leftMinimalPolynomial| |hitherPlane| + |squareFreePrim| |rk4qc| |lazyPrem| |s14abf| |dominantTerm| + |symmetricRemainder| |tanSum| |functionIsFracPolynomial?| |htrigs| + |varselect| |factors| |selectMultiDimensionalRoutines| + |doubleComplex?| |chainSubResultants| |decompose| |cAsin| + |totalDegree| |logpart| |bivariatePolynomials| |s17akf| + |bezoutDiscriminant| |sqfree| |trigs| |bothWays| |OMgetEndAtp| |key| + |associatedEquations| |iiexp| |listYoungTableaus| + |structuralConstants| |alternatingGroup| |subHeight| + |sturmVariationsOf| |outputForm| |empty| |maxPoints3D| |printCode| + |extendIfCan| |presuper| |goodnessOfFit| |deleteProperty!| |var1Steps| + |reindex| |halfExtendedSubResultantGcd1| |filename| |OMgetVariable| + |subResultantsChain| |adaptive3D?| |powern| |leftQuotient| |cosh2sech| + |setfirst!| |infLex?| |subst| |explicitEntries?| |lexGroebner| + |branchIfCan| |ParCondList| |interactiveEnv| |e02bbf| |maxColIndex| + |removeSuperfluousQuasiComponents| |formula| |parse| |iflist2Result| + |OMgetFloat| |semiSubResultantGcdEuclidean2| |uniform01| + |exactQuotient| |getDatabase| |ode2| |externalList| |setPrologue!| + |brillhartTrials| |rdregime| |pdct| |selectOptimizationRoutines| + |float?| |reflect| |hostByteOrder| |iiacsc| |packageCall| + |inputOutputBinaryFile| |cos2sec| |bumptab1| |fortranLogical| + |overbar| |fortranCarriageReturn| |palgint| |equation| |zeroDim?| + |charpol| |numberOfVariables| |arrayStack| |balancedBinaryTree| + |possiblyInfinite?| |nlde| |constantOpIfCan| |sechIfCan| |nrows| + |viewZoomDefault| |rootOf| |replaceKthElement| |An| |chvar| + |OMencodingBinary| |mirror| |rationalApproximation| |sort| + |OMputEndBind| |ncols| |intcompBasis| |typeList| |trunc| |objects| + |rewriteSetByReducingWithParticularGenerators| |mr| |tValues| + |asimpson| |quatern| |getMeasure| EQ |properties| |partitions| + |close!| |lyndonIfCan| |base| |magnitude| |constant?| |imagK| + |symbolTableOf| |normalize| |roughBase?| |ignore?| |stop| + |monomialIntegrate| |translate| |eof?| |putGraph| |stopTableGcd!| + |minGbasis| |socf2socdf| |OMserve| |OMputString| |OMread| |abs| + |viewWriteAvailable| |insertBottom!| |explicitlyFinite?| + |roughSubIdeal?| |setFormula!| |usingTable?| |unitsColorDefault| + |zero| |droot| |fixedPointExquo| |random| |B1solve| |extractPoint| + |csubst| |Hausdorff| |tanh2trigh| |OMgetObject| |removeSinSq| + |basisOfLeftNucleus| |equality| |Si| |symFunc| |testModulus| + |nonQsign| |normDeriv2| |recolor| |zCoord| |rangePascalTriangle| |And| + |derivative| |dequeue| |index| |create3Space| |primeFrobenius| + |nthExponent| |lcm| |isOr| |indicialEquationAtInfinity| |datalist| + |inf| |coleman| |s19aaf| |Or| |identitySquareMatrix| + |createNormalPoly| |domainOf| |complexSolve| |sumSquares| |e02dff| + |setref| |cAcos| |suchThat| |curveColorPalette| |solveid| |delete| + |radicalSolve| |Not| |minimalPolynomial| |cRationalPower| |iicsch| + |complexRoots| |append| |keys| |OMputEndBVar| |explicitlyEmpty?| + |endSubProgram| |extractProperty| |Is| |degreeSubResultant| |operator| + |minus!| |omError| |unitCanonical| |pair| |viewDeltaYDefault| |isExpt| + |gcd| |positive?| |fintegrate| |f01bsf| |isTimes| |value| + |completeSmith| |taylorRep| |hypergeometric0F1| |torsion?| |freeOf?| + |interpret| |outputArgs| |normFactors| |green| |stack| |false| + |hdmpToP| |ip4Address| |realSolve| |normalizedAssociate| |addiag| + |knownInfBasis| |shrinkable| |conjugate| |mathieu22| |scalarMatrix| + |polygon| |lazyIrreducibleFactors| |quadratic| |binomial| |quoByVar| + |one?| |divideExponents| |badValues| |linearDependence| + |ramifiedAtInfinity?| |showFortranOutputStack| |previous| + |genericRightDiscriminant| |tower| |integralDerivationMatrix| + |symmetricProduct| |stFuncN| |errorKind| |lagrange| |revert| |f01rdf| + |cSech| |factorSquareFree| |e04naf| |complexNormalize| |coerceImages| + |stoseInvertibleSetreg| |f02aaf| |tubeRadiusDefault| |cyclic?| + |addmod| |OMgetEndError| |d01anf| |#| |eigenMatrix| |separateDegrees| + |alternative?| |associative?| |fortranCharacter| |dim| + |leftRankPolynomial| |hex| |predicate| |rightRankPolynomial| |lexico| + |monomRDEsys| |subscript| |ratDsolve| |perfectNthPower?| |OMreadStr| + |f01rcf| |latex| |completeHensel| |leastPower| |normal01| |lazy?| + |mapUp!| |integralBasis| |atanhIfCan| |argscript| |lyndon?| |f02adf| + |nextSublist| |fractRadix| |middle| |linearMatrix| |UnVectorise| + |minPoints3D| |gcdprim| |leviCivitaSymbol| |increasePrecision| + |complexNumeric| |trivialIdeal?| |leadingSupport| |subset?| + |doubleResultant| |exprToXXP| |newReduc| |Frobenius| |f02aff| |eulerE| + |yCoord| |f01ref| |firstDenom| |HermiteIntegrate| LODO2FUN |variable?| + |part?| |univariatePolynomialsGcds| |enumerate| + |unrankImproperPartitions0| |exprHasLogarithmicWeights| |kernels| + |zeroVector| |norm| |copy!| |c06gbf| |minimumDegree| |byteBuffer| + |listBranches| |modifyPoint| |basis| |log10| |readUInt32!| |ddFact| + |d03eef| |univariate| |trigs2explogs| |setVariableOrder| + |rationalFunction| |explimitedint| |getIdentifier| F2FG |solveRetract| + |OMputApp| |updateStatus!| |bitand| |LiePolyIfCan| |arbitrary| + |rightFactorIfCan| |nextPrimitivePoly| |SturmHabichtMultiple| + |makeUnit| |shufflein| |listLoops| |createRandomElement| |printHeader| + |supDimElseRittWu?| |bitior| |partialQuotients| |quasiRegular| + |parameters| |useSingleFactorBound| |center| |monicDecomposeIfCan| + |simpson| |rootDirectory| |rewriteIdealWithQuasiMonicGenerators| + |permutation| |polynomialZeros| |csch2sinh| |factor| |iitan| + |numberOfDivisors| |implies| |nullary| |cSin| |mergeDifference| + |yellow| |measure2Result| |over| |sqrt| |coth2trigh| |setLength!| + |diagonal?| F |f04atf| |OMsend| |e04fdf| |asinIfCan| |pleskenSplit| + |leftMult| |bivariate?| |bumprow| |real| |push| |groebnerIdeal| + |status| |addPoint| |ode| |bipolarCylindrical| |reduceLODE| + |chiSquare| |setProperty| |strongGenerators| |currentCategoryFrame| + |imag| |universe| |hconcat| |iExquo| |oddInfiniteProduct| |isAnd| + |generalLambert| |resetAttributeButtons| |directProduct| |null| + |search| |tan2trig| |putColorInfo| |lowerCase!| |df2mf| |mpsode| + |showAllElements| |scan| |binary| |lfinfieldint| |comparison| |not| + |outputFixed| |f02awf| |s13adf| |generateIrredPoly| |rational?| + |c06eaf| |exprToUPS| |weighted| |purelyTranscendental?| |ipow| |and| + |power!| |just| |brace| |laurentIfCan| |interReduce| |mesh?| + |printingInfo?| |hexDigit?| |rightRegularRepresentation| |s17dhf| + |palglimint| |or| |operators| |OMputEndAttr| |ranges| |destruct| + |att2Result| |sinhIfCan| |differentialVariables| |baseRDE| + |rightRecip| |conditionP| |triangSolve| |xor| |reduced?| + |yCoordinates| |negative?| |graeffe| |noKaratsuba| |s21bcf| |weight| + |OMgetString| |unitVector| |nand| |case| |numerators| |trace2PowMod| + |matrixGcd| |pointColor| |binaryFunction| |s17acf| + |numericalOptimization| |c06ebf| |overset?| |torsionIfCan| |Zero| + |removeConstantTerm| |s17def| |basicSet| |ran| |measure| |rdHack1| + |elem?| |copyInto!| |simplify| |rightTrace| |One| |iterationVar| + |LagrangeInterpolation| |c06gqf| |monomial| + |semiResultantReduitEuclidean| |roughEqualIdeals?| |split| |hspace| Y + |duplicates?| |simplifyExp| |f04mbf| |genericLeftDiscriminant| + |lifting1| |elRow1!| |multivariate| |totolex| |iteratedInitials| + |initiallyReduce| |coerce| |setColumn!| |f04qaf| |OMgetEndObject| + |modularFactor| |separant| |commonDenominator| |eigenvalues| + |variables| |linearAssociatedLog| |normalForm| |OMopenString| + |construct| |tablePow| |failed?| |crushedSet| |discriminantEuclidean| + |cotIfCan| |pascalTriangle| |s14baf| |dualSignature| |cAtanh| + |removeRedundantFactorsInPols| |diagonalProduct| |polarCoordinates| + |clearTheSymbolTable| |routines| |OMwrite| |s19abf| |OMgetBind| + |shiftRoots| |evenlambert| |quotient| |integralRepresents| |sncndn| + |finite?| |splitLinear| |cn| |d01gaf| |sort!| |writeBytes!| + |radicalEigenvalues| |interpretString| |selectNonFiniteRoutines| + |pomopo!| |prepareSubResAlgo| |nullSpace| |e02bcf| |imagi| + |algebraicVariables| |recoverAfterFail| |fortranTypeOf| + |stoseInvertible?sqfreg| |iisqrt2| |constantIfCan| |showSummary| + |algint| |rootRadius| |harmonic| |head| |taylor| |closedCurve?| + |composites| |obj| |diagonal| |leftLcm| |setEpilogue!| + |var2StepsDefault| |jacobian| |semiDiscriminantEuclidean| |moebius| + |laurent| |showTheIFTable| |lastSubResultant| |create| + |mainSquareFreePart| |countRealRoots| |cache| |makeGraphImage| + |showAttributes| |d03faf| |preprocess| |puiseux| |d02raf| + |stripCommentsAndBlanks| |lift| |sqfrFactor| |writable?| |setStatus!| + |repeating| |bezoutResultant| |particularSolution| |lazyGintegrate| + |numberOfFactors| |rightLcm| |reduce| |OMgetError| |readInt16!| + |concat!| |pToDmp| |wronskianMatrix| |inv| |setAdaptive| + |initiallyReduced?| |f04faf| |padecf| |script| |showTheSymbolTable| + |linGenPos| |aQuadratic| |triangular?| |leftTrace| |ground?| |redPol| + |semiResultantEuclidean2| |name| |euclideanNormalForm| |fractionPart| + |dmp2rfi| |viewWriteDefault| |tab1| |permutationRepresentation| + |ground| |integerIfCan| |normalizeIfCan| |body| |cap| |perfectSqrt| + |s18aff| |isOpen?| |besselY| |totalfract| |outputAsScript| + |inverseIntegralMatrix| |resetBadValues| |leadingMonomial| + |stiffnessAndStabilityOfODEIF| |e02ahf| |tex| |remove| + |viewSizeDefault| |inverseIntegralMatrixAtInfinity| + |continuedFraction| |unary?| |removeZero| |integralBasisAtInfinity| + |leadingCoefficient| |deepestTail| |testDim| |f02wef| |escape| + |cAcosh| |singRicDE| |equiv| |OMgetApp| |indices| |cross| |f01mcf| + |last| |matrixConcat3D| |quotientByP| |expenseOfEvaluationIF| + |inHallBasis?| |members| |SturmHabichtCoefficients| + |diophantineSystem| |child| |assoc| |subPolSet?| |say| |trapezoidal| + |debug3D| |lfunc| |roughUnitIdeal?| |makeEq| |upperCase| |critB| + |wordsForStrongGenerators| |compound?| |symmetricPower| |selectsecond| + |rootOfIrreduciblePoly| |bits| |groebner| |radix| |powerSum| |bat1| + |s17ajf| |factorial| |makingStats?| |maximumExponent| + |transcendenceDegree| |cCsch| |stopTable!| |isEquiv| |cAsech| + |mainForm| |resetNew| |leftTraceMatrix| |distribute| |setPredicates| + |in?| |fmecg| |byte| |probablyZeroDim?| |kroneckerDelta| |OMgetType| + |supRittWu?| |bipolar| |numberOfCycles| |lazyVariations| |iroot| + |perfectSquare?| |OMsupportsCD?| |firstSubsetGray| |palgextint0| + |prologue| |leastMonomial| |palgintegrate| |internalDecompose| + |algebraicSort| |evaluateInverse| |randomR| |sequences| + |multiplyCoefficients| |exponents| |e04dgf| |mappingAst| |mapSolve| + |int| |removeIrreducibleRedundantFactors| |rightAlternative?| |nthr| + |rst| BY |getSyntaxFormsFromFile| |discreteLog| |positiveSolve| + |element?| |shade| |iicoth| |select!| |setTopPredicate| |isPower| + |determinant| |linearlyDependent?| |distance| |mkAnswer| |regime| + |reduceByQuasiMonic| |imaginary| |repeating?| |setrest!| |e04jaf| + |sinIfCan| |intPatternMatch| |square?| |light| |dioSolve| |d02ejf| + |primaryDecomp| |iiperm| |setScreenResolution3D| |cot2trig| + |semiResultantEuclidean1| |stoseInvertibleSet| |queue| + |pmComplexintegrate| FG2F |s17aef| |smith| |findBinding| + |primitivePart| |linkToFortran| |tanhIfCan| |superHeight| |infix| + |idealSimplify| |totalDifferential| + |generalizedContinuumHypothesisAssumed| |setleft!| |unvectorise| + |newLine| |algebraicDecompose| |bottom!| |getMultiplicationTable| + |frst| |iiacos| |PollardSmallFactor| |leftExtendedGcd| + |stoseInvertibleSetsqfreg| |complement| |unparse| NOT |maxrank| + |messagePrint| |fixedDivisor| |extendedResultant| |viewPhiDefault| + |iiasinh| |leftUnits| |setleaves!| |e02baf| OR |entry| |ref| + |fractRagits| |diagonalMatrix| |returns| |children| |figureUnits| + |mdeg| |iidsum| |normalDeriv| AND |toScale| |KrullNumber| + |generalInfiniteProduct| |trim| |lex| |biRank| |mindeg| + |extendedEuclidean| |OMencodingXML| |removeSquaresIfCan| + |createZechTable| |removeRoughlyRedundantFactorsInPol| + |internalAugment| D |hasPredicate?| |viewpoint| |contract| + |innerSolve| |reorder| |exponential| |rootPoly| |iicosh| |subTriSet?| + |maxint| |palgextint| |coefChoose| |find| |lighting| + |outputBinaryFile| |tanNa| |expt| |tubePlot| |frobenius| |coHeight| + |rightExactQuotient| |bubbleSort!| |LowTriBddDenomInv| + |lazyPseudoRemainder| |semiSubResultantGcdEuclidean1| + |functionIsOscillatory| |normalDenom| |linearDependenceOverZ| + |pointColorPalette| |genericRightTrace| |rootSplit| |split!| + |showAll?| |getPickedPoints| |nonSingularModel| |edf2df| |inR?| + |nsqfree| |stFunc2| |iisinh| |karatsubaOnce| |perfectNthRoot| + |univariateSolve| |char| |radicalRoots| |nilFactor| + |numberOfComposites| |simplifyLog| |directory| |gbasis| + |jacobiIdentity?| |OMputObject| |OMunhandledSymbol| |sts2stst| + |goodPoint| |fixedPoint| |resultantReduitEuclidean| |normInvertible?| + |external?| |leftPower| |plusInfinity| |setlast!| |sn| |red| |updatF| + |constantCoefficientRicDE| |OMreadFile| |specialTrigs| |s21baf| |is?| + |minusInfinity| |prem| |midpoints| |argumentList!| * |lfextlimint| + |checkForZero| |shellSort| |npcoef| |extensionDegree| |d02bbf| + |e01bef| |range| |generalTwoFactor| |rem| |moduleSum| + |toseSquareFreePart| |factorsOfDegree| |f04maf| |seed| |print| |repSq| + |f02agf| |sincos| |problemPoints| |f02bjf| |quo| |generalPosition| + |reverseLex| |elseBranch| |lexTriangular| |rootPower| |resolve| + |compdegd| |cAcsch| |OMgetBVar| |basisOfCentroid| |rubiksGroup| + |lifting| |screenResolution| = |float| |separate| |selectPDERoutines| + |raisePolynomial| |pushuconst| |ceiling| |dflist| |rk4| |div| + |scripted?| |pi| |normal?| |selectODEIVPRoutines| |physicalLength| + |type| |const| |delta| |hue| |internalSubQuasiComponent?| |complex?| + |interpolate| |iisech| |exquo| < |infinity| |d02kef| |mainContent| + |OMconnInDevice| |retractIfCan| |qinterval| |xn| |overlabel| |adjoint| + |mesh| ~= > |discriminant| |relationsIdeal| |overlap| |zeroSetSplit| + |blue| |wholeRadix| |multiplyExponents| |headAst| + |invertibleElseSplit?| ~ <= |node?| + |solveLinearPolynomialEquationByRecursion| |mainMonomials| |mathieu11| + |subtractIfCan| |heapSort| |semiDegreeSubResultantEuclidean| + |colorDef| |positiveRemainder| |ptree| |relerror| |signature| |kernel| + >= |fortranLiteral| |plotPolar| |erf| |typeLists| + |useSingleFactorBound?| |symmetricSquare| |readLineIfCan!| |linSolve| + |setClosed| |draw| |f02ajf| |cPower| |tanh2coth| |imagE| |fortran| + |padicFraction| |cyclotomicDecomposition| |rightRemainder| + |conditionsForIdempotents| |parent| |/\\| |max| |OMmakeConn| |radPoly| + |listOfMonoms| |doubleDisc| |semiLastSubResultantEuclidean| |notelem| + |permutations| |minimize| RF2UTS |\\/| GE |tanIfCan| + + |leftFactorIfCan| |graphState| |stirling2| |dilog| |lambda| + |printTypes| |isQuotient| |startPolynomial| |mainExpression| + |ScanArabic| |upperCase!| |leftAlternative?| |factorOfDegree| - + |fixPredicate| GT |wordInStrongGenerators| |sin| |shiftLeft| + |genericPosition| |fTable| |choosemon| |cyclicCopy| |makeObject| + |multiEuclidean| |s19acf| / |redmat| LE |endOfFile?| |cos| |map| + |graphCurves| |contractSolve| |linearlyDependentOverZ?| + |blankSeparate| |compose| |getProperties| |trueEqual| |cosIfCan| LT + |isMult| |tan| |currentEnv| |showTheFTable| |saturate| |rationalPower| + |e02zaf| |relativeApprox| |shift| |makeSin| |coef| |less?| + |showRegion| |cot| |clikeUniv| UTS2UP |plus!| |f04mcf| |triangulate| + |indiceSubResultant| |reducedContinuedFraction| + |numberOfIrreduciblePoly| |uniform| |quadraticForm| |sec| + |getMultiplicationMatrix| |height| |nextIrreduciblePoly| |mulmod| + |monomialIntPoly| |d03edf| |tracePowMod| |setButtonValue| + |rationalPoint?| |bivariateSLPEBR| |csc| |expressIdealMember| |ideal| + |patternVariable| |OMputEndApp| |OMlistCDs| |alphanumeric| |makeFR| + |represents| |xCoord| |asin| |convert| |property| |cycleRagits| + |partialNumerators| |definingPolynomial| |log2| + |stoseInternalLastSubResultant| |toseInvertible?| |d01amf| + |modifyPointData| |pair?| |acos| |sh| |cup| |clearTheFTable| + |lowerCase?| |low| |cond| |removeCoshSq| |setAdaptive3D| |subSet| + |integral| |atan| |clearTable!| |build| |ScanFloatIgnoreSpaces| + |graphImage| |digits| |makeop| |palginfieldint| |qqq| |character?| + |acot| |units| |localUnquote| |bfKeys| |stoseInvertible?reg| + |clearDenominator| |tubeRadius| |standardBasisOfCyclicSubmodule| + |idealiserMatrix| |finiteBound| |curve?| |asec| UP2UTS |constantLeft| + |factorByRecursion| |plenaryPower| |s18def| + |genericRightMinimalPolynomial| |asecIfCan| |kmax| |qelt| |po| + |factorSFBRlcUnit| |zeroSquareMatrix| |acsc| |rightGcd| |addBadValue| + |numberOfFractionalTerms| |stronglyReduce| |qsetelt| |bit?| + |setPosition| |viewDefaults| |cscIfCan| |sinh| |aQuartic| + |flexibleArray| |evaluate| |quadratic?| |OMputAtp| |recur| |xRange| + |unit| |integers| |pol| |cosh| |powerAssociative?| |invmod| |exptMod| + |screenResolution3D| |partition| |yRange| |resize| |iicos| + |integralLastSubResultant| |tanh| |monicCompleteDecompose| |code| + |expandTrigProducts| |normalElement| |key?| |bright| |mapmult| + |padicallyExpand| |printInfo| |declare| |bombieriNorm| |henselFact| + |identification| |coth| |curry| |subMatrix| |mvar| |polCase| |untab| + |pop!| |tail| |cycleElt| |c06fuf| |sech| |maxrow| |complexEigenvalues| + |logical?| |polyRicDE| |atoms| |makeprod| |modularGcdPrimitive| + |setMaxPoints| |signatureAst| |high| |csch| |drawToScale| |atom?| + |clipSurface| |calcRanges| |selectSumOfSquaresRoutines| |f02axf| + |cAcsc| |function| |even?| |leadingTerm| |asinh| |order| |outputList| + |constantToUnaryFunction| |rules| |failed| |powers| + |indicialEquations| |parametric?| |headRemainder| |zeroDimensional?| + |acosh| |push!| |elementary| |nextNormalPoly| |pushdterm| |permanent| + |box| |dom| |collect| |principal?| |unknown| |splitConstant| |eval| + |ramified?| |atanh| |rroot| |algebraic?| |genericLeftNorm| |f02abf| + |numberOfMonomials| |inGroundField?| |leader| |backOldPos| |e02aef| + |lambert| |rowEchelon| |acoth| |thenBranch| |primitiveElement| + |computeCycleLength| |algebraicOf| |iiacot| |f02xef| |cSec| + |isobaric?| |asech| |buildSyntax| |bezoutMatrix| |integer?| + |purelyAlgebraic?| |normalized?| |extractSplittingLeaf| + |getButtonValue| |dimension| |numFunEvals| |lhs| |validExponential| + |irreducible?| |unitNormalize| |OMputInteger| |string?| |superscript| + |iilog| |OMputAttr| |insertRoot!| |multiple| |rhs| |mightHaveRoots| + |identityMatrix| |s01eaf| |OMgetEndAttr| |OMencodingUnknown| |super| + |expenseOfEvaluation| |sorted?| |cLog| |li| |applyQuote| |diag| + |lowerCase| |title| |ldf2lst| |composite| |curveColor| |fixedPoints| + |youngGroup| |littleEndian| |solveLinearPolynomialEquationByFractions| + |critMonD1| |coordinates| |addMatchRestricted| |extend| + |antisymmetricTensors| |linearAssociatedExp| |triangularSystems| |eq?| + |difference| |inrootof| |optional?| |computeCycleEntry| |increment| + |modularGcd| |primlimitedint| |intChoose| |lazyPseudoQuotient| + |ruleset| |double| |e| |e02def| |scaleRoots| |slex| + |subscriptedVariables| |entries| |clipParametric| |multisect| + |rightDivide| |true| |denomLODE| |innerSolve1| |trapezoidalo| |f01qdf| + |rectangularMatrix| |univariatePolynomial| |schwerpunkt| + |unaryFunction| |subResultantGcdEuclidean| |root?| + |integralCoordinates| |insert!| |whatInfinity| |mathieu23| |monomials| + |s18aef| |ReduceOrder| |e04mbf| |nothing| |cycleTail| |delete!| + |rightUnits| |space| |firstNumer| |qualifier| |simpleBounds?| + |outputAsTex| |redpps| |parts| |maxPoints| |sizePascalTriangle| + |delay| |gradient| |subresultantVector| |swap!| |cAcot| |laguerre| + |symmetric?| |hostPlatform| |supersub| |semiResultantEuclideannaif| + |tanQ| |rowEch| |dfRange| |cartesian| |symmetricGroup| + |lazyResidueClass| |test| |completeEval| |se2rfi| |cfirst| |inspect| + |univcase| |rightScalarTimes!| |rCoord| |df2fi| |OMsetEncoding| + |iidprod| |declare!| |shanksDiscLogAlgorithm| |credPol| |s17dgf| + |leftGcd| |rightFactorCandidate| |inverseLaplace| |expandLog| + |finiteBasis| |double?| |currentSubProgram| |f01qef| |iicsc| + |oddintegers| |numberOfHues| |localIntegralBasis| + |leftCharacteristicPolynomial| |width| |cAtan| |setchildren!| + |complementaryBasis| |mapExpon| |OMgetEndBVar| |conjugates| + |newSubProgram| |e02bef| |generate| |eq| |drawStyle| |writeInt8!| + |selectAndPolynomials| |subNodeOf?| |lllp| |dn| |expandPower| + |bandedHessian| |sinhcosh| |iter| |pmintegrate| |digamma| |prefix| + |minRowIndex| |prime| |call| |leftRank| |integerBound| |palgLODE| + |isOp| |incrementBy| |infRittWu?| |flatten| |nthRoot| |Ci| |pr2dmp| + |leftRemainder| |singleFactorBound| |dequeue!| |mkPrim| |reverse!| + |child?| |expand| |lo| |elements| |stoseLastSubResultant| |limitPlus| + |lprop| |open| |rotatex| |fortranDoubleComplex| |safeFloor| + |firstUncouplingMatrix| |sPol| |filterWhile| |palgRDE0| |computeInt| + |whileLoop| |fractionFreeGauss!| |segment| |makeVariable| |acscIfCan| + |fortranReal| |prinshINFO| |merge| |filterUntil| |OMlistSymbols| + |realEigenvectors| |meatAxe| |deepCopy| |principalAncestors| |gethi| + |degreePartition| |nextPartition| |quasiRegular?| |select| |optional| + |univariatePolynomials| |rotatey| |representationType| |reify| + |prindINFO| |primitiveMonomials| |OMputBVar| |makeViewport3D| |s14aaf| + |qroot| |checkPrecision| |expPot| |rightZero| |autoReduced?| + |makeTerm| |operations| |s20acf| |reductum| |rightUnit| |closedCurve| + |parametersOf| |initials| |exp| |quote| |oblateSpheroidal| |getMatch| + |write!| |rotate| |basisOfRightNucleus| |cardinality| |setProperties!| + |shuffle| |qPot| |s13aaf| |satisfy?| |index?| |precision| |exists?| + |localReal?| |neglist| |style| |epilogue| |mat| |solid| |stFunc1| + |argumentListOf| |setprevious!| |rootProduct| |pointPlot| + |rootNormalize| |birth| |outerProduct| |csc2sin| |OMgetEndBind| |root| + |integralMatrixAtInfinity| |primextintfrac| |totalLex| |makeRecord| + |lastSubResultantEuclidean| |pushdown| |points| |expextendedint| + |mathieu24| |algebraicCoefficients?| |karatsubaDivide| |hessian| + |adaptive| |purelyAlgebraicLeadingMonomial?| |mkcomm| + |stronglyReduced?| |nil| |skewSFunction| |accuracyIF| |monicDivide| + |bitTruth| |prime?| SEGMENT |rightCharacteristicPolynomial| |makeSUP| + |linearPart| |f01qcf| |point?| |complexEigenvectors| |region| + |leadingCoefficientRicDE| |modulus| |module| |laplace| |d02gbf| + |boundOfCauchy| |curryRight| |complexNumericIfCan| |pointData| + |irreducibleFactors| |makeCos| |FormatRoman| |changeWeightLevel| + |exQuo| |deriv| |approximate| |bsolve| |doubleRank| + |nextsousResultant2| |iipow| |inverseColeman| |rightExtendedGcd| + |coefficient| |e01daf| |PDESolve| |complex| |exp1| |second| |log| + |randomLC| |stopMusserTrials| |numberOfComponents| |extractBottom!| + |interval| |associates?| |vark| |setMinPoints| |scalarTypeOf| |third| + |makeSketch| |twist| |setMaxPoints3D| |sumOfSquares| |weakBiRank| + |iifact| |rationalIfCan| |characteristic| |reduction| |sturmSequence| + |exprToGenUPS| |aromberg| |nary?| |coercePreimagesImages| |sdf2lst| + |sizeMultiplication| |innerint| |readIfCan!| |copies| |rischDEsys| + |alphanumeric?| |nthFlag| |reducedForm| |sum| |oddlambert| + |stiffnessAndStabilityFactor| |read!| |OMputBind| |rename| |position!| + |d01alf| |removeRoughlyRedundantFactorsInContents| + |linearAssociatedOrder| |extractTop!| |cAsinh| |sech2cosh| |floor| + |rquo| |concat| |rspace| |Aleph| |pdf2ef| |complexLimit| |any| + |largest| |check| |extractIndex| |bindings| |forLoop| |qfactor| + |e02ajf| |sub| |vectorise| |alphabetic?| |orbit| |systemCommand| + |lazyPquo| |zeroDimPrimary?| |companionBlocks| |gramschmidt| |c05nbf| + |completeEchelonBasis| |allRootsOf| |idealiser| |rightRank| + |removeRedundantFactors| |tryFunctionalDecomposition?| |c06fqf| |lp| + |ocf2ocdf| |clearFortranOutputStack| |removeZeroes| |bat| + |innerEigenvectors| |cycle| |direction| |OMconnOutDevice| |OMclose| + |f02aef| |rightNorm| |resultantnaif| |lastSubResultantElseSplit| + |intermediateResultsIF| |besselI| |generalizedEigenvector| |normal| + |sec2cos| |cycleEntry| |heap| |makeFloatFunction| |charthRoot| + |decreasePrecision| |adaptive?| |multMonom| |startTableGcd!| + |karatsuba| |coefficients| |denominators| |OMputEndError| |laurentRep| + |OMopenFile| |imports| |basisOfCommutingElements| |s15aef| |janko2| + |sin2csc| |source| |OMgetAttr| |setnext!| |closeComponent| + |unprotectedRemoveRedundantFactors| |category| |dmpToHdmp| |ratpart| + |secIfCan| |swapColumns!| |minset| |isPlus| |safeCeiling| + |extractClosed| |rotate!| |doublyTransitive?| |s17adf| |OMgetSymbol| + |basisOfRightNucloid| |domain| |primeFactor| |jordanAlgebra?| + |quotedOperators| |realZeros| |linear| |package| |prod| |complexForm| + |categoryFrame| |lSpaceBasis| |subResultantGcd| + |variationOfParameters| |stoseSquareFreePart| |show| |inverse| + |rischNormalize| |makeViewport2D| |binaryTournament| + |axesColorDefault| |btwFact| |iomode| |assign| |highCommonTerms| + |polynomial| |unravel| |inRadical?| |viewPosDefault| |ef2edf| |dec| + |target| |s15adf| |monicRightFactorIfCan| |rationalPoints| |trace| + |radicalOfLeftTraceForm| |every?| |substring?| |critMTonD1| + |swapRows!| |df2ef| |has?| |rarrow| |antiAssociative?| |divideIfCan!| + |nthFactor| |weights| |mapMatrixIfCan| |increase| |toroidal| + |setLabelValue| |currentScope| |next| |abelianGroup| + |mainCoefficients| |suffix?| |hdmpToDmp| |degree| + |partialDenominators| |iiatanh| |chebyshevU| |parabolicCylindrical| + |member?| |tube| |ravel| |leftOne| |reverse| |leftExactQuotient| + |setEmpty!| |extension| |ffactor| |selectPolynomials| |aCubic| + |addPoint2| |reshape| |unexpand| |sup| |intersect| + |oneDimensionalArray| |length| |basisOfLeftNucloid| + |exportedOperators| |mainDefiningPolynomial| |minColIndex| + |atrapezoidal| |surface| |patternMatch| |pointSizeDefault| |scripts| + |setelt| |parabolic| |solveLinear| |top| |times!| |writeUInt8!| + |hermiteH| |arg1| |e02bdf| |decimal| |pureLex| |tableau| |c02agf| + |LazardQuotient2| |comp| |var1StepsDefault| |complexExpand| + |radicalEigenvector| |eisensteinIrreducible?| |arg2| |quadraticNorm| + |copy| |moreAlgebraic?| |internalZeroSetSplit| |clearTheIFTable| + |topPredicate| |infieldIntegrate| |sumOfDivisors| |argument| + |halfExtendedResultant2| |exteriorDifferential| |lepol| |continue| + |chineseRemainder| |divisors| |ldf2vmf| |update| |mainPrimitivePart| + |stopTableInvSet!| |sumOfKthPowerDivisors| |conditions| + |generalizedContinuumHypothesisAssumed?| |processTemplate| |elliptic?| + |fglmIfCan| |algSplitSimple| |front| |colorFunction| |match| |getRef| + |autoCoerce| |atanIfCan| |Beta| |list| |commaSeparate| + |basisOfRightAnnihilator| |cyclotomic| |maxIndex| |conjug| |color| + |init| |objectOf| |result| |stirling1| |collectQuasiMonic| |cyclic| + |car| |writeLine!| |nextColeman| |minordet| |mainVariable| + |unknownEndian| |fortranInteger| |ricDsolve| |cdr| |nthExpon| + |primintegrate| |primitive?| |setScreenResolution| |setImagSteps| + |internalInfRittWu?| |subresultantSequence| |reset| |setDifference| + |countRealRootsMultiple| |checkRur| |position| |complexIntegrate| + |logIfCan| |distFact| |movedPoints| |kovacic| |setIntersection| + |numeric| |vspace| |BumInSepFFE| |optpair| |symbolTable| |thetaCoord| + |f01brf| |nthRootIfCan| |factorAndSplit| |hasoln| |realElementary| + |radical| |cSinh| |infiniteProduct| |write| |setUnion| |getOrder| + |match?| |numberOfOperations| |nativeModuleExtension| + |createPrimitiveNormalPoly| |merge!| |stoseInvertible?| |tree| + |central?| |save| |pushFortranOutputStack| |OMUnknownSymbol?| + |transcendentalDecompose| |apply| |replace| |factor1| + |listConjugateBases| |rename!| |approximants| |s18acf| |getConstant| + |mapCoef| |lintgcd| |popFortranOutputStack| |pquo| |divide| + |vertConcat| |palglimint0| |isAbsolutelyIrreducible?| + |leftRegularRepresentation| |transcendent?| |meshFun2Var| |rightPower| + |hash| |size| |minPoints| |outputAsFortran| |userOrdered?| |open?| + |intensity| |setErrorBound| |toseLastSubResultant| |solid?| |c05pbf| + |count| |debug| |edf2ef| |d01bbf| |minPoly| |unmakeSUP| + |numberOfNormalPoly| |outlineRender| |lazyPseudoDivide| + |invertibleSet| |eulerPhi| |removeSuperfluousCases| |setright!| + |zeroSetSplitIntoTriangularSystems| |getCode| |internalSubPolSet?| + |block| |coerceL| |depth| |hMonic| |printStats!| |lyndon| + |radicalEigenvectors| |combineFeatureCompatibility| + |absolutelyIrreducible?| |moduloP| |createPrimitiveElement| |first| + |arguments| |duplicates| |insertTop!| |integral?| |iprint| |getStream| + |generator| |removeCosSq| |sortConstraints| |limit| |c06ecf| |rest| + |monicLeftDivide| |getOperator| |s13acf| |dihedral| + |degreeSubResultantEuclidean| |c06gsf| |f02fjf| |useNagFunctions| + |genus| |indiceSubResultantEuclidean| |substitute| |isList| + |critpOrder| |solveInField| |dAndcExp| |normalizedDivide| |whitePoint| + |besselK| |removeDuplicates| |partialFraction| |removeSinhSq| |cAcoth| + |retractable?| |gcdcofact| |level| |coerceS| |rightQuotient| |badNum| + |pade| |axes| |prinb| |anticoord| |opeval| |bounds| |refine| + |extendedSubResultantGcd| |definingEquations| |nthCoef| |pseudoDivide| + |separateFactors| |rur| |modTree| |zoom| |laguerreL| |terms| |bag| + |localAbs| |numericalIntegration| |readByte!| |orthonormalBasis| + |f02akf| |internal?| |sparsityIF| |resultant| |multiset| |power| + |df2st| |readBytes!| |eigenvectors| |cyclicGroup| |mapBivariate| + |e01bff| |lfextendedint| |cAsec| |bringDown| |defineProperty| + |iisqrt3| |compiledFunction| |nextLatticePermutation| |matrix| + |extractIfCan| |numer| |wordInGenerators| |squareMatrix| |bytes| + |deleteRoutine!| |critT| |gensym| |fortranLiteralLine| |entry?| + |rischDE| |s21bdf| |denom| |s18adf| |getVariableOrder| |ptFunc| + |deepestInitial| |polygon?| |removeRoughlyRedundantFactorsInPols| + |vector| |OMcloseConn| |noLinearFactor?| |constDsolve| |gcdPolynomial| + |moebiusMu| |getOperands| |optAttributes| |mapExponents| + |approxNthRoot| |LyndonBasis| |differentiate| |iisin| |rootsOf| + |addMatch| |cCsc| |phiCoord| |ord| |createNormalPrimitivePoly| + |dimensionsOf| |bitCoef| |linears| |changeNameToObjf| |expint| + |tan2cot| |ksec| |squareFreeFactors| |categories| |paren| |chiSquare1| + |subNode?| |flexible?| |c06ekf| |outputFloating| |rk4f| + |solveLinearlyOverQ| |UP2ifCan| |isConnected?| |identity| |printInfo!| + |ellipticCylindrical| |commutator| |setProperty!| + |rewriteIdealWithHeadRemainder| |invmultisect| |readable?| |f01maf| + |iiasech| |groebner?| |writeByte!| |invertible?| |operation| + |divergence| |sayLength| |belong?| |characteristicPolynomial| + |getBadValues| |mapDown!| |cCoth| |d01asf| |inconsistent?| |id| + |resultantReduit| |d02cjf| |algDsolve| |rightOne| |denomRicDE| + |iiacoth| |quartic| |getProperty| |critBonD| |incr| |truncate| + |GospersMethod| |primPartElseUnitCanonical!| |explogs2trigs| |postfix| + |binding| |leftNorm| |prinpolINFO| |factorset| |table| |leadingIdeal| + |fibonacci| |readLine!| |setProperties| |binarySearchTree| |f04axf| + |setMinPoints3D| |jacobi| |characteristicSet| |loadNativeModule| |new| + |hi| |f04adf| |restorePrecision| |showScalarValues| |fortranComplex| + |insertMatch| |redPo| GF2FG |stoseIntegralLastSubResultant| + |insertionSort!| |insert| |algintegrate| |computePowers| + |evenInfiniteProduct| |iiGamma| |lquo| |unit?| |realEigenvalues| + |conical| |irreducibleFactor| |inc| |getExplanations| + |normalizeAtInfinity| |e01sbf| |readInt8!| + |solveLinearPolynomialEquation| |clearCache| |jordanAdmissible?| + |setsubMatrix!| |primlimintfrac| |deref| |options| |groebSolve| + |iiatan| |integralAtInfinity?| |minPol| |mainMonomial| |binaryTree| + |setPoly| |e02ddf| |nextsubResultant2| |parents| |multiEuclideanTree| + |vedf2vef| |createMultiplicationMatrix| |numberOfPrimitivePoly| + |leaves| |cubic| |createLowComplexityNormalBasis| |minIndex| |void| + |fill!| |generalSqFr| |back| |lowerPolynomial| |OMgetAtp| |column| + |closed?| |rightMult| |rk4a| |clipBoolean| |compactFraction| |string| + |noncommutativeJordanAlgebra?| |useEisensteinCriterion?| + |numFunEvals3D| |zerosOf| |symbolIfCan| |aspFilename| |collectUpper| + |c06gcf| |prepareDecompose| |zeroDimPrime?| |exponential1| + |numberOfChildren| |halfExtendedSubResultantGcd2| + |primPartElseUnitCanonical| |rotatez| |monicModulo| |mkIntegral| + |extendedIntegrate| |lfintegrate| |reopen!| |antiCommutative?| + |exprHasWeightCosWXorSinWX| |generic| |leftZero| |e01bgf| |exponent| + |mainValue| |LiePoly| |internalLastSubResultant| |airyAi| |realRoots| + |multiple?| |countable?| |e02gaf| |bigEndian| |beauzamyBound| |left| + |quasiComponent| |numericIfCan| |SturmHabichtSequence| |d01ajf| + |pushup| |euclideanSize| |nextItem| |HenselLift| |e02akf| |right| + |product| |romberg| |more?| |splitSquarefree| |symbol?| |safetyMargin| + |linearPolynomials| |imagJ| |weierstrass| |isNot| |e02daf| |mix| + |deepExpand| |plot| |cCos| |llprop| |OMputEndObject| |polyred| |elt| + |changeBase| |leaf?| |twoFactor| |goto| |ridHack1| + |reciprocalPolynomial| |makeSeries| |acosIfCan| |asinhIfCan| + |newTypeLists| |infinite?| |definingInequation| |leadingExponent| + |integrate| |multinomial| |startTable!| |nil?| |tanAn| |OMconnectTCP| + |output| |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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(|has| |#2| (-791)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2706 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2706 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1036 (-407 (-564)))) (|has| |#2| (-1097))) ((-614 (-564)) -2706 (|has| |#2| (-1047)) (-12 (|has| |#2| (-1036 (-564))) (|has| |#2| (-1097))) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-614 |#2|) -2706 (|has| |#2| (-1097)) (|has| |#2| (-172))) ((-611 (-860)) -2706 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-860))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1262 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1047)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1047))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1047)) ((-411 |#2|) |has| |#2| (-1097)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-644 (-564)) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 |#2|) -2706 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-646 |#2|) -2706 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-646 $) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-638 |#2|) -2706 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1047))) ((-637 |#2|) |has| |#2| (-1047)) ((-715 |#2|) -2706 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-724) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-724)) (|has| |#2| (-172))) ((-789) |has| |#2| (-846)) ((-790) -2706 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-791) |has| |#2| (-791)) ((-792) -2706 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-793) -2706 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-846) |has| |#2| (-846)) ((-848) -2706 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-898 (-1173)) -12 (|has| |#2| (-898 (-1173))) (|has| |#2| (-1047))) ((-1036 #0#) -12 (|has| |#2| (-1036 (-407 (-564)))) (|has| |#2| (-1097))) ((-1036 (-564)) -12 (|has| |#2| (-1036 (-564))) (|has| |#2| (-1097))) ((-1036 |#2|) |has| |#2| (-1097)) ((-1049 |#2|) -2706 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1049 $) |has| |#2| (-172)) ((-1054 |#2|) -2706 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1054 $) |has| |#2| (-172)) ((-1047) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-1055) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-1109) -2706 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-724)) (|has| |#2| (-172))) ((-1097) -2706 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1212) . T) ((-1269 |#2|) |has| |#2| (-363))) -((-1910 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1320 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-4358 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -1910 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1320 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4358 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-769) (-1212) (-1212)) (T -239)) -((-4358 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-769)) (-4 *6 (-1212)) (-4 *7 (-1212)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1320 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-769)) (-4 *6 (-1212)) (-4 *2 (-1212)) (-5 *1 (-239 *5 *6 *2)))) (-1910 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-769)) (-4 *7 (-1212)) (-4 *5 (-1212)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-724)) (PROGN (-6 (-724)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4407)) (-6 -4407) |%noBranch|) (IF (|has| |t#2| (-846)) (-6 (-846)) |%noBranch|) (IF (|has| |t#2| (-791)) (-6 (-791)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1269 |t#2|)) |%noBranch|))) +(((-21) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2805 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2805 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1036 (-407 (-564)))) (|has| |#2| (-1097))) ((-614 (-564)) -2805 (|has| |#2| (-1047)) (-12 (|has| |#2| (-1036 (-564))) (|has| |#2| (-1097))) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-614 |#2|) -2805 (|has| |#2| (-1097)) (|has| |#2| (-172))) ((-611 (-860)) -2805 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-860))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1262 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1047)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1047))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1047)) ((-411 |#2|) |has| |#2| (-1097)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-644 (-564)) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 |#2|) -2805 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-646 |#2|) -2805 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-646 $) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-638 |#2|) -2805 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1047))) ((-637 |#2|) |has| |#2| (-1047)) ((-715 |#2|) -2805 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-724) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-724)) (|has| |#2| (-172))) ((-789) |has| |#2| (-846)) ((-790) -2805 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-791) |has| |#2| (-791)) ((-792) -2805 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-793) -2805 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-846) |has| |#2| (-846)) ((-848) -2805 (|has| |#2| (-846)) (|has| |#2| (-791))) ((-898 (-1173)) -12 (|has| |#2| (-898 (-1173))) (|has| |#2| (-1047))) ((-1036 #0#) -12 (|has| |#2| (-1036 (-407 (-564)))) (|has| |#2| (-1097))) ((-1036 (-564)) -12 (|has| |#2| (-1036 (-564))) (|has| |#2| (-1097))) ((-1036 |#2|) |has| |#2| (-1097)) ((-1049 |#2|) -2805 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1049 $) |has| |#2| (-172)) ((-1054 |#2|) -2805 (|has| |#2| (-1047)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1054 $) |has| |#2| (-172)) ((-1047) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-1055) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-172))) ((-1109) -2805 (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-724)) (|has| |#2| (-172))) ((-1097) -2805 (|has| |#2| (-1097)) (|has| |#2| (-1047)) (|has| |#2| (-846)) (|has| |#2| (-791)) (|has| |#2| (-724)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1212) . T) ((-1269 |#2|) |has| |#2| (-363))) +((-2410 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2597 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3069 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2410 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2597 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3069 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-769) (-1212) (-1212)) (T -239)) +((-3069 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-769)) (-4 *6 (-1212)) (-4 *7 (-1212)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2597 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-769)) (-4 *6 (-1212)) (-4 *2 (-1212)) (-5 *1 (-239 *5 *6 *2)))) (-2410 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-769)) (-4 *7 (-1212)) (-4 *5 (-1212)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-638 #0#) |has| |#1| (-38 (-407 (-564)))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-715 #0#) |has| |#1| (-38 (-407 (-564)))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-724) . T) ((-898 (-1173)) |has| |#1| (-898 (-1173))) ((-898 |#3|) . T) ((-884 (-379)) -12 (|has| |#1| (-884 (-379))) (|has| |#3| (-884 (-379)))) ((-884 (-564)) -12 (|has| |#1| (-884 (-564))) (|has| |#3| (-884 (-564)))) ((-947 |#1| |#4| |#3|) . T) ((-907) |has| |#1| (-907)) ((-1036 (-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) ((-1036 (-564)) |has| |#1| (-1036 (-564))) ((-1036 |#1|) . T) ((-1036 |#2|) . T) ((-1036 |#3|) . T) ((-1049 #0#) |has| |#1| (-38 (-407 (-564)))) ((-1049 |#1|) . T) ((-1049 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-1054 #0#) |has| |#1| (-38 (-407 (-564)))) ((-1054 |#1|) . T) ((-1054 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1216) |has| |#1| (-907))) -((-2907 (((-112) $ $) 19 (|has| |#1| (-1097)))) (-3686 ((|#1| $) 55)) (-2362 ((|#1| $) 45)) (-3697 (((-112) $ (-769)) 8)) (-1976 (($) 7 T CONST)) (-4166 (($ $) 61)) (-2087 (($ $) 49)) (-1428 ((|#1| |#1| $) 47)) (-1744 ((|#1| $) 46)) (-2936 (((-642 |#1|) $) 31 (|has| $ (-6 -4410)))) (-3462 (((-112) $ (-769)) 9)) (-3234 (((-642 |#1|) $) 30 (|has| $ (-6 -4410)))) (-2776 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-2613 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4411)))) (-4358 (($ (-1 |#1| |#1|) $) 36)) (-3576 (((-112) $ (-769)) 10)) (-2480 (((-769) $) 62)) (-3315 (((-1155) $) 22 (|has| |#1| (-1097)))) (-2730 ((|#1| $) 40)) (-1704 ((|#1| |#1| $) 53)) (-3604 ((|#1| |#1| $) 52)) (-3183 (($ |#1| $) 41)) (-1295 (((-769) $) 56)) (-4033 (((-1117) $) 21 (|has| |#1| (-1097)))) (-1353 ((|#1| $) 63)) (-1479 ((|#1| $) 51)) (-1475 ((|#1| $) 50)) (-3388 ((|#1| $) 42)) (-2121 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4410)))) (-3215 (($ $ (-642 (-294 |#1|))) 27 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-294 |#1|)) 26 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-642 |#1|) (-642 |#1|)) 24 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))))) (-4245 (((-112) $ $) 14)) (-2311 ((|#1| |#1| $) 59)) (-3719 (((-112) $) 11)) (-2972 (($) 12)) (-1456 ((|#1| $) 60)) (-3945 (($) 58) (($ (-642 |#1|)) 57)) (-1930 (((-769) $) 44)) (-4043 (((-769) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4410))) (((-769) |#1| $) 29 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-3901 (($ $) 13)) (-2327 (((-860) $) 18 (|has| |#1| (-611 (-860))))) (-1825 ((|#1| $) 54)) (-1648 (((-112) $ $) 23 (|has| |#1| (-1097)))) (-4386 (($ (-642 |#1|)) 43)) (-1733 ((|#1| $) 64)) (-2710 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4410)))) (-2872 (((-112) $ $) 20 (|has| |#1| (-1097)))) (-2127 (((-769) $) 6 (|has| $ (-6 -4410))))) +((-3512 (*1 *2 *3) (-12 (-4 *4 (-1047)) (-4 *3 (-848)) (-4 *5 (-266 *3)) (-4 *6 (-791)) (-5 *2 (-1 *1 (-769))) (-4 *1 (-253 *4 *3 *5 *6)))) (-2444 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-642 *4)))) (-3259 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1047)) (-4 *3 (-848)) (-4 *5 (-266 *3)) (-4 *6 (-791)) (-5 *2 (-769)))) (-3259 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-769)))) (-3835 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1047)) (-4 *3 (-848)) (-4 *5 (-266 *3)) (-4 *6 (-791)) (-5 *2 (-769)))) (-3824 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-642 (-769))))) (-2456 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-769)))) (-3824 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1047)) (-4 *3 (-848)) (-4 *5 (-266 *3)) (-4 *6 (-791)) (-5 *2 (-642 (-769))))) (-2456 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1047)) (-4 *3 (-848)) (-4 *5 (-266 *3)) (-4 *6 (-791)) (-5 *2 (-769)))) (-3303 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-112)))) (-3290 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *2 *5)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-791)) (-4 *2 (-266 *4)))) (-1878 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1047)) (-4 *3 (-848)) (-4 *4 (-266 *3)) (-4 *5 (-791)))) (-2507 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1047)) (-4 *3 (-848)) (-4 *4 (-266 *3)) (-4 *5 (-791)))) (-3512 (*1 *2 *1) (-12 (-4 *3 (-233)) (-4 *3 (-1047)) (-4 *4 (-848)) (-4 *5 (-266 *4)) (-4 *6 (-791)) (-5 *2 (-1 *1 (-769))) (-4 *1 (-253 *3 *4 *5 *6))))) +(-13 (-947 |t#1| |t#4| |t#3|) (-231 |t#1|) (-1036 |t#2|) (-10 -8 (-15 -3512 ((-1 $ (-769)) |t#2|)) (-15 -2444 ((-642 |t#2|) $)) (-15 -3259 ((-769) $ |t#2|)) (-15 -3259 ((-769) $)) (-15 -3835 ((-769) $ |t#2|)) (-15 -3824 ((-642 (-769)) $)) (-15 -2456 ((-769) $)) (-15 -3824 ((-642 (-769)) $ |t#2|)) (-15 -2456 ((-769) $ |t#2|)) (-15 -3303 ((-112) $)) (-15 -3290 (|t#3| $)) (-15 -1878 ($ $)) (-15 -2507 ($ $)) (IF (|has| |t#1| (-233)) (PROGN (-6 (-514 |t#2| |t#1|)) (-6 (-514 |t#2| $)) (-6 (-309 $)) (-15 -3512 ((-1 $ (-769)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2805 (|has| |#1| (-1036 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-860)) . T) ((-172) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| |#1| (-612 (-536))) (|has| |#3| (-612 (-536)))) ((-612 (-890 (-379))) -12 (|has| |#1| (-612 (-890 (-379)))) (|has| |#3| (-612 (-890 (-379))))) ((-612 (-890 (-564))) -12 (|has| |#1| (-612 (-890 (-564)))) (|has| |#3| (-612 (-890 (-564))))) ((-231 |#1|) . T) ((-233) |has| |#1| (-233)) ((-290) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-309 $) . T) ((-326 |#1| |#4|) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2805 (|has| |#1| (-907)) (|has| |#1| (-452))) ((-514 |#2| |#1|) |has| |#1| (-233)) ((-514 |#2| $) |has| |#1| (-233)) ((-514 |#3| |#1|) . T) ((-514 |#3| $) . T) ((-514 $ $) . T) ((-556) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-644 #0#) |has| |#1| (-38 (-407 (-564)))) ((-644 (-564)) . T) ((-644 |#1|) . T) ((-644 $) . T) ((-646 #0#) |has| |#1| (-38 (-407 (-564)))) ((-646 |#1|) . T) ((-646 $) . T) ((-638 #0#) |has| |#1| (-38 (-407 (-564)))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-715 #0#) |has| |#1| (-38 (-407 (-564)))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-724) . T) ((-898 (-1173)) |has| |#1| (-898 (-1173))) ((-898 |#3|) . T) ((-884 (-379)) -12 (|has| |#1| (-884 (-379))) (|has| |#3| (-884 (-379)))) ((-884 (-564)) -12 (|has| |#1| (-884 (-564))) (|has| |#3| (-884 (-564)))) ((-947 |#1| |#4| |#3|) . T) ((-907) |has| |#1| (-907)) ((-1036 (-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) ((-1036 (-564)) |has| |#1| (-1036 (-564))) ((-1036 |#1|) . T) ((-1036 |#2|) . T) ((-1036 |#3|) . T) ((-1049 #0#) |has| |#1| (-38 (-407 (-564)))) ((-1049 |#1|) . T) ((-1049 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-1054 #0#) |has| |#1| (-38 (-407 (-564)))) ((-1054 |#1|) . T) ((-1054 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1216) |has| |#1| (-907))) +((-2976 (((-112) $ $) 19 (|has| |#1| (-1097)))) (-1606 ((|#1| $) 55)) (-3870 ((|#1| $) 45)) (-1725 (((-112) $ (-769)) 8)) (-1796 (($) 7 T CONST)) (-3773 (($ $) 61)) (-3492 (($ $) 49)) (-3270 ((|#1| |#1| $) 47)) (-3232 ((|#1| $) 46)) (-3404 (((-642 |#1|) $) 31 (|has| $ (-6 -4410)))) (-4354 (((-112) $ (-769)) 9)) (-2665 (((-642 |#1|) $) 30 (|has| $ (-6 -4410)))) (-3840 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-1356 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4411)))) (-3069 (($ (-1 |#1| |#1|) $) 36)) (-3090 (((-112) $ (-769)) 10)) (-3857 (((-769) $) 62)) (-2268 (((-1155) $) 22 (|has| |#1| (-1097)))) (-3427 ((|#1| $) 40)) (-4050 ((|#1| |#1| $) 53)) (-2115 ((|#1| |#1| $) 52)) (-3387 (($ |#1| $) 41)) (-3105 (((-769) $) 56)) (-4009 (((-1117) $) 21 (|has| |#1| (-1097)))) (-3913 ((|#1| $) 63)) (-3686 ((|#1| $) 51)) (-3646 ((|#1| $) 50)) (-1728 ((|#1| $) 42)) (-3814 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4410)))) (-3281 (($ $ (-642 (-294 |#1|))) 27 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-294 |#1|)) 26 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-642 |#1|) (-642 |#1|)) 24 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))))) (-3354 (((-112) $ $) 14)) (-1912 ((|#1| |#1| $) 59)) (-1955 (((-112) $) 11)) (-2002 (($) 12)) (-3490 ((|#1| $) 60)) (-2144 (($) 58) (($ (-642 |#1|)) 57)) (-4038 (((-769) $) 44)) (-4020 (((-769) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4410))) (((-769) |#1| $) 29 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-3888 (($ $) 13)) (-2502 (((-860) $) 18 (|has| |#1| (-611 (-860))))) (-2786 ((|#1| $) 54)) (-1681 (((-112) $ $) 23 (|has| |#1| (-1097)))) (-4105 (($ (-642 |#1|)) 43)) (-4295 ((|#1| $) 64)) (-1310 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4410)))) (-2941 (((-112) $ $) 20 (|has| |#1| (-1097)))) (-2250 (((-769) $) 6 (|has| $ (-6 -4410))))) (((-254 |#1|) (-140) (-1212)) (T -254)) -((-3945 (*1 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-3945 (*1 *1 *2) (-12 (-5 *2 (-642 *3)) (-4 *3 (-1212)) (-4 *1 (-254 *3)))) (-1295 (*1 *2 *1) (-12 (-4 *1 (-254 *3)) (-4 *3 (-1212)) (-5 *2 (-769)))) (-3686 (*1 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-1825 (*1 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-1704 (*1 *2 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-3604 (*1 *2 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-1479 (*1 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-1475 (*1 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212)))) (-2087 (*1 *1 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1212))))) -(-13 (-1118 |t#1|) (-993 |t#1|) (-10 -8 (-15 -3945 ($)) (-15 -3945 ($ (-642 |t#1|))) (-15 -1295 ((-769) $)) (-15 -3686 (|t#1| $)) (-15 -1825 (|t#1| $)) (-15 -1704 (|t#1| |t#1| $)) (-15 -3604 (|t#1| |t#1| $)) (-15 -1479 (|t#1| $)) (-15 -1475 (|t#1| $)) (-15 -2087 ($ $)))) -(((-34) . 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T) ((-111 #0# #0#) |has| |#1| (-556)) ((-111 |#1| |#1|) |has| |#1| (-172)) ((-111 $ $) |has| |#1| (-556)) ((-131) -2706 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#1| (-21))) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2706 (|has| |#1| (-1036 (-407 (-564)))) (|has| |#1| (-556))) ((-614 #1=(-407 (-950 |#1|))) |has| |#1| (-556)) ((-614 (-564)) -2706 (|has| |#1| (-1047)) (|has| |#1| (-1036 (-564))) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-614 #2=(-610 $)) . T) ((-614 #3=(-950 |#1|)) |has| |#1| (-1047)) ((-614 #4=(-1173)) . T) ((-614 |#1|) . T) ((-614 $) |has| |#1| (-556)) ((-611 (-860)) . T) ((-172) |has| |#1| (-556)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-890 (-379))) |has| |#1| (-612 (-890 (-379)))) ((-612 (-890 (-564))) |has| |#1| (-612 (-890 (-564)))) ((-243) |has| |#1| (-556)) ((-290) |has| |#1| (-556)) ((-307) |has| |#1| (-556)) ((-309 $) . T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1047)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 (-564)) -2706 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#1| (-21))) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2706 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-646 #0#) |has| |#1| (-556)) ((-646 |#1|) |has| |#1| (-172)) ((-646 $) -2706 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-638 #0#) |has| |#1| (-556)) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) |has| |#1| (-556)) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1047))) ((-637 |#1|) |has| |#1| (-1047)) ((-715 #0#) |has| |#1| (-556)) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) |has| |#1| (-556)) ((-724) -2706 (|has| |#1| (-1109)) (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-898 (-1173)) |has| |#1| (-1047)) ((-884 (-379)) |has| |#1| (-884 (-379))) ((-884 (-564)) |has| |#1| (-884 (-564))) ((-882 |#1|) . 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T) ((-918) |has| |#1| (-556)) ((-1036 (-407 (-564))) -2805 (|has| |#1| (-1036 (-407 (-564)))) (-12 (|has| |#1| (-556)) (|has| |#1| (-1036 (-564))))) ((-1036 #1#) |has| |#1| (-556)) ((-1036 (-564)) |has| |#1| (-1036 (-564))) ((-1036 #2#) . T) ((-1036 #3#) |has| |#1| (-1047)) ((-1036 #4#) . T) ((-1036 |#1|) . T) ((-1049 #0#) |has| |#1| (-556)) ((-1049 |#1|) |has| |#1| (-172)) ((-1049 $) |has| |#1| (-556)) ((-1054 #0#) |has| |#1| (-556)) ((-1054 |#1|) |has| |#1| (-172)) ((-1054 $) |has| |#1| (-556)) ((-1047) -2805 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1055) -2805 (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1109) -2805 (|has| |#1| (-1109)) (|has| |#1| (-1047)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1097) . T) ((-1212) . 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T) ((-644 |#1|) . T) ((-644 |#2|) |has| |#1| (-363)) ((-644 $) . T) ((-646 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-363)) ((-646 $) . T) ((-638 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-638 |#1|) |has| |#1| (-172)) ((-638 |#2|) |has| |#1| (-363)) ((-638 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-637 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((-637 |#2|) |has| |#1| (-363)) ((-715 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-715 |#1|) |has| |#1| (-172)) ((-715 |#2|) |has| |#1| (-363)) ((-715 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-724) . T) ((-789) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-790) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-792) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-793) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-818) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-846) -12 (|has| |#1| (-363)) (|has| |#2| (-818))) ((-848) -2706 (-12 (|has| |#1| (-363)) (|has| |#2| (-848))) (-12 (|has| |#1| (-363)) (|has| |#2| (-818)))) ((-898 (-1173)) -2706 (-12 (|has| |#1| (-363)) (|has| |#2| (-898 (-1173)))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-898 (-1173))))) ((-884 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-884 (-379)))) ((-884 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-884 (-564)))) ((-882 |#2|) |has| |#1| (-363)) ((-907) -12 (|has| |#1| (-363)) (|has| |#2| (-907))) ((-971 |#1| #0# (-1079)) . T) ((-918) |has| |#1| (-363)) ((-990 |#2|) |has| |#1| (-363)) ((-1000) |has| |#1| (-38 (-407 (-564)))) ((-1020) -12 (|has| |#1| (-363)) (|has| |#2| (-1020))) ((-1036 (-407 (-564))) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-564)))) ((-1036 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-564)))) ((-1036 #2#) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-1173)))) ((-1036 |#2|) . T) ((-1049 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1049 |#1|) . T) ((-1049 |#2|) |has| |#1| (-363)) ((-1049 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1054 |#1|) . T) ((-1054 |#2|) |has| |#1| (-363)) ((-1054 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1148) -12 (|has| |#1| (-363)) (|has| |#2| (-1148))) ((-1197) |has| |#1| (-38 (-407 (-564)))) ((-1200) |has| |#1| (-38 (-407 (-564)))) ((-1212) |has| |#1| (-363)) ((-1216) |has| |#1| (-363)) ((-1222 |#1|) . T) ((-1240 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-564)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-363)) ((-38 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-564)))) ((-95) |has| |#1| (-38 (-407 (-564)))) ((-102) . T) ((-111 #1# #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-363)) ((-111 $ $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) -2805 (-12 (|has| |#1| (-363)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2805 (-12 (|has| |#1| (-363)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-614 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1173)) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-1173)))) ((-614 |#1|) |has| |#1| (-172)) ((-614 |#2|) . T) ((-614 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-611 (-860)) . T) ((-172) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-225)) -12 (|has| |#1| (-363)) (|has| |#2| (-1020))) ((-612 (-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-1020))) ((-612 (-536)) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-536)))) ((-612 (-890 (-379))) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-890 (-379))))) ((-612 (-890 (-564))) -12 (|has| |#1| (-363)) (|has| |#2| (-612 (-890 (-564))))) ((-231 |#2|) |has| |#1| (-363)) ((-233) -2805 (-12 (|has| |#1| (-363)) (|has| |#2| (-233))) (|has| |#1| (-15 * (|#1| (-564) |#1|)))) ((-243) |has| |#1| (-363)) ((-284) |has| |#1| (-38 (-407 (-564)))) ((-286 |#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) ((-286 $ $) |has| (-564) (-1109)) ((-290) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-363) |has| |#1| (-363)) ((-338 |#2|) |has| |#1| (-363)) ((-377 |#2|) |has| |#1| (-363)) ((-400 |#2|) |has| |#1| (-363)) ((-452) |has| |#1| (-363)) ((-493) |has| |#1| (-38 (-407 (-564)))) ((-514 (-1173) |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-514 (-1173) |#2|))) ((-514 |#2| |#2|) -12 (|has| |#1| (-363)) (|has| |#2| (-309 |#2|))) ((-556) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-644 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-644 (-564)) . T) ((-644 |#1|) . T) ((-644 |#2|) |has| |#1| (-363)) ((-644 $) . T) ((-646 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-363)) ((-646 $) . T) ((-638 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-638 |#1|) |has| |#1| (-172)) ((-638 |#2|) |has| |#1| (-363)) ((-638 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-637 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((-637 |#2|) |has| |#1| (-363)) ((-715 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-715 |#1|) |has| |#1| (-172)) ((-715 |#2|) |has| |#1| (-363)) ((-715 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-724) . 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T) ((-918) |has| |#1| (-363)) ((-990 |#2|) |has| |#1| (-363)) ((-1000) |has| |#1| (-38 (-407 (-564)))) ((-1020) -12 (|has| |#1| (-363)) (|has| |#2| (-1020))) ((-1036 (-407 (-564))) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-564)))) ((-1036 (-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-564)))) ((-1036 #2#) -12 (|has| |#1| (-363)) (|has| |#2| (-1036 (-1173)))) ((-1036 |#2|) . T) ((-1049 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1049 |#1|) . T) ((-1049 |#2|) |has| |#1| (-363)) ((-1049 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1054 |#1|) . T) ((-1054 |#2|) |has| |#1| (-363)) ((-1054 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1148) -12 (|has| |#1| (-363)) (|has| |#2| (-1148))) ((-1197) |has| |#1| (-38 (-407 (-564)))) ((-1200) |has| |#1| (-38 (-407 (-564)))) ((-1212) |has| |#1| (-363)) ((-1216) |has| |#1| (-363)) ((-1222 |#1|) . T) ((-1240 |#1| #0#) . 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T) ((-172) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1079) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-890 (-379))) -12 (|has| (-1079) (-612 (-890 (-379)))) (|has| |#1| (-612 (-890 (-379))))) ((-612 (-890 (-564))) -12 (|has| (-1079) (-612 (-890 (-564)))) (|has| |#1| (-612 (-890 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2706 (|has| |#1| (-907)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 (-564)) . T) ((-644 |#1|) . T) ((-644 $) . T) ((-646 #1#) |has| |#1| (-38 (-407 (-564)))) ((-646 |#1|) . T) ((-646 $) . T) ((-638 #1#) |has| |#1| (-38 (-407 (-564)))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-715 #1#) |has| |#1| (-38 (-407 (-564)))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-724) . T) ((-898 #2#) . T) ((-898 (-1173)) |has| |#1| (-898 (-1173))) ((-884 (-379)) -12 (|has| (-1079) (-884 (-379))) (|has| |#1| (-884 (-379)))) ((-884 (-564)) -12 (|has| (-1079) (-884 (-564))) (|has| |#1| (-884 (-564)))) ((-947 |#1| #0# #2#) . T) ((-907) |has| |#1| (-907)) ((-918) |has| |#1| (-363)) ((-1036 (-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) ((-1036 (-564)) |has| |#1| (-1036 (-564))) ((-1036 #2#) . T) ((-1036 |#1|) . T) ((-1049 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1049 |#1|) . T) ((-1049 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1054 |#1|) . T) ((-1054 $) -2706 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1148) |has| |#1| (-1148)) ((-1216) |has| |#1| (-907))) -((-3802 (((-642 (-1079)) $) 34)) (-1718 (($ $) 31)) (-3774 (($ |#2| |#3|) NIL) (($ $ (-1079) |#3|) 28) (($ $ (-642 (-1079)) (-642 |#3|)) 27)) (-3950 (($ $) 14)) (-3962 ((|#2| $) 12)) (-2775 ((|#3| $) 10))) -(((-1239 |#1| |#2| |#3|) (-10 -8 (-15 -3802 ((-642 (-1079)) |#1|)) (-15 -3774 (|#1| |#1| (-642 (-1079)) (-642 |#3|))) (-15 -3774 (|#1| |#1| (-1079) |#3|)) (-15 -1718 (|#1| |#1|)) (-15 -3774 (|#1| |#2| |#3|)) (-15 -2775 (|#3| |#1|)) (-15 -3950 (|#1| |#1|)) (-15 -3962 (|#2| |#1|))) (-1240 |#2| |#3|) (-1047) (-790)) (T -1239)) -NIL -(-10 -8 (-15 -3802 ((-642 (-1079)) |#1|)) (-15 -3774 (|#1| |#1| (-642 (-1079)) (-642 |#3|))) (-15 -3774 (|#1| |#1| (-1079) |#3|)) (-15 -1718 (|#1| |#1|)) (-15 -3774 (|#1| |#2| |#3|)) (-15 -2775 (|#3| |#1|)) (-15 -3950 (|#1| |#1|)) (-15 -3962 (|#2| |#1|))) -((-2907 (((-112) $ $) 7)) (-2952 (((-112) $) 17)) (-3802 (((-642 (-1079)) $) 86)) (-3329 (((-1173) $) 115)) (-4039 (((-2 (|:| -3587 $) (|:| 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(($) 34 T CONST)) (-4044 (($ $ (-642 (-1173)) (-642 (-769))) 105 (-12 (|has| |#1| (-898 (-1173))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-1173) (-769)) 104 (-12 (|has| |#1| (-898 (-1173))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-642 (-1173))) 103 (-12 (|has| |#1| (-898 (-1173))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-1173)) 102 (-12 (|has| |#1| (-898 (-1173))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-769)) 97 (|has| |#1| (-15 * (|#1| |#2| |#1|)))) (($ $) 95 (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (-2872 (((-112) $ $) 6)) (-2998 (($ $ |#1|) 70 (|has| |#1| (-363)))) (-2987 (($ $) 23) (($ $ $) 22)) (-2974 (($ $ $) 15)) (** (($ $ (-919)) 28) (($ $ (-769)) 36)) (* (($ (-919) $) 14) (($ (-769) $) 16) (($ (-564) $) 24) (($ $ $) 27) (($ $ |#1|) 80) (($ |#1| $) 79) (($ (-407 (-564)) $) 68 (|has| |#1| (-38 (-407 (-564))))) (($ $ (-407 (-564))) 67 (|has| |#1| (-38 (-407 (-564))))))) +((-3705 (*1 *2 *1 *3) (-12 (-5 *3 (-769)) (-4 *1 (-1238 *4)) (-4 *4 (-1047)) (-5 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(-407 (-564))))))) +(-13 (-947 |t#1| (-769) (-1079)) (-286 |t#1| |t#1|) (-286 $ $) (-233) (-231 |t#1|) (-10 -8 (-15 -3705 ((-1262 |t#1|) $ (-769))) (-15 -3608 ((-1169 |t#1|) $)) (-15 -4025 ($ (-1169 |t#1|))) (-15 -2984 ($ $ (-769))) (-15 -2223 ((-3 $ "failed") $ (-769))) (-15 -3603 ((-2 (|:| -2534 $) (|:| -1410 $)) $ $)) (-15 -3594 ((-2 (|:| -2534 $) (|:| -1410 $)) $ (-769))) (-15 -1431 ($ $ (-769))) (-15 -3056 ($ $ (-769))) (-15 -1531 ($ $ $)) (-15 -4160 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1148)) (-6 (-1148)) |%noBranch|) (IF (|has| |t#1| (-172)) (PROGN (-15 -2978 (|t#1| $)) (-15 -4113 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-556)) (PROGN (-6 (-286 (-407 $) (-407 $))) (-15 -4370 ((-407 $) (-407 $) (-407 $))) (-15 -3259 ((-769) $ $)) (-15 -3789 ($ $ $)) (-15 -3341 ((-3 $ "failed") $ $)) (-15 -3341 ((-3 (-407 $) "failed") (-407 $) $)) (-15 -1792 ($ $ $)) (-15 -4098 ((-2 (|:| -3089 |t#1|) (|:| -2534 $) (|:| -1410 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-452)) (-15 -2943 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-363)) (PROGN (-6 (-307)) (-6 -4406) (-15 -4370 (|t#1| (-407 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-407 (-564)))) (-15 -4384 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-769)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2805 (|has| |#1| (-1036 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1079)) . T) ((-614 |#1|) . T) ((-614 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-860)) . T) ((-172) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1079) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-890 (-379))) -12 (|has| (-1079) (-612 (-890 (-379)))) (|has| |#1| (-612 (-890 (-379))))) ((-612 (-890 (-564))) -12 (|has| (-1079) (-612 (-890 (-564)))) (|has| |#1| (-612 (-890 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2805 (|has| |#1| (-907)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 (-564)) . T) ((-644 |#1|) . T) ((-644 $) . T) ((-646 #1#) |has| |#1| (-38 (-407 (-564)))) ((-646 |#1|) . T) ((-646 $) . T) ((-638 #1#) |has| |#1| (-38 (-407 (-564)))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-715 #1#) |has| |#1| (-38 (-407 (-564)))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-724) . T) ((-898 #2#) . T) ((-898 (-1173)) |has| |#1| (-898 (-1173))) ((-884 (-379)) -12 (|has| (-1079) (-884 (-379))) (|has| |#1| (-884 (-379)))) ((-884 (-564)) -12 (|has| (-1079) (-884 (-564))) (|has| |#1| (-884 (-564)))) ((-947 |#1| #0# #2#) . T) ((-907) |has| |#1| (-907)) ((-918) |has| |#1| (-363)) ((-1036 (-407 (-564))) |has| |#1| (-1036 (-407 (-564)))) ((-1036 (-564)) |has| |#1| (-1036 (-564))) ((-1036 #2#) . T) ((-1036 |#1|) . T) ((-1049 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1049 |#1|) . T) ((-1049 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1054 |#1|) . T) ((-1054 $) -2805 (|has| |#1| (-907)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1148) |has| |#1| (-1148)) ((-1216) |has| |#1| (-907))) +((-2510 (((-642 (-1079)) $) 34)) (-3546 (($ $) 31)) (-2486 (($ |#2| |#3|) NIL) (($ $ (-1079) |#3|) 28) (($ $ (-642 (-1079)) (-642 |#3|)) 27)) (-2637 (($ $) 14)) (-2648 ((|#2| $) 12)) (-3835 ((|#3| $) 10))) +(((-1239 |#1| |#2| |#3|) (-10 -8 (-15 -2510 ((-642 (-1079)) |#1|)) (-15 -2486 (|#1| |#1| (-642 (-1079)) (-642 |#3|))) (-15 -2486 (|#1| |#1| (-1079) |#3|)) (-15 -3546 (|#1| |#1|)) (-15 -2486 (|#1| |#2| |#3|)) (-15 -3835 (|#3| |#1|)) (-15 -2637 (|#1| |#1|)) (-15 -2648 (|#2| |#1|))) (-1240 |#2| |#3|) (-1047) (-790)) (T -1239)) +NIL +(-10 -8 (-15 -2510 ((-642 (-1079)) |#1|)) (-15 -2486 (|#1| |#1| (-642 (-1079)) (-642 |#3|))) (-15 -2486 (|#1| |#1| (-1079) |#3|)) (-15 -3546 (|#1| |#1|)) (-15 -2486 (|#1| |#2| |#3|)) (-15 -3835 (|#3| |#1|)) (-15 -2637 (|#1| |#1|)) (-15 -2648 (|#2| |#1|))) +((-2976 (((-112) $ $) 7)) (-1830 (((-112) $) 17)) (-2510 (((-642 (-1079)) $) 86)) (-1342 (((-1173) $) 115)) (-1829 (((-2 (|:| -3199 $) (|:| 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T) ((-638 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-715 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-724) . T) ((-898 (-1173)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-898 (-1173)))) ((-971 |#1| #0# (-1079)) . T) ((-918) |has| |#1| (-363)) ((-1000) |has| |#1| (-38 (-407 (-564)))) ((-1049 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1049 |#1|) . T) ((-1049 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) -2706 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1054 |#1|) . T) ((-1054 $) -2706 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1197) |has| |#1| (-38 (-407 (-564)))) ((-1200) |has| |#1| (-38 (-407 (-564)))) ((-1216) |has| |#1| (-363)) ((-1240 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-407 (-564))) . T) ((-25) . T) ((-38 #1=(-407 (-564))) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-35) |has| |#1| (-38 (-407 (-564)))) ((-95) |has| |#1| (-38 (-407 (-564)))) ((-102) . T) ((-111 #1# #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) |has| |#1| (-172)) ((-614 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-611 (-860)) . T) ((-172) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) ((-243) |has| |#1| (-363)) ((-284) |has| |#1| (-38 (-407 (-564)))) ((-286 $ $) |has| (-407 (-564)) (-1109)) ((-290) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-363) |has| |#1| (-363)) ((-452) |has| |#1| (-363)) ((-493) |has| |#1| (-38 (-407 (-564)))) ((-556) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-644 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-644 (-564)) . T) ((-644 |#1|) . T) ((-644 $) . T) ((-646 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-646 |#1|) . T) ((-646 $) . T) ((-638 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-638 |#1|) |has| |#1| (-172)) ((-638 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-715 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-715 |#1|) |has| |#1| (-172)) ((-715 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363))) ((-724) . T) ((-898 (-1173)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-898 (-1173)))) ((-971 |#1| #0# (-1079)) . T) ((-918) |has| |#1| (-363)) ((-1000) |has| |#1| (-38 (-407 (-564)))) ((-1049 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1049 |#1|) . T) ((-1049 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1054 #1#) -2805 (|has| |#1| (-363)) (|has| |#1| (-38 (-407 (-564))))) ((-1054 |#1|) . T) ((-1054 $) -2805 (|has| |#1| (-556)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1197) |has| |#1| (-38 (-407 (-564)))) ((-1200) |has| |#1| (-38 (-407 (-564)))) ((-1216) |has| |#1| (-363)) ((-1240 |#1| #0#) . 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NIL 2944423 NIL) (-1215 2942904 2942950 2943045 "UFD-" 2943050 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1214 2941986 2942169 2942385 "UDVO" 2942710 T UDVO (NIL) -7 NIL NIL NIL) (-1213 2939802 2940211 2940682 "UDPO" 2941550 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1212 2939735 2939740 2939770 "TYPE" 2939775 T TYPE (NIL) -9 NIL NIL NIL) (-1211 2939495 2939690 2939721 "TYPEAST" 2939726 T TYPEAST (NIL) -8 NIL NIL NIL) (-1210 2938466 2938668 2938908 "TWOFACT" 2939289 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1209 2937489 2937875 2938110 "TUPLE" 2938266 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1208 2935180 2935699 2936238 "TUBETOOL" 2936972 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1207 2934029 2934234 2934475 "TUBE" 2934973 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1206 2928758 2933001 2933284 "TS" 2933781 NIL TS (NIL T) -8 NIL NIL NIL) (-1205 2917398 2921517 2921614 "TSETCAT" 2926883 NIL TSETCAT (NIL T T T T) -9 NIL 2928414 NIL) (-1204 2912130 2913730 2915621 "TSETCAT-" 2915626 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1203 2906769 2907616 2908545 "TRMANIP" 2911266 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1202 2906210 2906273 2906436 "TRIMAT" 2906701 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1201 2904076 2904313 2904670 "TRIGMNIP" 2905959 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1200 2903596 2903709 2903739 "TRIGCAT" 2903952 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1199 2903265 2903344 2903485 "TRIGCAT-" 2903490 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1198 2900110 2902123 2902404 "TREE" 2903019 NIL TREE (NIL T) -8 NIL NIL NIL) (-1197 2899384 2899912 2899942 "TRANFUN" 2899977 T TRANFUN (NIL) -9 NIL 2900043 NIL) (-1196 2898663 2898854 2899134 "TRANFUN-" 2899139 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1195 2898467 2898499 2898560 "TOPSP" 2898624 T TOPSP (NIL) -7 NIL NIL NIL) (-1194 2897815 2897930 2898084 "TOOLSIGN" 2898348 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1193 2896449 2896992 2897231 "TEXTFILE" 2897598 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1192 2894361 2894902 2895331 "TEX" 2896042 T TEX (NIL) -8 NIL NIL NIL) (-1191 2894142 2894173 2894245 "TEX1" 2894324 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1190 2893790 2893853 2893943 "TEMUTL" 2894074 T TEMUTL (NIL) -7 NIL NIL NIL) (-1189 2891944 2892224 2892549 "TBCMPPK" 2893513 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1188 2883721 2890104 2890160 "TBAGG" 2890560 NIL TBAGG (NIL T T) -9 NIL 2890771 NIL) (-1187 2878791 2880279 2882033 "TBAGG-" 2882038 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1186 2878175 2878282 2878427 "TANEXP" 2878680 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1185 2871565 2878032 2878125 "TABLE" 2878130 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1184 2870977 2871076 2871214 "TABLEAU" 2871462 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1183 2865585 2866805 2868053 "TABLBUMP" 2869763 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1182 2864807 2864954 2865135 "SYSTEM" 2865426 T SYSTEM (NIL) -8 NIL NIL NIL) (-1181 2861266 2861965 2862748 "SYSSOLP" 2864058 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1180 2860310 2860815 2860934 "SYSNNI" 2861120 NIL SYSNNI (NIL NIL) -8 NIL NIL 2861205) (-1179 2859617 2860076 2860155 "SYSINT" 2860215 NIL SYSINT (NIL NIL) -8 NIL NIL 2860260) (-1178 2855949 2856895 2857605 "SYNTAX" 2858929 T SYNTAX (NIL) -8 NIL NIL NIL) (-1177 2853107 2853709 2854341 "SYMTAB" 2855339 T SYMTAB (NIL) -8 NIL NIL NIL) (-1176 2848356 2849258 2850241 "SYMS" 2852146 T SYMS (NIL) -8 NIL NIL NIL) (-1175 2845591 2847814 2848044 "SYMPOLY" 2848161 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1174 2845108 2845183 2845306 "SYMFUNC" 2845503 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1173 2841127 2842420 2843233 "SYMBOL" 2844317 T SYMBOL (NIL) -8 NIL NIL NIL) (-1172 2834666 2836355 2838075 "SWITCH" 2839429 T SWITCH (NIL) -8 NIL NIL NIL) (-1171 2827900 2833487 2833790 "SUTS" 2834421 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1170 2819966 2827147 2827420 "SUPXS" 2827685 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2811726 2819584 2819710 "SUP" 2819875 NIL SUP (NIL T) -8 NIL NIL NIL) (-1168 2810885 2811012 2811229 "SUPFRACF" 2811594 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1167 2810506 2810565 2810678 "SUP2" 2810820 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1166 2808954 2809228 2809584 "SUMRF" 2810205 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1165 2808289 2808355 2808547 "SUMFS" 2808875 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1164 2792256 2807466 2807717 "SULS" 2808096 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1163 2791858 2792078 2792148 "SUCHTAST" 2792208 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1162 2791153 2791383 2791523 "SUCH" 2791766 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1161 2785019 2786059 2787018 "SUBSPACE" 2790241 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1160 2784449 2784539 2784703 "SUBRESP" 2784907 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1159 2777814 2779114 2780425 "STTF" 2783185 NIL STTF (NIL T) -7 NIL NIL NIL) (-1158 2771987 2773107 2774254 "STTFNC" 2776714 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1157 2763298 2765169 2766963 "STTAYLOR" 2770228 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1156 2756428 2763162 2763245 "STRTBL" 2763250 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1155 2751792 2756383 2756414 "STRING" 2756419 T STRING (NIL) -8 NIL NIL NIL) (-1154 2746653 2751165 2751195 "STRICAT" 2751254 T STRICAT (NIL) -9 NIL 2751316 NIL) (-1153 2739407 2744272 2744883 "STREAM" 2746077 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1152 2738917 2738994 2739138 "STREAM3" 2739324 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1151 2737899 2738082 2738317 "STREAM2" 2738730 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1150 2737587 2737639 2737732 "STREAM1" 2737841 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1149 2736603 2736784 2737015 "STINPROD" 2737403 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1148 2736155 2736365 2736395 "STEP" 2736475 T STEP (NIL) -9 NIL 2736553 NIL) (-1147 2729587 2736054 2736131 "STBL" 2736136 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1146 2724713 2728808 2728851 "STAGG" 2729004 NIL STAGG (NIL T) -9 NIL 2729093 NIL) (-1145 2722415 2723017 2723889 "STAGG-" 2723894 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1144 2720562 2722185 2722277 "STACK" 2722358 NIL STACK (NIL T) -8 NIL NIL NIL) (-1143 2713257 2718703 2719159 "SREGSET" 2720192 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1142 2705682 2707051 2708564 "SRDCMPK" 2711863 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1141 2698599 2703122 2703152 "SRAGG" 2704455 T SRAGG (NIL) -9 NIL 2705063 NIL) (-1140 2697616 2697871 2698250 "SRAGG-" 2698255 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1139 2692076 2696563 2696984 "SQMATRIX" 2697242 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1138 2685761 2688794 2689521 "SPLTREE" 2691421 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1137 2681724 2682417 2683063 "SPLNODE" 2685187 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1136 2680771 2681004 2681034 "SPFCAT" 2681478 T SPFCAT (NIL) -9 NIL NIL NIL) (-1135 2679508 2679718 2679982 "SPECOUT" 2680529 T SPECOUT (NIL) -7 NIL NIL NIL) (-1134 2671134 2672904 2672934 "SPADXPT" 2677326 T SPADXPT (NIL) -9 NIL 2679360 NIL) (-1133 2670895 2670935 2671004 "SPADPRSR" 2671087 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1132 2669050 2670850 2670881 "SPADAST" 2670886 T SPADAST (NIL) -8 NIL NIL NIL) (-1131 2660995 2662768 2662811 "SPACEC" 2667184 NIL SPACEC (NIL T) -9 NIL 2669000 NIL) (-1130 2659125 2660927 2660976 "SPACE3" 2660981 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1129 2657877 2658048 2658339 "SORTPAK" 2658930 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1128 2655969 2656272 2656684 "SOLVETRA" 2657541 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1127 2655019 2655241 2655502 "SOLVESER" 2655742 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1126 2650321 2651211 2652206 "SOLVERAD" 2654071 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1125 2646136 2646745 2647474 "SOLVEFOR" 2649688 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1124 2640406 2645485 2645582 "SNTSCAT" 2645587 NIL SNTSCAT (NIL T T T T) -9 NIL 2645657 NIL) (-1123 2634512 2638729 2639120 "SMTS" 2640096 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1122 2629196 2634400 2634477 "SMP" 2634482 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1121 2627355 2627656 2628054 "SMITH" 2628893 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1120 2620068 2624264 2624367 "SMATCAT" 2625718 NIL SMATCAT (NIL NIL T T T) -9 NIL 2626268 NIL) (-1119 2617008 2617831 2619009 "SMATCAT-" 2619014 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1118 2614674 2616244 2616287 "SKAGG" 2616548 NIL SKAGG (NIL T) -9 NIL 2616683 NIL) (-1117 2610982 2614090 2614285 "SINT" 2614472 T SINT (NIL) -8 NIL NIL 2614645) (-1116 2610754 2610792 2610858 "SIMPAN" 2610938 T SIMPAN (NIL) -7 NIL NIL NIL) (-1115 2610033 2610289 2610429 "SIG" 2610636 T SIG (NIL) -8 NIL NIL NIL) (-1114 2608871 2609092 2609367 "SIGNRF" 2609792 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1113 2607704 2607855 2608139 "SIGNEF" 2608700 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1112 2607010 2607287 2607411 "SIGAST" 2607602 T SIGAST (NIL) -8 NIL NIL NIL) (-1111 2604699 2605154 2605660 "SHP" 2606551 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1110 2598551 2604600 2604676 "SHDP" 2604681 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1109 2598124 2598316 2598346 "SGROUP" 2598439 T SGROUP (NIL) -9 NIL 2598501 NIL) (-1108 2597982 2598008 2598081 "SGROUP-" 2598086 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1107 2594817 2595515 2596238 "SGCF" 2597281 T SGCF (NIL) -7 NIL NIL NIL) (-1106 2589185 2594264 2594361 "SFRTCAT" 2594366 NIL SFRTCAT (NIL T T T T) -9 NIL 2594405 NIL) (-1105 2582606 2583624 2584760 "SFRGCD" 2588168 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1104 2575732 2576805 2577991 "SFQCMPK" 2581539 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1103 2575352 2575441 2575552 "SFORT" 2575673 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1102 2574470 2575192 2575313 "SEXOF" 2575318 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1101 2573577 2574351 2574419 "SEX" 2574424 T SEX (NIL) -8 NIL NIL NIL) (-1100 2569090 2569805 2569900 "SEXCAT" 2572837 NIL SEXCAT (NIL T T T T T) -9 NIL 2573415 NIL) (-1099 2566243 2569024 2569072 "SET" 2569077 NIL SET (NIL T) -8 NIL NIL NIL) (-1098 2564467 2564956 2565261 "SETMN" 2565984 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1097 2563963 2564115 2564145 "SETCAT" 2564321 T SETCAT (NIL) -9 NIL 2564431 NIL) (-1096 2563655 2563733 2563863 "SETCAT-" 2563868 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1095 2560016 2562116 2562159 "SETAGG" 2563029 NIL SETAGG (NIL T) -9 NIL 2563369 NIL) (-1094 2559474 2559590 2559827 "SETAGG-" 2559832 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1093 2558917 2559170 2559271 "SEQAST" 2559395 T SEQAST (NIL) -8 NIL NIL NIL) (-1092 2558116 2558410 2558471 "SEGXCAT" 2558757 NIL SEGXCAT (NIL T T) -9 NIL 2558877 NIL) (-1091 2557122 2557782 2557964 "SEG" 2557969 NIL SEG (NIL T) -8 NIL NIL NIL) (-1090 2556101 2556315 2556358 "SEGCAT" 2556880 NIL SEGCAT (NIL T) -9 NIL 2557101 NIL) (-1089 2555102 2555480 2555680 "SEGBIND" 2555936 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1088 2554723 2554782 2554895 "SEGBIND2" 2555037 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1087 2554296 2554524 2554601 "SEGAST" 2554668 T SEGAST (NIL) -8 NIL NIL NIL) (-1086 2553515 2553641 2553845 "SEG2" 2554140 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1085 2552925 2553450 2553497 "SDVAR" 2553502 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1084 2545452 2552695 2552825 "SDPOL" 2552830 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1083 2544045 2544311 2544630 "SCPKG" 2545167 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1082 2543209 2543381 2543573 "SCOPE" 2543875 T SCOPE (NIL) -8 NIL NIL NIL) (-1081 2542429 2542563 2542742 "SCACHE" 2543064 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1080 2542075 2542261 2542291 "SASTCAT" 2542296 T SASTCAT (NIL) -9 NIL 2542309 NIL) (-1079 2541562 2541910 2541986 "SAOS" 2542021 T SAOS (NIL) -8 NIL NIL NIL) (-1078 2541127 2541162 2541335 "SAERFFC" 2541521 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1077 2535066 2541024 2541104 "SAE" 2541109 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1076 2534659 2534694 2534853 "SAEFACT" 2535025 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1075 2532980 2533294 2533695 "RURPK" 2534325 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1074 2531617 2531923 2532228 "RULESET" 2532814 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1073 2528840 2529370 2529828 "RULE" 2531298 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1072 2528452 2528634 2528717 "RULECOLD" 2528792 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1071 2528242 2528270 2528341 "RTVALUE" 2528403 T RTVALUE (NIL) -8 NIL NIL NIL) (-1070 2527713 2527959 2528053 "RSTRCAST" 2528170 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1069 2522561 2523356 2524276 "RSETGCD" 2526912 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1068 2511791 2516870 2516967 "RSETCAT" 2521086 NIL RSETCAT (NIL T T T T) -9 NIL 2522183 NIL) (-1067 2509718 2510257 2511081 "RSETCAT-" 2511086 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1066 2502103 2503480 2505000 "RSDCMPK" 2508317 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500082 2500549 2500623 "RRCC" 2501709 NIL RRCC (NIL T T) -9 NIL 2502053 NIL) (-1064 2499433 2499607 2499886 "RRCC-" 2499891 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1063 2498876 2499129 2499230 "RPTAST" 2499354 T RPTAST (NIL) -8 NIL NIL NIL) (-1062 2472727 2482084 2482151 "RPOLCAT" 2492815 NIL RPOLCAT (NIL T T T) -9 NIL 2495974 NIL) (-1061 2464225 2466565 2469687 "RPOLCAT-" 2469692 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1060 2455156 2462436 2462918 "ROUTINE" 2463765 T ROUTINE (NIL) -8 NIL NIL NIL) (-1059 2451954 2454782 2454922 "ROMAN" 2455038 T ROMAN (NIL) -8 NIL NIL NIL) (-1058 2450198 2450814 2451074 "ROIRC" 2451759 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1057 2446430 2448714 2448744 "RNS" 2449048 T RNS (NIL) -9 NIL 2449322 NIL) (-1056 2444939 2445322 2445856 "RNS-" 2445931 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1055 2444342 2444750 2444780 "RNG" 2444785 T RNG (NIL) -9 NIL 2444806 NIL) (-1054 2443741 2444129 2444172 "RMODULE" 2444177 NIL RMODULE (NIL T) -9 NIL 2444204 NIL) (-1053 2442577 2442671 2443007 "RMCAT2" 2443642 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1052 2439427 2441923 2442220 "RMATRIX" 2442339 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1051 2432254 2434514 2434629 "RMATCAT" 2437988 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2438970 NIL) (-1050 2431629 2431776 2432083 "RMATCAT-" 2432088 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1049 2431030 2431251 2431294 "RLINSET" 2431488 NIL RLINSET (NIL T) -9 NIL 2431579 NIL) (-1048 2430597 2430672 2430800 "RINTERP" 2430949 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1047 2429655 2430209 2430239 "RING" 2430295 T RING (NIL) -9 NIL 2430387 NIL) (-1046 2429447 2429491 2429588 "RING-" 2429593 NIL RING- (NIL T) -8 NIL NIL NIL) (-1045 2428288 2428525 2428783 "RIDIST" 2429211 T RIDIST (NIL) -7 NIL NIL NIL) (-1044 2419577 2427756 2427962 "RGCHAIN" 2428136 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1043 2418927 2419333 2419374 "RGBCSPC" 2419432 NIL RGBCSPC (NIL T) -9 NIL 2419484 NIL) (-1042 2418085 2418466 2418507 "RGBCMDL" 2418739 NIL RGBCMDL (NIL T) -9 NIL 2418853 NIL) (-1041 2415079 2415693 2416363 "RF" 2417449 NIL RF (NIL T) -7 NIL NIL NIL) (-1040 2414725 2414788 2414891 "RFFACTOR" 2415010 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1039 2414450 2414485 2414582 "RFFACT" 2414684 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1038 2412567 2412931 2413313 "RFDIST" 2414090 T RFDIST (NIL) -7 NIL NIL NIL) (-1037 2412020 2412112 2412275 "RETSOL" 2412469 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1036 2411656 2411736 2411779 "RETRACT" 2411912 NIL RETRACT (NIL T) -9 NIL 2411999 NIL) (-1035 2411505 2411530 2411617 "RETRACT-" 2411622 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1034 2411107 2411327 2411397 "RETAST" 2411457 T RETAST (NIL) -8 NIL NIL NIL) (-1033 2403845 2410760 2410887 "RESULT" 2411002 T RESULT (NIL) -8 NIL NIL NIL) (-1032 2402436 2403114 2403313 "RESRING" 2403748 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1031 2402072 2402121 2402219 "RESLATC" 2402373 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1030 2401777 2401812 2401919 "REPSQ" 2402031 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1029 2399199 2399779 2400381 "REP" 2401197 T REP (NIL) -7 NIL NIL NIL) (-1028 2398896 2398931 2399042 "REPDB" 2399158 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1027 2392796 2394185 2395408 "REP2" 2397708 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1026 2389173 2389854 2390662 "REP1" 2392023 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1025 2381869 2387314 2387770 "REGSET" 2388803 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1024 2380634 2381017 2381267 "REF" 2381654 NIL REF (NIL T) -8 NIL NIL NIL) (-1023 2380011 2380114 2380281 "REDORDER" 2380518 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1022 2375979 2379224 2379451 "RECLOS" 2379839 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1021 2375031 2375212 2375427 "REALSOLV" 2375786 T REALSOLV (NIL) -7 NIL NIL NIL) (-1020 2374877 2374918 2374948 "REAL" 2374953 T REAL (NIL) -9 NIL 2374988 NIL) (-1019 2371360 2372162 2373046 "REAL0Q" 2374042 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1018 2366961 2367949 2369010 "REAL0" 2370341 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1017 2366432 2366678 2366772 "RDUCEAST" 2366889 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1016 2365837 2365909 2366116 "RDIV" 2366354 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1015 2364905 2365079 2365292 "RDIST" 2365659 NIL RDIST (NIL T) -7 NIL NIL NIL) 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NIL NIL) (-860 1999154 2001392 2003592 "OUTFORM" 2008103 T OUTFORM (NIL) -8 NIL NIL NIL) (-859 1998490 1998751 1998878 "OUTBFILE" 1999047 T OUTBFILE (NIL) -8 NIL NIL NIL) (-858 1997797 1997962 1997990 "OUTBCON" 1998308 T OUTBCON (NIL) -9 NIL 1998474 NIL) (-857 1997398 1997510 1997667 "OUTBCON-" 1997672 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-856 1996778 1997127 1997216 "OSI" 1997329 T OSI (NIL) -8 NIL NIL NIL) (-855 1996308 1996646 1996674 "OSGROUP" 1996679 T OSGROUP (NIL) -9 NIL 1996701 NIL) (-854 1995053 1995280 1995565 "ORTHPOL" 1996055 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-853 1992604 1994888 1995009 "OREUP" 1995014 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-852 1990007 1992295 1992422 "ORESUP" 1992546 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-851 1987535 1988035 1988596 "OREPCTO" 1989496 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-850 1981221 1983422 1983463 "OREPCAT" 1985811 NIL OREPCAT (NIL T) -9 NIL 1986915 NIL) (-849 1978368 1979150 1980208 "OREPCAT-" 1980213 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-848 1977519 1977817 1977845 "ORDSET" 1978154 T ORDSET (NIL) -9 NIL 1978318 NIL) (-847 1976950 1977098 1977322 "ORDSET-" 1977327 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-846 1975515 1976306 1976334 "ORDRING" 1976536 T ORDRING (NIL) -9 NIL 1976661 NIL) (-845 1975160 1975254 1975398 "ORDRING-" 1975403 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-844 1974540 1975003 1975031 "ORDMON" 1975036 T ORDMON (NIL) -9 NIL 1975057 NIL) (-843 1973702 1973849 1974044 "ORDFUNS" 1974389 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-842 1973040 1973459 1973487 "ORDFIN" 1973552 T ORDFIN (NIL) -9 NIL 1973626 NIL) (-841 1969599 1971626 1972035 "ORDCOMP" 1972664 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-840 1968865 1968992 1969178 "ORDCOMP2" 1969459 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1965446 1966356 1967170 "OPTPROB" 1968071 T OPTPROB (NIL) -8 NIL NIL NIL) (-838 1962248 1962887 1963591 "OPTPACK" 1964762 T OPTPACK (NIL) -7 NIL NIL NIL) (-837 1959935 1960701 1960729 "OPTCAT" 1961548 T OPTCAT (NIL) -9 NIL 1962198 NIL) (-836 1959319 1959612 1959717 "OPSIG" 1959850 T OPSIG (NIL) -8 NIL NIL NIL) (-835 1959087 1959126 1959192 "OPQUERY" 1959273 T OPQUERY (NIL) -7 NIL NIL NIL) (-834 1956218 1957398 1957902 "OP" 1958616 NIL OP (NIL T) -8 NIL NIL NIL) (-833 1955592 1955818 1955859 "OPERCAT" 1956071 NIL OPERCAT (NIL T) -9 NIL 1956168 NIL) (-832 1955347 1955403 1955520 "OPERCAT-" 1955525 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-831 1952160 1954144 1954513 "ONECOMP" 1955011 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-830 1951465 1951580 1951754 "ONECOMP2" 1952032 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-829 1950884 1950990 1951120 "OMSERVER" 1951355 T OMSERVER (NIL) -7 NIL NIL NIL) (-828 1947746 1950324 1950364 "OMSAGG" 1950425 NIL OMSAGG (NIL T) -9 NIL 1950489 NIL) (-827 1946369 1946632 1946914 "OMPKG" 1947484 T OMPKG (NIL) -7 NIL NIL NIL) (-826 1945799 1945902 1945930 "OM" 1946229 T OM (NIL) -9 NIL NIL NIL) (-825 1944346 1945348 1945517 "OMLO" 1945680 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-824 1943306 1943453 1943673 "OMEXPR" 1944172 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-823 1942597 1942852 1942988 "OMERR" 1943190 T OMERR (NIL) -8 NIL NIL NIL) (-822 1941748 1942018 1942178 "OMERRK" 1942457 T OMERRK (NIL) -8 NIL NIL NIL) (-821 1941199 1941425 1941533 "OMENC" 1941660 T OMENC (NIL) -8 NIL NIL NIL) (-820 1935094 1936279 1937450 "OMDEV" 1940048 T OMDEV (NIL) -8 NIL NIL NIL) (-819 1934163 1934334 1934528 "OMCONN" 1934920 T OMCONN (NIL) -8 NIL NIL NIL) (-818 1932684 1933660 1933688 "OINTDOM" 1933693 T OINTDOM (NIL) -9 NIL 1933714 NIL) (-817 1928463 1929674 1930390 "OFMONOID" 1932000 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-816 1927874 1928400 1928445 "ODVAR" 1928450 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-815 1925297 1927619 1927774 "ODR" 1927779 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-814 1917878 1925073 1925199 "ODPOL" 1925204 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-813 1911700 1917750 1917855 "ODP" 1917860 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-812 1910466 1910681 1910956 "ODETOOLS" 1911474 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-811 1907433 1908091 1908807 "ODESYS" 1909799 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-810 1902315 1903223 1904248 "ODERTRIC" 1906508 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-809 1901741 1901823 1902017 "ODERED" 1902227 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-808 1898629 1899177 1899854 "ODERAT" 1901164 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-807 1895586 1896053 1896650 "ODEPRRIC" 1898158 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-806 1893529 1894125 1894611 "ODEPROB" 1895120 T ODEPROB (NIL) -8 NIL NIL NIL) (-805 1890049 1890534 1891181 "ODEPRIM" 1893008 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-804 1889298 1889400 1889660 "ODEPAL" 1889941 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-803 1885460 1886251 1887115 "ODEPACK" 1888454 T ODEPACK (NIL) -7 NIL NIL NIL) (-802 1884521 1884628 1884850 "ODEINT" 1885349 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-801 1878622 1880047 1881494 "ODEIFTBL" 1883094 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-800 1874020 1874806 1875758 "ODEEF" 1877781 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-799 1873369 1873458 1873681 "ODECONST" 1873925 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-798 1871494 1872155 1872183 "ODECAT" 1872788 T ODECAT (NIL) -9 NIL 1873319 NIL) (-797 1868366 1871206 1871325 "OCT" 1871407 NIL OCT (NIL T) -8 NIL NIL NIL) (-796 1868004 1868047 1868174 "OCTCT2" 1868317 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-795 1862653 1865088 1865128 "OC" 1866225 NIL OC (NIL T) -9 NIL 1867083 NIL) (-794 1859880 1860628 1861618 "OC-" 1861712 NIL OC- (NIL T T) -8 NIL NIL NIL) (-793 1859232 1859700 1859728 "OCAMON" 1859733 T OCAMON (NIL) -9 NIL 1859754 NIL) (-792 1858763 1859104 1859132 "OASGP" 1859137 T OASGP (NIL) -9 NIL 1859157 NIL) (-791 1858024 1858513 1858541 "OAMONS" 1858581 T OAMONS (NIL) -9 NIL 1858624 NIL) (-790 1857438 1857871 1857899 "OAMON" 1857904 T OAMON (NIL) -9 NIL 1857924 NIL) (-789 1856696 1857214 1857242 "OAGROUP" 1857247 T OAGROUP (NIL) -9 NIL 1857267 NIL) (-788 1856386 1856436 1856524 "NUMTUBE" 1856640 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-787 1849959 1851477 1853013 "NUMQUAD" 1854870 T NUMQUAD (NIL) -7 NIL NIL NIL) (-786 1845715 1846703 1847728 "NUMODE" 1848954 T NUMODE (NIL) -7 NIL NIL NIL) (-785 1843070 1843950 1843978 "NUMINT" 1844901 T NUMINT (NIL) -9 NIL 1845665 NIL) (-784 1842018 1842215 1842433 "NUMFMT" 1842872 T NUMFMT (NIL) -7 NIL NIL NIL) (-783 1828377 1831322 1833854 "NUMERIC" 1839525 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-782 1822747 1827826 1827921 "NTSCAT" 1827926 NIL NTSCAT (NIL T T T T) -9 NIL 1827965 NIL) (-781 1821941 1822106 1822299 "NTPOLFN" 1822586 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-780 1810018 1818766 1819578 "NSUP" 1821162 NIL NSUP (NIL T) -8 NIL NIL NIL) (-779 1809650 1809707 1809816 "NSUP2" 1809955 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-778 1799878 1809424 1809557 "NSMP" 1809562 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-777 1798310 1798611 1798968 "NREP" 1799566 NIL NREP (NIL T) -7 NIL NIL NIL) (-776 1796901 1797153 1797511 "NPCOEF" 1798053 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-775 1795967 1796082 1796298 "NORMRETR" 1796782 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-774 1794008 1794298 1794707 "NORMPK" 1795675 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-773 1793693 1793721 1793845 "NORMMA" 1793974 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-772 1793493 1793650 1793679 "NONE" 1793684 T NONE (NIL) -8 NIL NIL NIL) (-771 1793282 1793311 1793380 "NONE1" 1793457 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-770 1792779 1792841 1793020 "NODE1" 1793214 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-769 1791059 1791910 1792165 "NNI" 1792512 T NNI (NIL) -8 NIL NIL 1792747) (-768 1789479 1789792 1790156 "NLINSOL" 1790727 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-767 1785720 1786715 1787614 "NIPROB" 1788600 T NIPROB (NIL) -8 NIL NIL NIL) (-766 1784477 1784711 1785013 "NFINTBAS" 1785482 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-765 1783651 1784127 1784168 "NETCLT" 1784340 NIL NETCLT (NIL T) -9 NIL 1784422 NIL) (-764 1782359 1782590 1782871 "NCODIV" 1783419 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-763 1782121 1782158 1782233 "NCNTFRAC" 1782316 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-762 1780301 1780665 1781085 "NCEP" 1781746 NIL NCEP (NIL T) -7 NIL NIL NIL) (-761 1779152 1779925 1779953 "NASRING" 1780063 T NASRING (NIL) -9 NIL 1780143 NIL) (-760 1778947 1778991 1779085 "NASRING-" 1779090 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-759 1778054 1778579 1778607 "NARNG" 1778724 T NARNG (NIL) -9 NIL 1778815 NIL) (-758 1777746 1777813 1777947 "NARNG-" 1777952 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-757 1776625 1776832 1777067 "NAGSP" 1777531 T NAGSP (NIL) -7 NIL NIL NIL) (-756 1767897 1769581 1771254 "NAGS" 1774972 T NAGS (NIL) -7 NIL NIL NIL) (-755 1766445 1766753 1767084 "NAGF07" 1767586 T NAGF07 (NIL) -7 NIL NIL NIL) (-754 1760983 1762274 1763581 "NAGF04" 1765158 T NAGF04 (NIL) -7 NIL NIL NIL) (-753 1753951 1755565 1757198 "NAGF02" 1759370 T NAGF02 (NIL) -7 NIL NIL NIL) (-752 1749175 1750275 1751392 "NAGF01" 1752854 T NAGF01 (NIL) -7 NIL NIL NIL) (-751 1742803 1744369 1745954 "NAGE04" 1747610 T NAGE04 (NIL) -7 NIL NIL NIL) (-750 1733972 1736093 1738223 "NAGE02" 1740693 T NAGE02 (NIL) -7 NIL NIL NIL) (-749 1729925 1730872 1731836 "NAGE01" 1733028 T NAGE01 (NIL) -7 NIL NIL NIL) (-748 1727720 1728254 1728812 "NAGD03" 1729387 T NAGD03 (NIL) -7 NIL NIL NIL) (-747 1719470 1721398 1723352 "NAGD02" 1725786 T NAGD02 (NIL) -7 NIL NIL NIL) (-746 1713281 1714706 1716146 "NAGD01" 1718050 T NAGD01 (NIL) -7 NIL NIL NIL) (-745 1709490 1710312 1711149 "NAGC06" 1712464 T NAGC06 (NIL) -7 NIL NIL NIL) (-744 1707955 1708287 1708643 "NAGC05" 1709154 T NAGC05 (NIL) -7 NIL NIL NIL) (-743 1707331 1707450 1707594 "NAGC02" 1707831 T NAGC02 (NIL) -7 NIL NIL NIL) (-742 1706290 1706873 1706913 "NAALG" 1706992 NIL NAALG (NIL T) -9 NIL 1707053 NIL) (-741 1706125 1706154 1706244 "NAALG-" 1706249 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-740 1700075 1701183 1702370 "MULTSQFR" 1705021 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-739 1699394 1699469 1699653 "MULTFACT" 1699987 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-738 1692118 1696031 1696084 "MTSCAT" 1697154 NIL MTSCAT (NIL T T) -9 NIL 1697669 NIL) (-737 1691830 1691884 1691976 "MTHING" 1692058 NIL MTHING (NIL T) -7 NIL NIL NIL) (-736 1691622 1691655 1691715 "MSYSCMD" 1691790 T MSYSCMD (NIL) -7 NIL NIL NIL) (-735 1687704 1690377 1690697 "MSET" 1691335 NIL MSET (NIL T) -8 NIL NIL NIL) (-734 1684773 1687265 1687306 "MSETAGG" 1687311 NIL MSETAGG (NIL T) -9 NIL 1687345 NIL) (-733 1680614 1682152 1682897 "MRING" 1684073 NIL MRING (NIL T T) -8 NIL NIL NIL) (-732 1680180 1680247 1680378 "MRF2" 1680541 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-731 1679798 1679833 1679977 "MRATFAC" 1680139 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-730 1677410 1677705 1678136 "MPRFF" 1679503 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-729 1671707 1677264 1677361 "MPOLY" 1677366 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-728 1671197 1671232 1671440 "MPCPF" 1671666 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-727 1670711 1670754 1670938 "MPC3" 1671148 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-726 1669906 1669987 1670208 "MPC2" 1670626 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1668207 1668544 1668934 "MONOTOOL" 1669566 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-724 1667432 1667749 1667777 "MONOID" 1667996 T MONOID (NIL) -9 NIL 1668143 NIL) (-723 1666978 1667097 1667278 "MONOID-" 1667283 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-722 1657453 1663404 1663463 "MONOGEN" 1664137 NIL MONOGEN (NIL T T) -9 NIL 1664593 NIL) (-721 1654671 1655406 1656406 "MONOGEN-" 1656525 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-720 1653504 1653950 1653978 "MONADWU" 1654370 T MONADWU (NIL) -9 NIL 1654608 NIL) (-719 1652876 1653035 1653283 "MONADWU-" 1653288 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-718 1652235 1652479 1652507 "MONAD" 1652714 T MONAD (NIL) -9 NIL 1652826 NIL) (-717 1651920 1651998 1652130 "MONAD-" 1652135 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-716 1650209 1650833 1651112 "MOEBIUS" 1651673 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-715 1649487 1649891 1649931 "MODULE" 1649936 NIL MODULE (NIL T) -9 NIL 1649975 NIL) (-714 1649055 1649151 1649341 "MODULE-" 1649346 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-713 1646735 1647419 1647746 "MODRING" 1648879 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-712 1643679 1644840 1645361 "MODOP" 1646264 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-711 1642267 1642746 1643023 "MODMONOM" 1643542 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-710 1632308 1640558 1640972 "MODMON" 1641904 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-709 1629464 1631152 1631428 "MODFIELD" 1632183 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1628441 1628745 1628935 "MMLFORM" 1629294 T MMLFORM (NIL) -8 NIL NIL NIL) (-707 1627967 1628010 1628189 "MMAP" 1628392 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-706 1626046 1626813 1626854 "MLO" 1627277 NIL MLO (NIL T) -9 NIL 1627519 NIL) (-705 1623412 1623928 1624530 "MLIFT" 1625527 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-704 1622803 1622887 1623041 "MKUCFUNC" 1623323 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-703 1622402 1622472 1622595 "MKRECORD" 1622726 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-702 1621449 1621611 1621839 "MKFUNC" 1622213 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-701 1620837 1620941 1621097 "MKFLCFN" 1621332 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-700 1620114 1620216 1620401 "MKBCFUNC" 1620730 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-699 1616821 1619668 1619804 "MINT" 1619998 T MINT (NIL) -8 NIL NIL NIL) (-698 1615633 1615876 1616153 "MHROWRED" 1616576 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-697 1611013 1614168 1614573 "MFLOAT" 1615248 T MFLOAT (NIL) -8 NIL NIL NIL) (-696 1610370 1610446 1610617 "MFINFACT" 1610925 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-695 1606685 1607533 1608417 "MESH" 1609506 T MESH (NIL) -7 NIL NIL NIL) (-694 1605075 1605387 1605740 "MDDFACT" 1606372 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-693 1601870 1604234 1604275 "MDAGG" 1604530 NIL MDAGG (NIL T) -9 NIL 1604673 NIL) (-692 1591610 1601163 1601370 "MCMPLX" 1601683 T MCMPLX (NIL) -8 NIL NIL NIL) (-691 1590751 1590897 1591097 "MCDEN" 1591459 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-690 1588641 1588911 1589291 "MCALCFN" 1590481 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-689 1587566 1587806 1588039 "MAYBE" 1588447 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-688 1585178 1585701 1586263 "MATSTOR" 1587037 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-687 1581135 1584550 1584798 "MATRIX" 1584963 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-686 1576899 1577608 1578344 "MATLIN" 1580492 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-685 1567005 1570191 1570268 "MATCAT" 1575148 NIL MATCAT (NIL T T T) -9 NIL 1576565 NIL) (-684 1563361 1564382 1565738 "MATCAT-" 1565743 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-683 1561955 1562108 1562441 "MATCAT2" 1563196 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-682 1560067 1560391 1560775 "MAPPKG3" 1561630 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-681 1559048 1559221 1559443 "MAPPKG2" 1559891 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-680 1557547 1557831 1558158 "MAPPKG1" 1558754 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-679 1556626 1556953 1557130 "MAPPAST" 1557390 T MAPPAST (NIL) -8 NIL NIL NIL) (-678 1556237 1556295 1556418 "MAPHACK3" 1556562 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-677 1555829 1555890 1556004 "MAPHACK2" 1556169 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-676 1555266 1555370 1555512 "MAPHACK1" 1555720 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-675 1553345 1553966 1554270 "MAGMA" 1554994 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-674 1552824 1553069 1553160 "MACROAST" 1553274 T MACROAST (NIL) -8 NIL NIL NIL) (-673 1549242 1551063 1551524 "M3D" 1552396 NIL M3D (NIL T) -8 NIL NIL NIL) (-672 1543348 1547611 1547652 "LZSTAGG" 1548434 NIL LZSTAGG (NIL T) -9 NIL 1548729 NIL) (-671 1539305 1540479 1541936 "LZSTAGG-" 1541941 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-670 1536392 1537196 1537683 "LWORD" 1538850 NIL LWORD (NIL T) -8 NIL NIL NIL) (-669 1535968 1536196 1536271 "LSTAST" 1536337 T LSTAST (NIL) -8 NIL NIL NIL) (-668 1529134 1535739 1535873 "LSQM" 1535878 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-667 1528358 1528497 1528725 "LSPP" 1528989 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-666 1526170 1526471 1526927 "LSMP" 1528047 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-665 1522949 1523623 1524353 "LSMP1" 1525472 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-664 1516826 1522116 1522157 "LSAGG" 1522219 NIL LSAGG (NIL T) -9 NIL 1522297 NIL) (-663 1513521 1514445 1515658 "LSAGG-" 1515663 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-662 1511120 1512665 1512914 "LPOLY" 1513316 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-661 1510702 1510787 1510910 "LPEFRAC" 1511029 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-660 1509023 1509796 1510049 "LO" 1510534 NIL LO (NIL T T T) -8 NIL NIL NIL) (-659 1508675 1508787 1508815 "LOGIC" 1508926 T LOGIC (NIL) -9 NIL 1509007 NIL) (-658 1508537 1508560 1508631 "LOGIC-" 1508636 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-657 1507730 1507870 1508063 "LODOOPS" 1508393 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-656 1505153 1507646 1507712 "LODO" 1507717 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-655 1503691 1503926 1504279 "LODOF" 1504900 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-654 1499909 1502340 1502381 "LODOCAT" 1502819 NIL LODOCAT (NIL T) -9 NIL 1503030 NIL) (-653 1499642 1499700 1499827 "LODOCAT-" 1499832 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-652 1496962 1499483 1499601 "LODO2" 1499606 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-651 1494397 1496899 1496944 "LODO1" 1496949 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-650 1493278 1493443 1493748 "LODEEF" 1494220 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-649 1488517 1491408 1491449 "LNAGG" 1492396 NIL LNAGG (NIL T) -9 NIL 1492840 NIL) (-648 1487664 1487878 1488220 "LNAGG-" 1488225 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-647 1483800 1484589 1485228 "LMOPS" 1487079 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-646 1483203 1483591 1483632 "LMODULE" 1483637 NIL LMODULE (NIL T) -9 NIL 1483663 NIL) (-645 1480401 1482848 1482971 "LMDICT" 1483113 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-644 1479807 1480028 1480069 "LLINSET" 1480260 NIL LLINSET (NIL T) -9 NIL 1480351 NIL) (-643 1479506 1479715 1479775 "LITERAL" 1479780 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-642 1472689 1478452 1478750 "LIST" 1479241 NIL LIST (NIL T) -8 NIL NIL NIL) (-641 1472214 1472288 1472427 "LIST3" 1472609 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-640 1471221 1471399 1471627 "LIST2" 1472032 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-639 1469355 1469667 1470066 "LIST2MAP" 1470868 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-638 1468951 1469188 1469229 "LINSET" 1469234 NIL LINSET (NIL T) -9 NIL 1469268 NIL) (-637 1467612 1468282 1468323 "LINEXP" 1468578 NIL LINEXP (NIL T) -9 NIL 1468727 NIL) (-636 1466259 1466519 1466816 "LINDEP" 1467364 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1463026 1463745 1464522 "LIMITRF" 1465514 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1461329 1461625 1462034 "LIMITPS" 1462721 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1455757 1460840 1461068 "LIE" 1461150 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1454705 1455174 1455214 "LIECAT" 1455354 NIL LIECAT (NIL T) -9 NIL 1455505 NIL) (-631 1454546 1454573 1454661 "LIECAT-" 1454666 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1447042 1453995 1454160 "LIB" 1454401 T LIB (NIL) -8 NIL NIL NIL) (-629 1442677 1443560 1444495 "LGROBP" 1446159 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1440675 1440949 1441299 "LF" 1442398 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1439515 1440207 1440235 "LFCAT" 1440442 T LFCAT (NIL) -9 NIL 1440581 NIL) (-626 1436417 1437047 1437735 "LEXTRIPK" 1438879 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1433161 1433987 1434490 "LEXP" 1435997 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1432637 1432882 1432974 "LETAST" 1433089 T LETAST (NIL) -8 NIL NIL NIL) (-623 1431035 1431348 1431749 "LEADCDET" 1432319 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1430225 1430299 1430528 "LAZM3PK" 1430956 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1425142 1428302 1428840 "LAUPOL" 1429737 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1424721 1424765 1424926 "LAPLACE" 1425092 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1422660 1423822 1424073 "LA" 1424554 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1421654 1422238 1422279 "LALG" 1422341 NIL LALG (NIL T) -9 NIL 1422400 NIL) (-617 1421368 1421427 1421563 "LALG-" 1421568 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1421203 1421227 1421268 "KVTFROM" 1421330 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1420126 1420570 1420755 "KTVLOGIC" 1421038 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1419961 1419985 1420026 "KRCFROM" 1420088 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1418865 1419052 1419351 "KOVACIC" 1419761 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1418700 1418724 1418765 "KONVERT" 1418827 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1418535 1418559 1418600 "KOERCE" 1418662 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1416217 1417005 1417406 "KERNEL" 1418167 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1415713 1415794 1415926 "KERNEL2" 1416131 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1409483 1414252 1414306 "KDAGG" 1414683 NIL KDAGG (NIL T T) -9 NIL 1414889 NIL) (-607 1409012 1409136 1409341 "KDAGG-" 1409346 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1402160 1408673 1408828 "KAFILE" 1408890 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1396588 1401671 1401899 "JORDAN" 1401981 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1395967 1396237 1396358 "JOINAST" 1396487 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1395813 1395872 1395927 "JAVACODE" 1395932 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1392065 1394018 1394072 "IXAGG" 1395001 NIL IXAGG (NIL T T) -9 NIL 1395460 NIL) (-601 1390984 1391290 1391709 "IXAGG-" 1391714 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386514 1390906 1390965 "IVECTOR" 1390970 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1385280 1385517 1385783 "ITUPLE" 1386281 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1383782 1383959 1384254 "ITRIGMNP" 1385102 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1382527 1382731 1383014 "ITFUN3" 1383558 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1382159 1382216 1382325 "ITFUN2" 1382464 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1379961 1381021 1381320 "ITAYLOR" 1381893 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1368906 1374098 1375261 "ISUPS" 1378831 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1368010 1368150 1368386 "ISUMP" 1368753 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1363224 1367811 1367890 "ISTRING" 1367963 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1362700 1362945 1363037 "ISAST" 1363152 T ISAST (NIL) -8 NIL NIL NIL) (-590 1361909 1361991 1362207 "IRURPK" 1362614 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1360845 1361046 1361286 "IRSN" 1361689 T IRSN (NIL) -7 NIL NIL NIL) (-588 1358916 1359271 1359700 "IRRF2F" 1360483 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1358663 1358701 1358777 "IRREDFFX" 1358872 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1357278 1357537 1357836 "IROOT" 1358396 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1353882 1354962 1355654 "IR" 1356618 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1351495 1351990 1352556 "IR2" 1353360 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1350595 1350708 1350922 "IR2F" 1351378 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1350386 1350420 1350480 "IPRNTPK" 1350555 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1346966 1350275 1350344 "IPF" 1350349 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1345293 1346891 1346948 "IPADIC" 1346953 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1344605 1344853 1344983 "IP4ADDR" 1345183 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1344078 1344309 1344419 "IOMODE" 1344515 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1343151 1343675 1343802 "IOBFILE" 1343971 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1342639 1343055 1343083 "IOBCON" 1343088 T IOBCON (NIL) -9 NIL 1343109 NIL) (-575 1342150 1342208 1342391 "INVLAPLA" 1342575 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1331798 1334152 1336538 "INTTR" 1339814 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1328133 1328875 1329740 "INTTOOLS" 1330983 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1327719 1327810 1327927 "INTSLPE" 1328036 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1325673 1327642 1327701 "INTRVL" 1327706 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1323275 1323787 1324362 "INTRF" 1325158 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1322686 1322783 1322925 "INTRET" 1323173 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1320683 1321072 1321542 "INTRAT" 1322294 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1317946 1318529 1319148 "INTPM" 1320168 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1314690 1315290 1316028 "INTPAF" 1317332 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1309869 1310831 1311882 "INTPACK" 1313659 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1306746 1309598 1309725 "INT" 1309762 T INT (NIL) -8 NIL NIL NIL) (-563 1305998 1306150 1306358 "INTHERTR" 1306588 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1305437 1305517 1305705 "INTHERAL" 1305912 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1303283 1303726 1304183 "INTHEORY" 1305000 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1294689 1296310 1298082 "INTG0" 1301635 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1275262 1280052 1284862 "INTFTBL" 1289899 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1274511 1274649 1274822 "INTFACT" 1275121 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1271938 1272384 1272941 "INTEF" 1274065 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1270305 1271044 1271072 "INTDOM" 1271373 T INTDOM (NIL) -9 NIL 1271580 NIL) (-555 1269674 1269848 1270090 "INTDOM-" 1270095 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1266062 1267990 1268044 "INTCAT" 1268843 NIL INTCAT (NIL T) -9 NIL 1269164 NIL) (-553 1265534 1265637 1265765 "INTBIT" 1265954 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1264233 1264387 1264694 "INTALG" 1265379 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1263716 1263806 1263963 "INTAF" 1264137 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1257059 1263526 1263666 "INTABL" 1263671 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1256400 1256866 1256931 "INT8" 1256965 T INT8 (NIL) -8 NIL NIL 1257010) (-548 1255740 1256206 1256271 "INT64" 1256305 T INT64 (NIL) -8 NIL NIL 1256350) (-547 1255080 1255546 1255611 "INT32" 1255645 T INT32 (NIL) -8 NIL NIL 1255690) (-546 1254420 1254886 1254951 "INT16" 1254985 T INT16 (NIL) -8 NIL NIL 1255030) (-545 1249330 1252043 1252071 "INS" 1253005 T INS (NIL) -9 NIL 1253670 NIL) (-544 1246570 1247341 1248315 "INS-" 1248388 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1245345 1245572 1245870 "INPSIGN" 1246323 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1244463 1244580 1244777 "INPRODPF" 1245225 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1243357 1243474 1243711 "INPRODFF" 1244343 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1242357 1242509 1242769 "INNMFACT" 1243193 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1241554 1241651 1241839 "INMODGCD" 1242256 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1240062 1240307 1240631 "INFSP" 1241299 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1239246 1239363 1239546 "INFPROD0" 1239942 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1236101 1237311 1237826 "INFORM" 1238739 T INFORM (NIL) -8 NIL NIL NIL) (-535 1235711 1235771 1235869 "INFORM1" 1236036 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1235234 1235323 1235437 "INFINITY" 1235617 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1234410 1234954 1235055 "INETCLTS" 1235153 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1233026 1233276 1233597 "INEP" 1234158 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1232275 1232923 1232988 "INDE" 1232993 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1231839 1231907 1232024 "INCRMAPS" 1232202 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1230657 1231108 1231314 "INBFILE" 1231653 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1225957 1226893 1227837 "INBFF" 1229745 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1224865 1225134 1225162 "INBCON" 1225675 T INBCON (NIL) -9 NIL 1225941 NIL) (-526 1224117 1224340 1224616 "INBCON-" 1224621 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1223596 1223841 1223932 "INAST" 1224046 T INAST (NIL) -8 NIL NIL NIL) (-524 1223023 1223275 1223381 "IMPTAST" 1223510 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1219469 1222867 1222971 "IMATRIX" 1222976 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1218181 1218304 1218619 "IMATQF" 1219325 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1216401 1216628 1216965 "IMATLIN" 1217937 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1210979 1216325 1216383 "ILIST" 1216388 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1208884 1210839 1210952 "IIARRAY2" 1210957 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1204282 1208795 1208859 "IFF" 1208864 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1203629 1203899 1204015 "IFAST" 1204186 T IFAST (NIL) -8 NIL NIL NIL) (-516 1198624 1202921 1203109 "IFARRAY" 1203486 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1197804 1198528 1198601 "IFAMON" 1198606 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1197388 1197453 1197507 "IEVALAB" 1197714 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1197063 1197131 1197291 "IEVALAB-" 1197296 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1196694 1196977 1197040 "IDPO" 1197045 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1195944 1196583 1196658 "IDPOAMS" 1196663 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1195251 1195833 1195908 "IDPOAM" 1195913 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1194310 1194586 1194639 "IDPC" 1195052 NIL IDPC (NIL T T) -9 NIL 1195201 NIL) (-508 1193779 1194202 1194275 "IDPAM" 1194280 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1193155 1193671 1193744 "IDPAG" 1193749 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1192800 1192991 1193066 "IDENT" 1193100 T IDENT (NIL) -8 NIL NIL NIL) (-505 1189055 1189903 1190798 "IDECOMP" 1191957 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1181891 1182978 1184025 "IDEAL" 1188091 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1181055 1181167 1181366 "ICDEN" 1181775 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1180126 1180535 1180682 "ICARD" 1180928 T ICARD (NIL) -8 NIL NIL NIL) (-501 1178186 1178499 1178904 "IBPTOOLS" 1179803 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1173793 1177806 1177919 "IBITS" 1178105 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1170516 1171092 1171787 "IBATOOL" 1173210 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1168295 1168757 1169290 "IBACHIN" 1170051 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1166124 1168141 1168244 "IARRAY2" 1168249 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1162230 1166050 1166107 "IARRAY1" 1166112 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1156339 1160642 1161123 "IAN" 1161769 T IAN (NIL) -8 NIL NIL NIL) (-494 1155850 1155907 1156080 "IALGFACT" 1156276 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1155378 1155491 1155519 "HYPCAT" 1155726 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1154916 1155033 1155219 "HYPCAT-" 1155224 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1154511 1154711 1154794 "HOSTNAME" 1154853 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1154356 1154393 1154434 "HOMOTOP" 1154439 NIL HOMOTOP (NIL T) -9 NIL 1154472 NIL) (-489 1150988 1152366 1152407 "HOAGG" 1153388 NIL HOAGG (NIL T) -9 NIL 1154067 NIL) (-488 1149582 1149981 1150507 "HOAGG-" 1150512 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1143586 1149177 1149326 "HEXADEC" 1149453 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1142334 1142556 1142819 "HEUGCD" 1143363 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1141410 1142171 1142301 "HELLFDIV" 1142306 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1139589 1141187 1141275 "HEAP" 1141354 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1138852 1139141 1139275 "HEADAST" 1139475 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1132718 1138767 1138829 "HDP" 1138834 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1126706 1132353 1132505 "HDMP" 1132619 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1126030 1126170 1126334 "HB" 1126562 T HB (NIL) -7 NIL NIL NIL) (-479 1119416 1125876 1125980 "HASHTBL" 1125985 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1118892 1119137 1119229 "HASAST" 1119344 T HASAST (NIL) -8 NIL NIL NIL) (-477 1116670 1118514 1118696 "HACKPI" 1118730 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1112338 1116523 1116636 "GTSET" 1116641 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1105753 1112216 1112314 "GSTBL" 1112319 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1098031 1104784 1105049 "GSERIES" 1105544 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1097172 1097589 1097617 "GROUP" 1097820 T GROUP (NIL) -9 NIL 1097954 NIL) (-472 1096538 1096697 1096948 "GROUP-" 1096953 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1094905 1095226 1095613 "GROEBSOL" 1096215 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1093819 1094107 1094158 "GRMOD" 1094687 NIL GRMOD (NIL T T) -9 NIL 1094855 NIL) (-469 1093587 1093623 1093751 "GRMOD-" 1093756 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1088877 1089941 1090941 "GRIMAGE" 1092607 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1087343 1087604 1087928 "GRDEF" 1088573 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1086787 1086903 1087044 "GRAY" 1087222 T GRAY (NIL) -7 NIL NIL NIL) (-465 1085974 1086380 1086431 "GRALG" 1086584 NIL GRALG (NIL T T) -9 NIL 1086677 NIL) (-464 1085635 1085708 1085871 "GRALG-" 1085876 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1082412 1085220 1085398 "GPOLSET" 1085542 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1081766 1081823 1082081 "GOSPER" 1082349 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1077498 1078204 1078730 "GMODPOL" 1081465 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1076503 1076687 1076925 "GHENSEL" 1077310 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1070659 1071502 1072522 "GENUPS" 1075587 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1070356 1070407 1070496 "GENUFACT" 1070602 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1069768 1069845 1070010 "GENPGCD" 1070274 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1069242 1069277 1069490 "GENMFACT" 1069727 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1067808 1068065 1068372 "GENEEZ" 1068985 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1061953 1067419 1067581 "GDMP" 1067731 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1051295 1055724 1056830 "GCNAALG" 1060936 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1049622 1050484 1050512 "GCDDOM" 1050767 T GCDDOM (NIL) -9 NIL 1050924 NIL) (-451 1049092 1049219 1049434 "GCDDOM-" 1049439 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1047764 1047949 1048253 "GB" 1048871 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1036380 1038710 1041102 "GBINTERN" 1045455 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1034217 1034509 1034930 "GBF" 1036055 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1032998 1033163 1033430 "GBEUCLID" 1034033 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1032347 1032472 1032621 "GAUSSFAC" 1032869 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1030714 1031016 1031330 "GALUTIL" 1032066 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1029022 1029296 1029620 "GALPOLYU" 1030441 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1026387 1026677 1027084 "GALFACTU" 1028719 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1018192 1019692 1021300 "GALFACT" 1024819 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1015580 1016238 1016266 "FVFUN" 1017422 T FVFUN (NIL) -9 NIL 1018142 NIL) (-440 1014846 1015028 1015056 "FVC" 1015347 T FVC (NIL) -9 NIL 1015530 NIL) (-439 1014489 1014671 1014739 "FUNDESC" 1014798 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1014104 1014286 1014367 "FUNCTION" 1014441 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1011848 1012426 1012892 "FT" 1013658 T FT (NIL) -8 NIL NIL NIL) (-436 1010639 1011149 1011352 "FTEM" 1011665 T FTEM (NIL) -8 NIL NIL NIL) (-435 1008930 1009219 1009616 "FSUPFACT" 1010330 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1007327 1007616 1007948 "FST" 1008618 T FST (NIL) -8 NIL NIL NIL) (-433 1006526 1006632 1006820 "FSRED" 1007209 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1005225 1005481 1005828 "FSPRMELT" 1006241 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 1002531 1002969 1003455 "FSPECF" 1004788 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 984169 992500 992541 "FS" 996425 NIL FS (NIL T) -9 NIL 998714 NIL) (-429 972812 975805 979862 "FS-" 980162 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 972340 972394 972564 "FSINT" 972753 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 970632 971333 971636 "FSERIES" 972119 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 969674 969790 970014 "FSCINT" 970512 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 965882 968618 968659 "FSAGG" 969029 NIL FSAGG (NIL T) -9 NIL 969288 NIL) (-424 963644 964245 965041 "FSAGG-" 965136 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 962686 962829 963056 "FSAGG2" 963497 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 960368 960648 961195 "FS2UPS" 962404 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 960002 960045 960174 "FS2" 960319 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 958880 959051 959353 "FS2EXPXP" 959827 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 958306 958421 958573 "FRUTIL" 958760 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 949719 953801 955159 "FR" 956980 NIL FR (NIL T) -8 NIL NIL NIL) (-417 944688 947362 947402 "FRNAALG" 948798 NIL FRNAALG (NIL T) -9 NIL 949405 NIL) (-416 940361 941437 942712 "FRNAALG-" 943462 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 939999 940042 940169 "FRNAAF2" 940312 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 938379 938853 939148 "FRMOD" 939811 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 936130 936762 937079 "FRIDEAL" 938170 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 935325 935412 935701 "FRIDEAL2" 936037 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 934458 934872 934913 "FRETRCT" 934918 NIL FRETRCT (NIL T) -9 NIL 935094 NIL) (-410 933570 933801 934152 "FRETRCT-" 934157 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 930658 931868 931927 "FRAMALG" 932809 NIL FRAMALG (NIL T T) -9 NIL 933101 NIL) (-408 928792 929247 929877 "FRAMALG-" 930100 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 922713 928267 928543 "FRAC" 928548 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 922349 922406 922513 "FRAC2" 922650 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 921985 922042 922149 "FR2" 922286 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 916498 919391 919419 "FPS" 920538 T FPS (NIL) -9 NIL 921095 NIL) (-403 915947 916056 916220 "FPS-" 916366 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 913249 914918 914946 "FPC" 915171 T FPC (NIL) -9 NIL 915313 NIL) (-401 913042 913082 913179 "FPC-" 913184 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 911832 912530 912571 "FPATMAB" 912576 NIL FPATMAB (NIL T) -9 NIL 912728 NIL) (-399 909505 910008 910434 "FPARFRAC" 911469 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 904898 905397 906079 "FORTRAN" 908937 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 902614 903114 903653 "FORT" 904379 T FORT (NIL) -7 NIL NIL NIL) (-396 900290 900852 900880 "FORTFN" 901940 T FORTFN (NIL) -9 NIL 902564 NIL) (-395 900054 900104 900132 "FORTCAT" 900191 T FORTCAT (NIL) -9 NIL 900253 NIL) (-394 898160 898670 899060 "FORMULA" 899684 T FORMULA (NIL) -8 NIL NIL NIL) (-393 897948 897978 898047 "FORMULA1" 898124 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 897471 897523 897696 "FORDER" 897890 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 896567 896731 896924 "FOP" 897298 T FOP (NIL) -7 NIL NIL NIL) (-390 895148 895847 896021 "FNLA" 896449 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 893877 894292 894320 "FNCAT" 894780 T FNCAT (NIL) -9 NIL 895040 NIL) (-388 893416 893836 893864 "FNAME" 893869 T FNAME (NIL) -8 NIL NIL NIL) (-387 891979 892942 892970 "FMTC" 892975 T FMTC (NIL) -9 NIL 893011 NIL) (-386 888312 889502 890131 "FMONOID" 891383 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 887504 888054 888203 "FM" 888208 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 884928 885574 885602 "FMFUN" 886746 T FMFUN (NIL) -9 NIL 887454 NIL) (-383 884197 884378 884406 "FMC" 884696 T FMC (NIL) -9 NIL 884878 NIL) (-382 881276 882136 882190 "FMCAT" 883385 NIL FMCAT (NIL T T) -9 NIL 883880 NIL) (-381 880142 881042 881142 "FM1" 881221 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 877916 878332 878826 "FLOATRP" 879693 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 871490 875645 876266 "FLOAT" 877315 T FLOAT (NIL) -8 NIL NIL NIL) (-378 868928 869428 870006 "FLOATCP" 870957 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 867668 868506 868547 "FLINEXP" 868552 NIL FLINEXP (NIL T) -9 NIL 868645 NIL) (-376 866822 867057 867385 "FLINEXP-" 867390 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 865898 866042 866266 "FLASORT" 866674 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 863014 863882 863934 "FLALG" 865161 NIL FLALG (NIL T T) -9 NIL 865628 NIL) (-373 856750 860500 860541 "FLAGG" 861803 NIL FLAGG (NIL T) -9 NIL 862455 NIL) (-372 855476 855815 856305 "FLAGG-" 856310 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 854518 854661 854888 "FLAGG2" 855329 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 851369 852377 852436 "FINRALG" 853564 NIL FINRALG (NIL T T) -9 NIL 854072 NIL) (-369 850529 850758 851097 "FINRALG-" 851102 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 849909 850148 850176 "FINITE" 850372 T FINITE (NIL) -9 NIL 850479 NIL) (-367 842266 844453 844493 "FINAALG" 848160 NIL FINAALG (NIL T) -9 NIL 849613 NIL) (-366 837598 838648 839792 "FINAALG-" 841171 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 836966 837353 837456 "FILE" 837528 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 835624 835962 836016 "FILECAT" 836700 NIL FILECAT (NIL T T) -9 NIL 836916 NIL) (-363 833340 834868 834896 "FIELD" 834936 T FIELD (NIL) -9 NIL 835016 NIL) (-362 831960 832345 832856 "FIELD-" 832861 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 829810 830595 830942 "FGROUP" 831646 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 828900 829064 829284 "FGLMICPK" 829642 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 824732 828825 828882 "FFX" 828887 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 824333 824394 824529 "FFSLPE" 824665 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 820322 821105 821901 "FFPOLY" 823569 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 819826 819862 820071 "FFPOLY2" 820280 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 815669 819745 819808 "FFP" 819813 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 811067 815580 815644 "FF" 815649 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 806193 810410 810600 "FFNBX" 810921 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 801122 805328 805586 "FFNBP" 806047 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 795755 800406 800617 "FFNB" 800955 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 794587 794785 795100 "FFINTBAS" 795552 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 790656 792876 792904 "FFIELDC" 793524 T FFIELDC (NIL) -9 NIL 793900 NIL) (-348 789318 789689 790186 "FFIELDC-" 790191 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 788887 788933 789057 "FFHOM" 789260 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 786582 787069 787586 "FFF" 788402 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 782200 786324 786425 "FFCGX" 786525 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 777821 781932 782039 "FFCGP" 782143 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 773004 777548 777656 "FFCG" 777757 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 754400 763481 763567 "FFCAT" 768732 NIL FFCAT (NIL T T T) -9 NIL 770183 NIL) (-341 749598 750645 751959 "FFCAT-" 753189 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 749009 749052 749287 "FFCAT2" 749549 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 738330 741981 743201 "FEXPR" 747861 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 737330 737765 737806 "FEVALAB" 737890 NIL FEVALAB (NIL T) -9 NIL 738151 NIL) (-337 736489 736699 737037 "FEVALAB-" 737042 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 735055 735872 736075 "FDIV" 736388 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 732075 732816 732931 "FDIVCAT" 734499 NIL FDIVCAT (NIL T T T T) -9 NIL 734936 NIL) (-334 731837 731864 732034 "FDIVCAT-" 732039 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 731057 731144 731421 "FDIV2" 731744 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 729743 730002 730291 "FCPAK1" 730788 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 728842 729243 729384 "FCOMP" 729634 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 712544 715992 719530 "FC" 725324 T FC (NIL) -8 NIL NIL NIL) (-329 704907 708935 708975 "FAXF" 710777 NIL FAXF (NIL T) -9 NIL 711469 NIL) (-328 702183 702841 703666 "FAXF-" 704131 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 697235 701559 701735 "FARRAY" 702040 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 692129 694196 694249 "FAMR" 695272 NIL FAMR (NIL T T) -9 NIL 695732 NIL) (-325 691019 691321 691756 "FAMR-" 691761 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 690188 690941 690994 "FAMONOID" 690999 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 687974 688684 688737 "FAMONC" 689678 NIL FAMONC (NIL T T) -9 NIL 690064 NIL) (-322 686639 687728 687865 "FAGROUP" 687870 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 684434 684753 685156 "FACUTIL" 686320 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 683533 683718 683940 "FACTFUNC" 684244 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 675955 682836 683035 "EXPUPXS" 683389 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 673438 673978 674564 "EXPRTUBE" 675389 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 669709 670301 671031 "EXPRODE" 672777 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 655194 668358 668787 "EXPR" 669313 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 649748 650335 651141 "EXPR2UPS" 654492 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 649380 649437 649546 "EXPR2" 649685 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 640771 648533 648823 "EXPEXPAN" 649217 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 640571 640728 640757 "EXIT" 640762 T EXIT (NIL) -8 NIL NIL NIL) (-311 640051 640295 640386 "EXITAST" 640500 T EXITAST (NIL) -8 NIL NIL NIL) (-310 639678 639740 639853 "EVALCYC" 639983 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 639219 639337 639378 "EVALAB" 639548 NIL EVALAB (NIL T) -9 NIL 639652 NIL) (-308 638700 638822 639043 "EVALAB-" 639048 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 636068 637370 637398 "EUCDOM" 637953 T EUCDOM (NIL) -9 NIL 638303 NIL) (-306 634473 634915 635505 "EUCDOM-" 635510 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 622011 624771 627521 "ESTOOLS" 631743 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 621643 621700 621809 "ESTOOLS2" 621948 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 621394 621436 621516 "ESTOOLS1" 621595 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 615431 617039 617067 "ES" 619835 T ES (NIL) -9 NIL 621245 NIL) (-301 610378 611665 613482 "ES-" 613646 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 606752 607513 608293 "ESCONT" 609618 T ESCONT (NIL) -7 NIL NIL NIL) (-299 606497 606529 606611 "ESCONT1" 606714 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 606172 606222 606322 "ES2" 606441 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 605802 605860 605969 "ES1" 606108 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 605018 605147 605323 "ERROR" 605646 T ERROR (NIL) -7 NIL NIL NIL) (-295 598410 604877 604968 "EQTBL" 604973 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 590913 593724 595173 "EQ" 596994 NIL -2010 (NIL T) -8 NIL NIL NIL) (-293 590545 590602 590711 "EQ2" 590850 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 585834 586883 587976 "EP" 589484 NIL EP (NIL T) -7 NIL NIL NIL) (-291 584434 584725 585031 "ENV" 585548 T ENV (NIL) -8 NIL NIL NIL) (-290 583528 584082 584110 "ENTIRER" 584115 T ENTIRER (NIL) -9 NIL 584161 NIL) (-289 579995 581483 581853 "EMR" 583327 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 579139 579324 579378 "ELTAGG" 579758 NIL ELTAGG (NIL T T) -9 NIL 579969 NIL) (-287 578858 578920 579061 "ELTAGG-" 579066 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 578647 578676 578730 "ELTAB" 578814 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 577773 577919 578118 "ELFUTS" 578498 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 577515 577571 577599 "ELEMFUN" 577704 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 577385 577406 577474 "ELEMFUN-" 577479 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 572229 575485 575526 "ELAGG" 576466 NIL ELAGG (NIL T) -9 NIL 576929 NIL) (-281 570514 570948 571611 "ELAGG-" 571616 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 569179 569457 569750 "ELABEXPR" 570241 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 562043 563846 564673 "EFUPXS" 568455 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 555493 557294 558104 "EFULS" 561319 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 552978 553336 553808 "EFSTRUC" 555125 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 542769 544335 545883 "EF" 551493 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 541843 542254 542403 "EAB" 542640 T EAB (NIL) -8 NIL NIL NIL) (-274 541025 541802 541830 "E04UCFA" 541835 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 540207 540984 541012 "E04NAFA" 541017 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 539389 540166 540194 "E04MBFA" 540199 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 538571 539348 539376 "E04JAFA" 539381 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 537755 538530 538558 "E04GCFA" 538563 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 536939 537714 537742 "E04FDFA" 537747 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 536121 536898 536926 "E04DGFA" 536931 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 530294 531646 533010 "E04AGNT" 534777 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 528974 529480 529520 "DVARCAT" 529995 NIL DVARCAT (NIL T) -9 NIL 530194 NIL) (-265 528178 528390 528704 "DVARCAT-" 528709 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 521315 527977 528106 "DSMP" 528111 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 516097 517260 518328 "DROPT" 520267 T DROPT (NIL) -8 NIL NIL NIL) (-262 515762 515821 515919 "DROPT1" 516032 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 510877 512003 513140 "DROPT0" 514645 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 509222 509547 509933 "DRAWPT" 510511 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 503809 504732 505811 "DRAW" 508196 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 503442 503495 503613 "DRAWHACK" 503750 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 502173 502442 502733 "DRAWCX" 503171 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 501688 501757 501908 "DRAWCURV" 502099 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 492156 494118 496233 "DRAWCFUN" 499593 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 488922 490851 490892 "DQAGG" 491521 NIL DQAGG (NIL T) -9 NIL 491794 NIL) (-253 477046 483515 483598 "DPOLCAT" 485450 NIL DPOLCAT (NIL T T T T) -9 NIL 485995 NIL) (-252 471882 473231 475189 "DPOLCAT-" 475194 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 465004 471743 471841 "DPMO" 471846 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 458029 464784 464951 "DPMM" 464956 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 457602 457948 457996 "DOMCTOR" 458001 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456870 457124 457261 "DOMAIN" 457485 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450858 456505 456657 "DMP" 456771 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450458 450514 450658 "DLP" 450796 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444280 449785 449975 "DLIST" 450300 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 441077 443133 443174 "DLAGG" 443724 NIL DLAGG (NIL T) -9 NIL 443954 NIL) (-243 439753 440417 440445 "DIVRING" 440537 T DIVRING (NIL) -9 NIL 440620 NIL) (-242 438990 439180 439480 "DIVRING-" 439485 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437092 437449 437855 "DISPLAY" 438604 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430980 437006 437069 "DIRPROD" 437074 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429828 430031 430296 "DIRPROD2" 430773 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418603 424609 424662 "DIRPCAT" 425072 NIL DIRPCAT (NIL NIL T) -9 NIL 425912 NIL) (-237 415929 416571 417452 "DIRPCAT-" 417789 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415216 415376 415562 "DIOSP" 415763 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411871 414128 414169 "DIOPS" 414603 NIL DIOPS (NIL T) -9 NIL 414832 NIL) (-234 411420 411534 411725 "DIOPS-" 411730 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410243 410871 410899 "DIFRING" 411086 T DIFRING (NIL) -9 NIL 411196 NIL) (-232 409889 409966 410118 "DIFRING-" 410123 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407625 408897 408938 "DIFEXT" 409301 NIL DIFEXT (NIL T) -9 NIL 409595 NIL) (-230 405910 406338 407004 "DIFEXT-" 407009 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403185 405442 405483 "DIAGG" 405488 NIL DIAGG (NIL T) -9 NIL 405508 NIL) (-228 402569 402726 402978 "DIAGG-" 402983 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397986 401528 401805 "DHMATRIX" 402338 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393598 394507 395517 "DFSFUN" 396996 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388676 392529 392841 "DFLOAT" 393306 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386939 387220 387609 "DFINTTLS" 388384 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383968 384960 385360 "DERHAM" 386605 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381769 383743 383832 "DEQUEUE" 383912 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 381023 381156 381339 "DEGRED" 381631 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377453 378198 379044 "DEFINTRF" 380251 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 375008 375477 376069 "DEFINTEF" 376972 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374358 374628 374743 "DEFAST" 374913 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368362 373953 374102 "DECIMAL" 374229 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365873 366332 366838 "DDFACT" 367906 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365469 365512 365663 "DBLRESP" 365824 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363341 363702 364062 "DBASE" 365236 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362583 362821 362967 "DATAARY" 363240 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361689 362542 362570 "D03FAFA" 362575 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360796 361648 361676 "D03EEFA" 361681 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358746 359212 359701 "D03AGNT" 360327 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 358035 358705 358733 "D02EJFA" 358738 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357324 357994 358022 "D02CJFA" 358027 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356613 357283 357311 "D02BHFA" 357316 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355902 356572 356600 "D02BBFA" 356605 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349099 350688 352294 "D02AGNT" 354316 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346867 347390 347936 "D01WGTS" 348573 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345934 346826 346854 "D01TRNS" 346859 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 345002 345893 345921 "D01GBFA" 345926 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 344070 344961 344989 "D01FCFA" 344994 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343138 344029 344057 "D01ASFA" 344062 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342206 343097 343125 "D01AQFA" 343130 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341274 342165 342193 "D01APFA" 342198 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340342 341233 341261 "D01ANFA" 341266 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339410 340301 340329 "D01AMFA" 340334 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338478 339369 339397 "D01ALFA" 339402 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337546 338437 338465 "D01AKFA" 338470 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336614 337505 337533 "D01AJFA" 337538 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329909 331462 333023 "D01AGNT" 335073 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329246 329374 329526 "CYCLOTOM" 329777 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325981 326694 327421 "CYCLES" 328539 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325293 325427 325598 "CVMP" 325842 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323134 323392 323761 "CTRIGMNP" 325021 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322570 322928 323001 "CTOR" 323081 T CTOR (NIL) -8 NIL NIL NIL) (-186 322079 322301 322402 "CTORKIND" 322489 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321370 321686 321714 "CTORCAT" 321896 T CTORCAT (NIL) -9 NIL 322009 NIL) (-184 320968 321079 321238 "CTORCAT-" 321243 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320457 320671 320769 "CTORCALL" 320890 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319831 319930 320083 "CSTTOOLS" 320354 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315630 316287 317045 "CRFP" 319143 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315105 315351 315443 "CRCEAST" 315558 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314152 314337 314565 "CRAPACK" 314909 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313536 313637 313841 "CPMATCH" 314028 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313261 313289 313395 "CPIMA" 313502 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309609 310281 311000 "COORDSYS" 312596 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 309021 309142 309284 "CONTOUR" 309487 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304912 307024 307516 "CONTFRAC" 308561 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304792 304813 304841 "CONDUIT" 304878 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303880 304434 304462 "COMRING" 304467 T COMRING (NIL) -9 NIL 304519 NIL) (-171 302934 303238 303422 "COMPPROP" 303716 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302595 302630 302758 "COMPLPAT" 302893 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292886 302404 302513 "COMPLEX" 302518 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292522 292579 292686 "COMPLEX2" 292823 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292240 292275 292373 "COMPFACT" 292481 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276320 286314 286354 "COMPCAT" 287358 NIL COMPCAT (NIL T) -9 NIL 288706 NIL) (-165 265830 268759 272386 "COMPCAT-" 272742 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265559 265587 265690 "COMMUPC" 265796 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265353 265387 265446 "COMMONOP" 265520 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264909 265104 265191 "COMM" 265286 T COMM (NIL) -8 NIL NIL NIL) (-161 264485 264713 264788 "COMMAAST" 264854 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263734 263928 263956 "COMBOPC" 264294 T COMBOPC (NIL) -9 NIL 264469 NIL) (-159 262630 262840 263082 "COMBINAT" 263524 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 259087 259661 260288 "COMBF" 262052 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257845 258203 258438 "COLOR" 258872 T COLOR (NIL) -8 NIL NIL NIL) (-156 257321 257566 257658 "COLONAST" 257773 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256961 257008 257133 "CMPLXRT" 257268 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256409 256661 256760 "CLLCTAST" 256882 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251909 252939 254019 "CLIP" 255349 T CLIP (NIL) -7 NIL NIL NIL) (-152 250255 251015 251254 "CLIF" 251736 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246430 248401 248442 "CLAGG" 249371 NIL CLAGG (NIL T) -9 NIL 249907 NIL) (-150 244852 245309 245892 "CLAGG-" 245897 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244396 244481 244621 "CINTSLPE" 244761 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241897 242368 242916 "CHVAR" 243924 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 241071 241625 241653 "CHARZ" 241658 T CHARZ (NIL) -9 NIL 241673 NIL) (-146 240825 240865 240943 "CHARPOL" 241025 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239883 240470 240498 "CHARNZ" 240545 T CHARNZ (NIL) -9 NIL 240601 NIL) (-144 237845 238573 238908 "CHAR" 239568 T CHAR (NIL) -8 NIL NIL NIL) (-143 237571 237632 237660 "CFCAT" 237771 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236816 236927 237109 "CDEN" 237455 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232781 235969 236249 "CCLASS" 236556 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232088 232231 232394 "CATEGORY" 232638 T -10 (NIL) -8 NIL NIL NIL) (-139 231661 232007 232055 "CATCTOR" 232060 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231112 231364 231462 "CATAST" 231583 T CATAST (NIL) -8 NIL NIL NIL) (-137 230588 230833 230925 "CASEAST" 231040 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225597 226617 227370 "CARTEN" 229891 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224705 224853 225074 "CARTEN2" 225444 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 223020 223855 224112 "CARD" 224468 T CARD (NIL) -8 NIL NIL NIL) (-133 222596 222824 222899 "CAPSLAST" 222965 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222100 222308 222336 "CACHSET" 222468 T CACHSET (NIL) -9 NIL 222546 NIL) (-131 221570 221892 221920 "CABMON" 221970 T CABMON (NIL) -9 NIL 222026 NIL) (-130 221043 221274 221384 "BYTEORD" 221480 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 220019 220577 220719 "BYTE" 220882 T BYTE (NIL) -8 NIL NIL 221004) (-128 215369 219524 219696 "BYTEBUF" 219867 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212878 215061 215168 "BTREE" 215295 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210327 212526 212648 "BTOURN" 212788 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207697 209797 209838 "BTCAT" 209906 NIL BTCAT (NIL T) -9 NIL 209983 NIL) (-124 207364 207444 207593 "BTCAT-" 207598 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202629 206507 206535 "BTAGG" 206757 T BTAGG (NIL) -9 NIL 206918 NIL) (-122 202119 202244 202450 "BTAGG-" 202455 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199114 201397 201612 "BSTREE" 201936 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198252 198378 198562 "BRILL" 198970 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194904 196978 197019 "BRAGG" 197668 NIL BRAGG (NIL T) -9 NIL 197926 NIL) (-118 193433 193839 194394 "BRAGG-" 194399 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186662 192779 192963 "BPADICRT" 193281 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184977 186599 186644 "BPADIC" 186649 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184675 184705 184819 "BOUNDZRO" 184941 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179903 181101 182013 "BOP" 183783 T BOP (NIL) -8 NIL NIL NIL) (-113 177684 178088 178563 "BOP1" 179461 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176509 177258 177407 "BOOLEAN" 177555 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175788 176192 176246 "BMODULE" 176251 NIL BMODULE (NIL T T) -9 NIL 176316 NIL) (-110 171589 175586 175659 "BITS" 175735 T BITS (NIL) -8 NIL NIL NIL) (-109 171010 171129 171269 "BINDING" 171469 T BINDING (NIL) -8 NIL NIL NIL) (-108 165017 170607 170755 "BINARY" 170882 T BINARY (NIL) -8 NIL NIL NIL) (-107 162797 164272 164313 "BGAGG" 164573 NIL BGAGG (NIL T) -9 NIL 164710 NIL) (-106 162628 162660 162751 "BGAGG-" 162756 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161699 162012 162217 "BFUNCT" 162443 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160389 160567 160855 "BEZOUT" 161523 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156858 159241 159571 "BBTREE" 160092 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156592 156645 156673 "BASTYPE" 156792 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156444 156473 156546 "BASTYPE-" 156551 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155878 155954 156106 "BALFACT" 156355 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154734 155293 155479 "AUTOMOR" 155723 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154460 154465 154491 "ATTREG" 154496 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152712 153157 153509 "ATTRBUT" 154126 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152320 152540 152606 "ATTRAST" 152664 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151856 151969 151995 "ATRIG" 152196 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151665 151706 151793 "ATRIG-" 151798 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151310 151496 151522 "ASTCAT" 151527 T ASTCAT (NIL) -9 NIL 151557 NIL) (-92 151037 151096 151215 "ASTCAT-" 151220 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149186 150813 150901 "ASTACK" 150980 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147691 147988 148353 "ASSOCEQ" 148868 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146723 147350 147474 "ASP9" 147598 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146486 146671 146710 "ASP8" 146715 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145354 146091 146233 "ASP80" 146375 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144252 144989 145121 "ASP7" 145253 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143206 143929 144047 "ASP78" 144165 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142175 142886 143003 "ASP77" 143120 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141087 141813 141944 "ASP74" 142075 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139987 140722 140854 "ASP73" 140986 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139091 139813 139913 "ASP6" 139918 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 138035 138768 138886 "ASP55" 139004 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136984 137709 137828 "ASP50" 137947 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 136072 136685 136795 "ASP4" 136905 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135160 135773 135883 "ASP49" 135993 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133944 134699 134867 "ASP42" 135049 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132720 133477 133647 "ASP41" 133831 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131670 132397 132515 "ASP35" 132633 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131435 131618 131657 "ASP34" 131662 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131172 131239 131315 "ASP33" 131390 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 130065 130807 130939 "ASP31" 131071 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129830 130013 130052 "ASP30" 130057 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129565 129634 129710 "ASP29" 129785 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129330 129513 129552 "ASP28" 129557 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129095 129278 129317 "ASP27" 129322 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128179 128793 128904 "ASP24" 129015 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127255 127981 128093 "ASP20" 128098 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126343 126956 127066 "ASP1" 127176 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125285 126017 126136 "ASP19" 126255 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 125022 125089 125165 "ASP12" 125240 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123874 124621 124765 "ASP10" 124909 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121725 123718 123809 "ARRAY2" 123814 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117490 121373 121487 "ARRAY1" 121642 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116522 116695 116916 "ARRAY12" 117313 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110834 112752 112827 "ARR2CAT" 115457 NIL ARR2CAT (NIL T T T) -9 NIL 116215 NIL) (-56 108268 109012 109966 "ARR2CAT-" 109971 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107585 107895 108020 "ARITY" 108161 T ARITY (NIL) -8 NIL NIL NIL) (-54 106361 106513 106812 "APPRULE" 107421 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 106012 106060 106179 "APPLYORE" 106307 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104959 105277 105472 "ANY" 105835 T ANY (NIL) -8 NIL NIL NIL) (-51 104237 104360 104517 "ANY1" 104833 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101767 102674 103001 "ANTISYM" 103961 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101259 101474 101570 "ANON" 101689 T ANON (NIL) -8 NIL NIL NIL) (-48 95508 99798 100252 "AN" 100823 T AN (NIL) -8 NIL NIL NIL) (-47 91406 92794 92845 "AMR" 93593 NIL AMR (NIL T T) -9 NIL 94193 NIL) (-46 90518 90739 91102 "AMR-" 91107 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74957 90435 90496 "ALIST" 90501 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71759 74551 74720 "ALGSC" 74875 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68314 68869 69476 "ALGPKG" 71199 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67591 67692 67876 "ALGMFACT" 68200 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64149 64767 "ALGMANIP" 67151 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3219886 3219891 3219896 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3219871 3219876 3219881 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3219856 3219861 3219866 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3219841 3219846 3219851 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1290 3218984 3219716 3219793 "ZMOD" 3219798 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1289 3218094 3218258 3218467 "ZLINDEP" 3218816 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1288 3207394 3209162 3211134 "ZDSOLVE" 3216224 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1287 3206640 3206781 3206970 "YSTREAM" 3207240 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1286 3204414 3205941 3206145 "XRPOLY" 3206483 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1285 3200967 3202285 3202860 "XPR" 3203886 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1284 3198688 3200298 3200502 "XPOLY" 3200798 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1283 3196341 3197709 3197764 "XPOLYC" 3198052 NIL XPOLYC (NIL T T) -9 NIL 3198165 NIL) (-1282 3192716 3194858 3195246 "XPBWPOLY" 3195999 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1281 3188411 3190706 3190748 "XF" 3191369 NIL XF (NIL T) -9 NIL 3191769 NIL) (-1280 3188032 3188120 3188289 "XF-" 3188294 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1279 3183228 3184517 3184572 "XFALG" 3186744 NIL XFALG (NIL T T) -9 NIL 3187533 NIL) (-1278 3182361 3182465 3182670 "XEXPPKG" 3183120 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1277 3180470 3182211 3182307 "XDPOLY" 3182312 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1276 3179277 3179877 3179920 "XALG" 3179925 NIL XALG (NIL T) -9 NIL 3180036 NIL) (-1275 3172719 3177254 3177748 "WUTSET" 3178869 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1274 3170975 3171771 3172094 "WP" 3172530 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1273 3170577 3170797 3170867 "WHILEAST" 3170927 T WHILEAST (NIL) -8 NIL NIL NIL) (-1272 3170049 3170294 3170388 "WHEREAST" 3170505 T WHEREAST (NIL) -8 NIL NIL NIL) (-1271 3168935 3169133 3169428 "WFFINTBS" 3169846 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1270 3166839 3167266 3167728 "WEIER" 3168507 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1269 3165885 3166335 3166377 "VSPACE" 3166513 NIL VSPACE (NIL T) -9 NIL 3166587 NIL) (-1268 3165723 3165750 3165841 "VSPACE-" 3165846 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1267 3165531 3165574 3165642 "VOID" 3165677 T VOID (NIL) -8 NIL NIL NIL) (-1266 3163667 3164026 3164432 "VIEW" 3165147 T VIEW (NIL) -7 NIL NIL NIL) (-1265 3160091 3160730 3161467 "VIEWDEF" 3162952 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1264 3149395 3151639 3153812 "VIEW3D" 3157940 T VIEW3D (NIL) -8 NIL NIL NIL) (-1263 3141646 3143306 3144885 "VIEW2D" 3147838 T VIEW2D (NIL) -8 NIL NIL NIL) (-1262 3136998 3141416 3141508 "VECTOR" 3141589 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1261 3135575 3135834 3136152 "VECTOR2" 3136728 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1260 3129049 3133356 3133399 "VECTCAT" 3134394 NIL VECTCAT (NIL T) -9 NIL 3134981 NIL) (-1259 3128063 3128317 3128707 "VECTCAT-" 3128712 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1258 3127517 3127714 3127834 "VARIABLE" 3127978 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1257 3127450 3127455 3127485 "UTYPE" 3127490 T UTYPE (NIL) -9 NIL NIL NIL) (-1256 3126280 3126434 3126696 "UTSODETL" 3127276 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1255 3123720 3124180 3124704 "UTSODE" 3125821 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1254 3115557 3121346 3121835 "UTS" 3123289 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1253 3106431 3111798 3111841 "UTSCAT" 3112953 NIL UTSCAT (NIL T) -9 NIL 3113711 NIL) (-1252 3103778 3104501 3105490 "UTSCAT-" 3105495 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1251 3103405 3103448 3103581 "UTS2" 3103729 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3097631 3100243 3100286 "URAGG" 3102356 NIL URAGG (NIL T) -9 NIL 3103079 NIL) (-1249 3094570 3095433 3096556 "URAGG-" 3096561 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1248 3090280 3093205 3093670 "UPXSSING" 3094234 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1247 3082346 3089527 3089800 "UPXS" 3090065 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1246 3075419 3082250 3082322 "UPXSCONS" 3082327 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1245 3065164 3071957 3072019 "UPXSCCA" 3072593 NIL UPXSCCA (NIL T T) -9 NIL 3072826 NIL) (-1244 3064802 3064887 3065061 "UPXSCCA-" 3065066 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1243 3054399 3060965 3061008 "UPXSCAT" 3061656 NIL UPXSCAT (NIL T) -9 NIL 3062265 NIL) (-1242 3053829 3053908 3054087 "UPXS2" 3054314 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1241 3052483 3052736 3053087 "UPSQFREE" 3053572 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1240 3045904 3048961 3049016 "UPSCAT" 3050177 NIL UPSCAT (NIL T T) -9 NIL 3050951 NIL) (-1239 3045108 3045315 3045642 "UPSCAT-" 3045647 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1238 3030763 3038531 3038574 "UPOLYC" 3040675 NIL UPOLYC (NIL T) -9 NIL 3041896 NIL) (-1237 3022091 3024517 3027664 "UPOLYC-" 3027669 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1236 3021718 3021761 3021894 "UPOLYC2" 3022042 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1235 3013529 3021401 3021530 "UP" 3021637 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1234 3012868 3012975 3013139 "UPMP" 3013418 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1233 3012421 3012502 3012641 "UPDIVP" 3012781 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1232 3010989 3011238 3011554 "UPDECOMP" 3012170 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1231 3010224 3010336 3010521 "UPCDEN" 3010873 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1230 3009743 3009812 3009961 "UP2" 3010149 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1229 3008210 3008947 3009224 "UNISEG" 3009501 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1228 3007425 3007552 3007757 "UNISEG2" 3008053 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1227 3006485 3006665 3006891 "UNIFACT" 3007241 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1226 2990417 3005662 3005913 "ULS" 3006292 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1225 2978416 2990321 2990393 "ULSCONS" 2990398 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1224 2960435 2972420 2972482 "ULSCCAT" 2973120 NIL ULSCCAT (NIL T T) -9 NIL 2973408 NIL) (-1223 2959485 2959730 2960118 "ULSCCAT-" 2960123 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1222 2948859 2955339 2955382 "ULSCAT" 2956245 NIL ULSCAT (NIL T) -9 NIL 2956976 NIL) (-1221 2948289 2948368 2948547 "ULS2" 2948774 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1220 2947416 2947926 2948033 "UINT8" 2948144 T UINT8 (NIL) -8 NIL NIL 2948229) (-1219 2946542 2947052 2947159 "UINT64" 2947270 T UINT64 (NIL) -8 NIL NIL 2947355) (-1218 2945668 2946178 2946285 "UINT32" 2946396 T UINT32 (NIL) -8 NIL NIL 2946481) (-1217 2944794 2945304 2945411 "UINT16" 2945522 T UINT16 (NIL) -8 NIL NIL 2945607) (-1216 2943097 2944054 2944084 "UFD" 2944296 T UFD (NIL) -9 NIL 2944410 NIL) (-1215 2942891 2942937 2943032 "UFD-" 2943037 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1214 2941973 2942156 2942372 "UDVO" 2942697 T UDVO (NIL) -7 NIL NIL NIL) (-1213 2939789 2940198 2940669 "UDPO" 2941537 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1212 2939722 2939727 2939757 "TYPE" 2939762 T TYPE (NIL) -9 NIL NIL NIL) (-1211 2939482 2939677 2939708 "TYPEAST" 2939713 T TYPEAST (NIL) -8 NIL NIL NIL) (-1210 2938453 2938655 2938895 "TWOFACT" 2939276 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1209 2937476 2937862 2938097 "TUPLE" 2938253 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1208 2935167 2935686 2936225 "TUBETOOL" 2936959 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1207 2934016 2934221 2934462 "TUBE" 2934960 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1206 2928745 2932988 2933271 "TS" 2933768 NIL TS (NIL T) -8 NIL NIL NIL) (-1205 2917385 2921504 2921601 "TSETCAT" 2926870 NIL TSETCAT (NIL T T T T) -9 NIL 2928401 NIL) (-1204 2912117 2913717 2915608 "TSETCAT-" 2915613 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1203 2906756 2907603 2908532 "TRMANIP" 2911253 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1202 2906197 2906260 2906423 "TRIMAT" 2906688 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1201 2904063 2904300 2904657 "TRIGMNIP" 2905946 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1200 2903583 2903696 2903726 "TRIGCAT" 2903939 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1199 2903252 2903331 2903472 "TRIGCAT-" 2903477 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1198 2900097 2902110 2902391 "TREE" 2903006 NIL TREE (NIL T) -8 NIL NIL NIL) (-1197 2899371 2899899 2899929 "TRANFUN" 2899964 T TRANFUN (NIL) -9 NIL 2900030 NIL) (-1196 2898650 2898841 2899121 "TRANFUN-" 2899126 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1195 2898454 2898486 2898547 "TOPSP" 2898611 T TOPSP (NIL) -7 NIL NIL NIL) (-1194 2897802 2897917 2898071 "TOOLSIGN" 2898335 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1193 2896436 2896979 2897218 "TEXTFILE" 2897585 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1192 2894348 2894889 2895318 "TEX" 2896029 T TEX (NIL) -8 NIL NIL NIL) (-1191 2894129 2894160 2894232 "TEX1" 2894311 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1190 2893777 2893840 2893930 "TEMUTL" 2894061 T TEMUTL (NIL) -7 NIL NIL NIL) (-1189 2891931 2892211 2892536 "TBCMPPK" 2893500 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1188 2883708 2890091 2890147 "TBAGG" 2890547 NIL TBAGG (NIL T T) -9 NIL 2890758 NIL) (-1187 2878778 2880266 2882020 "TBAGG-" 2882025 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1186 2878162 2878269 2878414 "TANEXP" 2878667 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1185 2871552 2878019 2878112 "TABLE" 2878117 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1184 2870964 2871063 2871201 "TABLEAU" 2871449 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1183 2865572 2866792 2868040 "TABLBUMP" 2869750 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1182 2864794 2864941 2865122 "SYSTEM" 2865413 T SYSTEM (NIL) -8 NIL NIL NIL) (-1181 2861253 2861952 2862735 "SYSSOLP" 2864045 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1180 2860297 2860802 2860921 "SYSNNI" 2861107 NIL SYSNNI (NIL NIL) -8 NIL NIL 2861192) (-1179 2859604 2860063 2860142 "SYSINT" 2860202 NIL SYSINT (NIL NIL) -8 NIL NIL 2860247) (-1178 2855936 2856882 2857592 "SYNTAX" 2858916 T SYNTAX (NIL) -8 NIL NIL NIL) (-1177 2853094 2853696 2854328 "SYMTAB" 2855326 T SYMTAB (NIL) -8 NIL NIL NIL) (-1176 2848343 2849245 2850228 "SYMS" 2852133 T SYMS (NIL) -8 NIL NIL NIL) (-1175 2845578 2847801 2848031 "SYMPOLY" 2848148 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1174 2845095 2845170 2845293 "SYMFUNC" 2845490 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1173 2841114 2842407 2843220 "SYMBOL" 2844304 T SYMBOL (NIL) -8 NIL NIL NIL) (-1172 2834653 2836342 2838062 "SWITCH" 2839416 T SWITCH (NIL) -8 NIL NIL NIL) (-1171 2827887 2833474 2833777 "SUTS" 2834408 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1170 2819953 2827134 2827407 "SUPXS" 2827672 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2811713 2819571 2819697 "SUP" 2819862 NIL SUP (NIL T) -8 NIL NIL NIL) (-1168 2810872 2810999 2811216 "SUPFRACF" 2811581 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1167 2810493 2810552 2810665 "SUP2" 2810807 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1166 2808941 2809215 2809571 "SUMRF" 2810192 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1165 2808276 2808342 2808534 "SUMFS" 2808862 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1164 2792243 2807453 2807704 "SULS" 2808083 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1163 2791845 2792065 2792135 "SUCHTAST" 2792195 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1162 2791140 2791370 2791510 "SUCH" 2791753 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1161 2785006 2786046 2787005 "SUBSPACE" 2790228 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1160 2784436 2784526 2784690 "SUBRESP" 2784894 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1159 2777801 2779101 2780412 "STTF" 2783172 NIL STTF (NIL T) -7 NIL NIL NIL) (-1158 2771974 2773094 2774241 "STTFNC" 2776701 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1157 2763285 2765156 2766950 "STTAYLOR" 2770215 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1156 2756415 2763149 2763232 "STRTBL" 2763237 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1155 2751779 2756370 2756401 "STRING" 2756406 T STRING (NIL) -8 NIL NIL NIL) (-1154 2746640 2751152 2751182 "STRICAT" 2751241 T STRICAT (NIL) -9 NIL 2751303 NIL) (-1153 2739394 2744259 2744870 "STREAM" 2746064 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1152 2738904 2738981 2739125 "STREAM3" 2739311 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1151 2737886 2738069 2738304 "STREAM2" 2738717 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1150 2737574 2737626 2737719 "STREAM1" 2737828 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1149 2736590 2736771 2737002 "STINPROD" 2737390 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1148 2736142 2736352 2736382 "STEP" 2736462 T STEP (NIL) -9 NIL 2736540 NIL) (-1147 2729574 2736041 2736118 "STBL" 2736123 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1146 2724700 2728795 2728838 "STAGG" 2728991 NIL STAGG (NIL T) -9 NIL 2729080 NIL) (-1145 2722402 2723004 2723876 "STAGG-" 2723881 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1144 2720549 2722172 2722264 "STACK" 2722345 NIL STACK (NIL T) -8 NIL NIL NIL) (-1143 2713244 2718690 2719146 "SREGSET" 2720179 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1142 2705669 2707038 2708551 "SRDCMPK" 2711850 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1141 2698586 2703109 2703139 "SRAGG" 2704442 T SRAGG (NIL) -9 NIL 2705050 NIL) (-1140 2697603 2697858 2698237 "SRAGG-" 2698242 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1139 2692063 2696550 2696971 "SQMATRIX" 2697229 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1138 2685748 2688781 2689508 "SPLTREE" 2691408 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1137 2681711 2682404 2683050 "SPLNODE" 2685174 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1136 2680758 2680991 2681021 "SPFCAT" 2681465 T SPFCAT (NIL) -9 NIL NIL NIL) (-1135 2679495 2679705 2679969 "SPECOUT" 2680516 T SPECOUT (NIL) -7 NIL NIL NIL) (-1134 2671121 2672891 2672921 "SPADXPT" 2677313 T SPADXPT (NIL) -9 NIL 2679347 NIL) (-1133 2670882 2670922 2670991 "SPADPRSR" 2671074 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1132 2669037 2670837 2670868 "SPADAST" 2670873 T SPADAST (NIL) -8 NIL NIL NIL) (-1131 2660982 2662755 2662798 "SPACEC" 2667171 NIL SPACEC (NIL T) -9 NIL 2668987 NIL) (-1130 2659112 2660914 2660963 "SPACE3" 2660968 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1129 2657864 2658035 2658326 "SORTPAK" 2658917 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1128 2655956 2656259 2656671 "SOLVETRA" 2657528 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1127 2655006 2655228 2655489 "SOLVESER" 2655729 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1126 2650308 2651198 2652193 "SOLVERAD" 2654058 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1125 2646123 2646732 2647461 "SOLVEFOR" 2649675 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1124 2640393 2645472 2645569 "SNTSCAT" 2645574 NIL SNTSCAT (NIL T T T T) -9 NIL 2645644 NIL) (-1123 2634499 2638716 2639107 "SMTS" 2640083 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1122 2629183 2634387 2634464 "SMP" 2634469 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1121 2627342 2627643 2628041 "SMITH" 2628880 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1120 2620055 2624251 2624354 "SMATCAT" 2625705 NIL SMATCAT (NIL NIL T T T) -9 NIL 2626255 NIL) (-1119 2616995 2617818 2618996 "SMATCAT-" 2619001 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1118 2614661 2616231 2616274 "SKAGG" 2616535 NIL SKAGG (NIL T) -9 NIL 2616670 NIL) (-1117 2610972 2614077 2614272 "SINT" 2614459 T SINT (NIL) -8 NIL NIL 2614632) (-1116 2610744 2610782 2610848 "SIMPAN" 2610928 T SIMPAN (NIL) -7 NIL NIL NIL) (-1115 2610023 2610279 2610419 "SIG" 2610626 T SIG (NIL) -8 NIL NIL NIL) (-1114 2608861 2609082 2609357 "SIGNRF" 2609782 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1113 2607694 2607845 2608129 "SIGNEF" 2608690 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1112 2607000 2607277 2607401 "SIGAST" 2607592 T SIGAST (NIL) -8 NIL NIL NIL) (-1111 2604689 2605144 2605650 "SHP" 2606541 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1110 2598541 2604590 2604666 "SHDP" 2604671 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1109 2598114 2598306 2598336 "SGROUP" 2598429 T SGROUP (NIL) -9 NIL 2598491 NIL) (-1108 2597972 2597998 2598071 "SGROUP-" 2598076 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1107 2594807 2595505 2596228 "SGCF" 2597271 T SGCF (NIL) -7 NIL NIL NIL) (-1106 2589175 2594254 2594351 "SFRTCAT" 2594356 NIL SFRTCAT (NIL T T T T) -9 NIL 2594395 NIL) (-1105 2582596 2583614 2584750 "SFRGCD" 2588158 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1104 2575722 2576795 2577981 "SFQCMPK" 2581529 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1103 2575342 2575431 2575542 "SFORT" 2575663 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1102 2574460 2575182 2575303 "SEXOF" 2575308 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1101 2573567 2574341 2574409 "SEX" 2574414 T SEX (NIL) -8 NIL NIL NIL) (-1100 2569080 2569795 2569890 "SEXCAT" 2572827 NIL SEXCAT (NIL T T T T T) -9 NIL 2573405 NIL) (-1099 2566233 2569014 2569062 "SET" 2569067 NIL SET (NIL T) -8 NIL NIL NIL) (-1098 2564457 2564946 2565251 "SETMN" 2565974 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1097 2563953 2564105 2564135 "SETCAT" 2564311 T SETCAT (NIL) -9 NIL 2564421 NIL) (-1096 2563645 2563723 2563853 "SETCAT-" 2563858 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1095 2560006 2562106 2562149 "SETAGG" 2563019 NIL SETAGG (NIL T) -9 NIL 2563359 NIL) (-1094 2559464 2559580 2559817 "SETAGG-" 2559822 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1093 2558907 2559160 2559261 "SEQAST" 2559385 T SEQAST (NIL) -8 NIL NIL NIL) (-1092 2558106 2558400 2558461 "SEGXCAT" 2558747 NIL SEGXCAT (NIL T T) -9 NIL 2558867 NIL) (-1091 2557112 2557772 2557954 "SEG" 2557959 NIL SEG (NIL T) -8 NIL NIL NIL) (-1090 2556091 2556305 2556348 "SEGCAT" 2556870 NIL SEGCAT (NIL T) -9 NIL 2557091 NIL) (-1089 2555092 2555470 2555670 "SEGBIND" 2555926 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1088 2554713 2554772 2554885 "SEGBIND2" 2555027 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1087 2554286 2554514 2554591 "SEGAST" 2554658 T SEGAST (NIL) -8 NIL NIL NIL) (-1086 2553505 2553631 2553835 "SEG2" 2554130 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1085 2552915 2553440 2553487 "SDVAR" 2553492 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1084 2545442 2552685 2552815 "SDPOL" 2552820 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1083 2544035 2544301 2544620 "SCPKG" 2545157 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1082 2543199 2543371 2543563 "SCOPE" 2543865 T SCOPE (NIL) -8 NIL NIL NIL) (-1081 2542419 2542553 2542732 "SCACHE" 2543054 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1080 2542065 2542251 2542281 "SASTCAT" 2542286 T SASTCAT (NIL) -9 NIL 2542299 NIL) (-1079 2541552 2541900 2541976 "SAOS" 2542011 T SAOS (NIL) -8 NIL NIL NIL) (-1078 2541117 2541152 2541325 "SAERFFC" 2541511 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1077 2535056 2541014 2541094 "SAE" 2541099 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1076 2534649 2534684 2534843 "SAEFACT" 2535015 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1075 2532970 2533284 2533685 "RURPK" 2534315 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1074 2531607 2531913 2532218 "RULESET" 2532804 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1073 2528830 2529360 2529818 "RULE" 2531288 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1072 2528442 2528624 2528707 "RULECOLD" 2528782 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1071 2528232 2528260 2528331 "RTVALUE" 2528393 T RTVALUE (NIL) -8 NIL NIL NIL) (-1070 2527703 2527949 2528043 "RSTRCAST" 2528160 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1069 2522551 2523346 2524266 "RSETGCD" 2526902 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1068 2511781 2516860 2516957 "RSETCAT" 2521076 NIL RSETCAT (NIL T T T T) -9 NIL 2522173 NIL) (-1067 2509708 2510247 2511071 "RSETCAT-" 2511076 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1066 2502093 2503470 2504990 "RSDCMPK" 2508307 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500072 2500539 2500613 "RRCC" 2501699 NIL RRCC (NIL T T) -9 NIL 2502043 NIL) (-1064 2499423 2499597 2499876 "RRCC-" 2499881 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1063 2498866 2499119 2499220 "RPTAST" 2499344 T RPTAST (NIL) -8 NIL NIL NIL) (-1062 2472717 2482074 2482141 "RPOLCAT" 2492805 NIL RPOLCAT (NIL T T T) -9 NIL 2495964 NIL) (-1061 2464215 2466555 2469677 "RPOLCAT-" 2469682 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1060 2455146 2462426 2462908 "ROUTINE" 2463755 T ROUTINE (NIL) -8 NIL NIL NIL) (-1059 2451944 2454772 2454912 "ROMAN" 2455028 T ROMAN (NIL) -8 NIL NIL NIL) (-1058 2450188 2450804 2451064 "ROIRC" 2451749 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1057 2446420 2448704 2448734 "RNS" 2449038 T RNS (NIL) -9 NIL 2449312 NIL) (-1056 2444929 2445312 2445846 "RNS-" 2445921 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1055 2444332 2444740 2444770 "RNG" 2444775 T RNG (NIL) -9 NIL 2444796 NIL) (-1054 2443731 2444119 2444162 "RMODULE" 2444167 NIL RMODULE (NIL T) -9 NIL 2444194 NIL) (-1053 2442567 2442661 2442997 "RMCAT2" 2443632 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1052 2439417 2441913 2442210 "RMATRIX" 2442329 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1051 2432244 2434504 2434619 "RMATCAT" 2437978 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2438960 NIL) (-1050 2431619 2431766 2432073 "RMATCAT-" 2432078 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1049 2431020 2431241 2431284 "RLINSET" 2431478 NIL RLINSET (NIL T) -9 NIL 2431569 NIL) (-1048 2430587 2430662 2430790 "RINTERP" 2430939 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1047 2429645 2430199 2430229 "RING" 2430285 T RING (NIL) -9 NIL 2430377 NIL) (-1046 2429437 2429481 2429578 "RING-" 2429583 NIL RING- (NIL T) -8 NIL NIL NIL) (-1045 2428278 2428515 2428773 "RIDIST" 2429201 T RIDIST (NIL) -7 NIL NIL NIL) (-1044 2419567 2427746 2427952 "RGCHAIN" 2428126 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1043 2418917 2419323 2419364 "RGBCSPC" 2419422 NIL RGBCSPC (NIL T) -9 NIL 2419474 NIL) (-1042 2418075 2418456 2418497 "RGBCMDL" 2418729 NIL RGBCMDL (NIL T) -9 NIL 2418843 NIL) (-1041 2415069 2415683 2416353 "RF" 2417439 NIL RF (NIL T) -7 NIL NIL NIL) (-1040 2414715 2414778 2414881 "RFFACTOR" 2415000 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1039 2414440 2414475 2414572 "RFFACT" 2414674 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1038 2412557 2412921 2413303 "RFDIST" 2414080 T RFDIST (NIL) -7 NIL NIL NIL) (-1037 2412010 2412102 2412265 "RETSOL" 2412459 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1036 2411646 2411726 2411769 "RETRACT" 2411902 NIL RETRACT (NIL T) -9 NIL 2411989 NIL) (-1035 2411495 2411520 2411607 "RETRACT-" 2411612 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1034 2411097 2411317 2411387 "RETAST" 2411447 T RETAST (NIL) -8 NIL NIL NIL) (-1033 2403835 2410750 2410877 "RESULT" 2410992 T RESULT (NIL) -8 NIL NIL NIL) (-1032 2402426 2403104 2403303 "RESRING" 2403738 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1031 2402062 2402111 2402209 "RESLATC" 2402363 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1030 2401767 2401802 2401909 "REPSQ" 2402021 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1029 2399189 2399769 2400371 "REP" 2401187 T REP (NIL) -7 NIL NIL NIL) (-1028 2398886 2398921 2399032 "REPDB" 2399148 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1027 2392786 2394175 2395398 "REP2" 2397698 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1026 2389163 2389844 2390652 "REP1" 2392013 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1025 2381859 2387304 2387760 "REGSET" 2388793 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1024 2380624 2381007 2381257 "REF" 2381644 NIL REF (NIL T) -8 NIL NIL NIL) (-1023 2380001 2380104 2380271 "REDORDER" 2380508 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1022 2375969 2379214 2379441 "RECLOS" 2379829 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1021 2375021 2375202 2375417 "REALSOLV" 2375776 T REALSOLV (NIL) -7 NIL NIL NIL) (-1020 2374867 2374908 2374938 "REAL" 2374943 T REAL (NIL) -9 NIL 2374978 NIL) (-1019 2371350 2372152 2373036 "REAL0Q" 2374032 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1018 2366951 2367939 2369000 "REAL0" 2370331 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1017 2366422 2366668 2366762 "RDUCEAST" 2366879 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1016 2365827 2365899 2366106 "RDIV" 2366344 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1015 2364895 2365069 2365282 "RDIST" 2365649 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1014 2363492 2363779 2364151 "RDETRS" 2364603 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1013 2361304 2361758 2362296 "RDETR" 2363034 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1012 2359929 2360207 2360604 "RDEEFS" 2361020 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1011 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NIL) (-999 2328556 2328604 2328702 "RADCAT-" 2328707 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-998 2326659 2328331 2328420 "QUEUE" 2328500 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-997 2323200 2326596 2326641 "QUAT" 2326646 NIL QUAT (NIL T) -8 NIL NIL NIL) (-996 2322838 2322881 2323008 "QUATCT2" 2323151 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-995 2316300 2319645 2319685 "QUATCAT" 2320465 NIL QUATCAT (NIL T) -9 NIL 2321231 NIL) (-994 2312444 2313481 2314868 "QUATCAT-" 2314962 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-993 2309917 2311528 2311569 "QUAGG" 2311944 NIL QUAGG (NIL T) -9 NIL 2312119 NIL) (-992 2309522 2309742 2309810 "QQUTAST" 2309869 T QQUTAST (NIL) -8 NIL NIL NIL) (-991 2308420 2308920 2309092 "QFORM" 2309394 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-990 2299425 2304664 2304704 "QFCAT" 2305362 NIL QFCAT (NIL T) -9 NIL 2306363 NIL) (-989 2294997 2296198 2297789 "QFCAT-" 2297883 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-988 2294635 2294678 2294805 "QFCAT2" 2294948 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294095 2294205 2294335 "QEQUAT" 2294525 T QEQUAT (NIL) -8 NIL NIL NIL) (-986 2287242 2288314 2289498 "QCMPACK" 2293028 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-985 2284791 2285239 2285667 "QALGSET" 2286897 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-984 2284036 2284210 2284442 "QALGSET2" 2284611 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-983 2282726 2282950 2283267 "PWFFINTB" 2283809 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-982 2280908 2281076 2281430 "PUSHVAR" 2282540 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-981 2276826 2277880 2277921 "PTRANFN" 2279805 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-980 2275228 2275519 2275841 "PTPACK" 2276537 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-979 2274860 2274917 2275026 "PTFUNC2" 2275165 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-978 2269337 2273732 2273773 "PTCAT" 2274069 NIL PTCAT (NIL T) -9 NIL 2274222 NIL) (-977 2268995 2269030 2269154 "PSQFR" 2269296 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-976 2267590 2267888 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1997388 1997500 1997657 "OUTBCON-" 1997662 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-856 1996768 1997117 1997206 "OSI" 1997319 T OSI (NIL) -8 NIL NIL NIL) (-855 1996298 1996636 1996664 "OSGROUP" 1996669 T OSGROUP (NIL) -9 NIL 1996691 NIL) (-854 1995043 1995270 1995555 "ORTHPOL" 1996045 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-853 1992594 1994878 1994999 "OREUP" 1995004 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-852 1989997 1992285 1992412 "ORESUP" 1992536 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-851 1987525 1988025 1988586 "OREPCTO" 1989486 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-850 1981211 1983412 1983453 "OREPCAT" 1985801 NIL OREPCAT (NIL T) -9 NIL 1986905 NIL) (-849 1978358 1979140 1980198 "OREPCAT-" 1980203 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-848 1977509 1977807 1977835 "ORDSET" 1978144 T ORDSET (NIL) -9 NIL 1978308 NIL) (-847 1976940 1977088 1977312 "ORDSET-" 1977317 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-846 1975505 1976296 1976324 "ORDRING" 1976526 T ORDRING (NIL) -9 NIL 1976651 NIL) (-845 1975150 1975244 1975388 "ORDRING-" 1975393 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-844 1974530 1974993 1975021 "ORDMON" 1975026 T ORDMON (NIL) -9 NIL 1975047 NIL) (-843 1973692 1973839 1974034 "ORDFUNS" 1974379 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-842 1973030 1973449 1973477 "ORDFIN" 1973542 T ORDFIN (NIL) -9 NIL 1973616 NIL) (-841 1969589 1971616 1972025 "ORDCOMP" 1972654 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-840 1968855 1968982 1969168 "ORDCOMP2" 1969449 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1965436 1966346 1967160 "OPTPROB" 1968061 T OPTPROB (NIL) -8 NIL NIL NIL) (-838 1962238 1962877 1963581 "OPTPACK" 1964752 T OPTPACK (NIL) -7 NIL NIL NIL) (-837 1959925 1960691 1960719 "OPTCAT" 1961538 T OPTCAT (NIL) -9 NIL 1962188 NIL) (-836 1959309 1959602 1959707 "OPSIG" 1959840 T OPSIG (NIL) -8 NIL NIL NIL) (-835 1959077 1959116 1959182 "OPQUERY" 1959263 T OPQUERY (NIL) -7 NIL NIL NIL) (-834 1956208 1957388 1957892 "OP" 1958606 NIL OP (NIL T) -8 NIL NIL NIL) (-833 1955582 1955808 1955849 "OPERCAT" 1956061 NIL OPERCAT (NIL T) -9 NIL 1956158 NIL) (-832 1955337 1955393 1955510 "OPERCAT-" 1955515 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-831 1952150 1954134 1954503 "ONECOMP" 1955001 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-830 1951455 1951570 1951744 "ONECOMP2" 1952022 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-829 1950874 1950980 1951110 "OMSERVER" 1951345 T OMSERVER (NIL) -7 NIL NIL NIL) (-828 1947736 1950314 1950354 "OMSAGG" 1950415 NIL OMSAGG (NIL T) -9 NIL 1950479 NIL) (-827 1946359 1946622 1946904 "OMPKG" 1947474 T OMPKG (NIL) -7 NIL NIL NIL) (-826 1945789 1945892 1945920 "OM" 1946219 T OM (NIL) -9 NIL NIL NIL) (-825 1944336 1945338 1945507 "OMLO" 1945670 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-824 1943296 1943443 1943663 "OMEXPR" 1944162 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-823 1942587 1942842 1942978 "OMERR" 1943180 T OMERR (NIL) -8 NIL NIL NIL) (-822 1941738 1942008 1942168 "OMERRK" 1942447 T OMERRK (NIL) -8 NIL NIL NIL) (-821 1941189 1941415 1941523 "OMENC" 1941650 T OMENC (NIL) -8 NIL NIL NIL) (-820 1935084 1936269 1937440 "OMDEV" 1940038 T OMDEV (NIL) -8 NIL NIL NIL) (-819 1934153 1934324 1934518 "OMCONN" 1934910 T OMCONN (NIL) -8 NIL NIL NIL) (-818 1932674 1933650 1933678 "OINTDOM" 1933683 T OINTDOM (NIL) -9 NIL 1933704 NIL) (-817 1928453 1929664 1930380 "OFMONOID" 1931990 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-816 1927864 1928390 1928435 "ODVAR" 1928440 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-815 1925287 1927609 1927764 "ODR" 1927769 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-814 1917868 1925063 1925189 "ODPOL" 1925194 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-813 1911690 1917740 1917845 "ODP" 1917850 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-812 1910456 1910671 1910946 "ODETOOLS" 1911464 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-811 1907423 1908081 1908797 "ODESYS" 1909789 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-810 1902305 1903213 1904238 "ODERTRIC" 1906498 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-809 1901731 1901813 1902007 "ODERED" 1902217 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-808 1898619 1899167 1899844 "ODERAT" 1901154 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-807 1895576 1896043 1896640 "ODEPRRIC" 1898148 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-806 1893519 1894115 1894601 "ODEPROB" 1895110 T ODEPROB (NIL) -8 NIL NIL NIL) (-805 1890039 1890524 1891171 "ODEPRIM" 1892998 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-804 1889288 1889390 1889650 "ODEPAL" 1889931 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-803 1885450 1886241 1887105 "ODEPACK" 1888444 T ODEPACK (NIL) -7 NIL NIL NIL) (-802 1884511 1884618 1884840 "ODEINT" 1885339 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-801 1878612 1880037 1881484 "ODEIFTBL" 1883084 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-800 1874010 1874796 1875748 "ODEEF" 1877771 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-799 1873359 1873448 1873671 "ODECONST" 1873915 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-798 1871484 1872145 1872173 "ODECAT" 1872778 T ODECAT (NIL) -9 NIL 1873309 NIL) (-797 1868356 1871196 1871315 "OCT" 1871397 NIL OCT (NIL T) -8 NIL NIL NIL) (-796 1867994 1868037 1868164 "OCTCT2" 1868307 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-795 1862643 1865078 1865118 "OC" 1866215 NIL OC (NIL T) -9 NIL 1867073 NIL) (-794 1859870 1860618 1861608 "OC-" 1861702 NIL OC- (NIL T T) -8 NIL NIL NIL) (-793 1859222 1859690 1859718 "OCAMON" 1859723 T OCAMON (NIL) -9 NIL 1859744 NIL) (-792 1858753 1859094 1859122 "OASGP" 1859127 T OASGP (NIL) -9 NIL 1859147 NIL) (-791 1858014 1858503 1858531 "OAMONS" 1858571 T OAMONS (NIL) -9 NIL 1858614 NIL) (-790 1857428 1857861 1857889 "OAMON" 1857894 T OAMON (NIL) -9 NIL 1857914 NIL) (-789 1856686 1857204 1857232 "OAGROUP" 1857237 T OAGROUP (NIL) -9 NIL 1857257 NIL) (-788 1856376 1856426 1856514 "NUMTUBE" 1856630 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-787 1849949 1851467 1853003 "NUMQUAD" 1854860 T NUMQUAD (NIL) -7 NIL NIL NIL) (-786 1845705 1846693 1847718 "NUMODE" 1848944 T NUMODE (NIL) -7 NIL NIL NIL) (-785 1843060 1843940 1843968 "NUMINT" 1844891 T NUMINT (NIL) -9 NIL 1845655 NIL) (-784 1842008 1842205 1842423 "NUMFMT" 1842862 T NUMFMT (NIL) -7 NIL NIL NIL) (-783 1828367 1831312 1833844 "NUMERIC" 1839515 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-782 1822737 1827816 1827911 "NTSCAT" 1827916 NIL NTSCAT (NIL T T T T) -9 NIL 1827955 NIL) (-781 1821931 1822096 1822289 "NTPOLFN" 1822576 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-780 1810008 1818756 1819568 "NSUP" 1821152 NIL NSUP (NIL T) -8 NIL NIL NIL) (-779 1809640 1809697 1809806 "NSUP2" 1809945 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-778 1799868 1809414 1809547 "NSMP" 1809552 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-777 1798300 1798601 1798958 "NREP" 1799556 NIL NREP (NIL T) -7 NIL NIL NIL) (-776 1796891 1797143 1797501 "NPCOEF" 1798043 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-775 1795957 1796072 1796288 "NORMRETR" 1796772 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-774 1793998 1794288 1794697 "NORMPK" 1795665 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-773 1793683 1793711 1793835 "NORMMA" 1793964 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-772 1793483 1793640 1793669 "NONE" 1793674 T NONE (NIL) -8 NIL NIL NIL) (-771 1793272 1793301 1793370 "NONE1" 1793447 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-770 1792769 1792831 1793010 "NODE1" 1793204 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-769 1791049 1791900 1792155 "NNI" 1792502 T NNI (NIL) -8 NIL NIL 1792737) (-768 1789469 1789782 1790146 "NLINSOL" 1790717 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-767 1785710 1786705 1787604 "NIPROB" 1788590 T NIPROB (NIL) -8 NIL NIL NIL) (-766 1784467 1784701 1785003 "NFINTBAS" 1785472 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-765 1783641 1784117 1784158 "NETCLT" 1784330 NIL NETCLT (NIL T) -9 NIL 1784412 NIL) (-764 1782349 1782580 1782861 "NCODIV" 1783409 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-763 1782111 1782148 1782223 "NCNTFRAC" 1782306 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-762 1780291 1780655 1781075 "NCEP" 1781736 NIL NCEP (NIL T) -7 NIL NIL NIL) (-761 1779142 1779915 1779943 "NASRING" 1780053 T NASRING (NIL) -9 NIL 1780133 NIL) (-760 1778937 1778981 1779075 "NASRING-" 1779080 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-759 1778044 1778569 1778597 "NARNG" 1778714 T NARNG (NIL) -9 NIL 1778805 NIL) (-758 1777736 1777803 1777937 "NARNG-" 1777942 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-757 1776615 1776822 1777057 "NAGSP" 1777521 T NAGSP (NIL) -7 NIL NIL NIL) (-756 1767887 1769571 1771244 "NAGS" 1774962 T NAGS (NIL) -7 NIL NIL NIL) (-755 1766435 1766743 1767074 "NAGF07" 1767576 T NAGF07 (NIL) -7 NIL NIL NIL) (-754 1760973 1762264 1763571 "NAGF04" 1765148 T NAGF04 (NIL) -7 NIL NIL NIL) (-753 1753941 1755555 1757188 "NAGF02" 1759360 T NAGF02 (NIL) -7 NIL NIL NIL) (-752 1749165 1750265 1751382 "NAGF01" 1752844 T NAGF01 (NIL) -7 NIL NIL NIL) (-751 1742793 1744359 1745944 "NAGE04" 1747600 T NAGE04 (NIL) -7 NIL NIL NIL) (-750 1733962 1736083 1738213 "NAGE02" 1740683 T NAGE02 (NIL) -7 NIL NIL NIL) (-749 1729915 1730862 1731826 "NAGE01" 1733018 T NAGE01 (NIL) -7 NIL NIL NIL) (-748 1727710 1728244 1728802 "NAGD03" 1729377 T NAGD03 (NIL) -7 NIL NIL NIL) (-747 1719460 1721388 1723342 "NAGD02" 1725776 T NAGD02 (NIL) -7 NIL NIL NIL) (-746 1713271 1714696 1716136 "NAGD01" 1718040 T NAGD01 (NIL) -7 NIL NIL NIL) (-745 1709480 1710302 1711139 "NAGC06" 1712454 T NAGC06 (NIL) -7 NIL NIL NIL) (-744 1707945 1708277 1708633 "NAGC05" 1709144 T NAGC05 (NIL) -7 NIL NIL NIL) (-743 1707321 1707440 1707584 "NAGC02" 1707821 T NAGC02 (NIL) -7 NIL NIL NIL) (-742 1706280 1706863 1706903 "NAALG" 1706982 NIL NAALG (NIL T) -9 NIL 1707043 NIL) (-741 1706115 1706144 1706234 "NAALG-" 1706239 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-740 1700065 1701173 1702360 "MULTSQFR" 1705011 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-739 1699384 1699459 1699643 "MULTFACT" 1699977 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-738 1692108 1696021 1696074 "MTSCAT" 1697144 NIL MTSCAT (NIL T T) -9 NIL 1697659 NIL) (-737 1691820 1691874 1691966 "MTHING" 1692048 NIL MTHING (NIL T) -7 NIL NIL NIL) (-736 1691612 1691645 1691705 "MSYSCMD" 1691780 T MSYSCMD (NIL) -7 NIL NIL NIL) (-735 1687694 1690367 1690687 "MSET" 1691325 NIL MSET (NIL T) -8 NIL NIL NIL) (-734 1684763 1687255 1687296 "MSETAGG" 1687301 NIL MSETAGG (NIL T) -9 NIL 1687335 NIL) (-733 1680604 1682142 1682887 "MRING" 1684063 NIL MRING (NIL T T) -8 NIL NIL NIL) (-732 1680170 1680237 1680368 "MRF2" 1680531 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-731 1679788 1679823 1679967 "MRATFAC" 1680129 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-730 1677400 1677695 1678126 "MPRFF" 1679493 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-729 1671697 1677254 1677351 "MPOLY" 1677356 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-728 1671187 1671222 1671430 "MPCPF" 1671656 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-727 1670701 1670744 1670928 "MPC3" 1671138 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-726 1669896 1669977 1670198 "MPC2" 1670616 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1668197 1668534 1668924 "MONOTOOL" 1669556 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-724 1667422 1667739 1667767 "MONOID" 1667986 T MONOID (NIL) -9 NIL 1668133 NIL) (-723 1666968 1667087 1667268 "MONOID-" 1667273 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-722 1657443 1663394 1663453 "MONOGEN" 1664127 NIL MONOGEN (NIL T T) -9 NIL 1664583 NIL) (-721 1654661 1655396 1656396 "MONOGEN-" 1656515 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-720 1653494 1653940 1653968 "MONADWU" 1654360 T MONADWU (NIL) -9 NIL 1654598 NIL) (-719 1652866 1653025 1653273 "MONADWU-" 1653278 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-718 1652225 1652469 1652497 "MONAD" 1652704 T MONAD (NIL) -9 NIL 1652816 NIL) (-717 1651910 1651988 1652120 "MONAD-" 1652125 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-716 1650199 1650823 1651102 "MOEBIUS" 1651663 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-715 1649477 1649881 1649921 "MODULE" 1649926 NIL MODULE (NIL T) -9 NIL 1649965 NIL) (-714 1649045 1649141 1649331 "MODULE-" 1649336 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-713 1646725 1647409 1647736 "MODRING" 1648869 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-712 1643669 1644830 1645351 "MODOP" 1646254 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-711 1642257 1642736 1643013 "MODMONOM" 1643532 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-710 1632298 1640548 1640962 "MODMON" 1641894 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-709 1629454 1631142 1631418 "MODFIELD" 1632173 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1628431 1628735 1628925 "MMLFORM" 1629284 T MMLFORM (NIL) -8 NIL NIL NIL) (-707 1627957 1628000 1628179 "MMAP" 1628382 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-706 1626036 1626803 1626844 "MLO" 1627267 NIL MLO (NIL T) -9 NIL 1627509 NIL) (-705 1623402 1623918 1624520 "MLIFT" 1625517 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-704 1622793 1622877 1623031 "MKUCFUNC" 1623313 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-703 1622392 1622462 1622585 "MKRECORD" 1622716 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-702 1621439 1621601 1621829 "MKFUNC" 1622203 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-701 1620827 1620931 1621087 "MKFLCFN" 1621322 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-700 1620104 1620206 1620391 "MKBCFUNC" 1620720 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-699 1616811 1619658 1619794 "MINT" 1619988 T MINT (NIL) -8 NIL NIL NIL) (-698 1615623 1615866 1616143 "MHROWRED" 1616566 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-697 1611003 1614158 1614563 "MFLOAT" 1615238 T MFLOAT (NIL) -8 NIL NIL NIL) (-696 1610360 1610436 1610607 "MFINFACT" 1610915 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-695 1606675 1607523 1608407 "MESH" 1609496 T MESH (NIL) -7 NIL NIL NIL) (-694 1605065 1605377 1605730 "MDDFACT" 1606362 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-693 1601860 1604224 1604265 "MDAGG" 1604520 NIL MDAGG (NIL T) -9 NIL 1604663 NIL) (-692 1591600 1601153 1601360 "MCMPLX" 1601673 T MCMPLX (NIL) -8 NIL NIL NIL) (-691 1590741 1590887 1591087 "MCDEN" 1591449 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-690 1588631 1588901 1589281 "MCALCFN" 1590471 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-689 1587556 1587796 1588029 "MAYBE" 1588437 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-688 1585168 1585691 1586253 "MATSTOR" 1587027 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-687 1581125 1584540 1584788 "MATRIX" 1584953 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-686 1576889 1577598 1578334 "MATLIN" 1580482 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-685 1566995 1570181 1570258 "MATCAT" 1575138 NIL MATCAT (NIL T T T) -9 NIL 1576555 NIL) (-684 1563351 1564372 1565728 "MATCAT-" 1565733 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-683 1561945 1562098 1562431 "MATCAT2" 1563186 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-682 1560057 1560381 1560765 "MAPPKG3" 1561620 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-681 1559038 1559211 1559433 "MAPPKG2" 1559881 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-680 1557537 1557821 1558148 "MAPPKG1" 1558744 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-679 1556616 1556943 1557120 "MAPPAST" 1557380 T MAPPAST (NIL) -8 NIL NIL NIL) (-678 1556227 1556285 1556408 "MAPHACK3" 1556552 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-677 1555819 1555880 1555994 "MAPHACK2" 1556159 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-676 1555256 1555360 1555502 "MAPHACK1" 1555710 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-675 1553335 1553956 1554260 "MAGMA" 1554984 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-674 1552814 1553059 1553150 "MACROAST" 1553264 T MACROAST (NIL) -8 NIL NIL NIL) (-673 1549232 1551053 1551514 "M3D" 1552386 NIL M3D (NIL T) -8 NIL NIL NIL) (-672 1543338 1547601 1547642 "LZSTAGG" 1548424 NIL LZSTAGG (NIL T) -9 NIL 1548719 NIL) (-671 1539295 1540469 1541926 "LZSTAGG-" 1541931 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-670 1536382 1537186 1537673 "LWORD" 1538840 NIL LWORD (NIL T) -8 NIL NIL NIL) (-669 1535958 1536186 1536261 "LSTAST" 1536327 T LSTAST (NIL) -8 NIL NIL NIL) (-668 1529124 1535729 1535863 "LSQM" 1535868 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-667 1528348 1528487 1528715 "LSPP" 1528979 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-666 1526160 1526461 1526917 "LSMP" 1528037 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-665 1522939 1523613 1524343 "LSMP1" 1525462 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-664 1516816 1522106 1522147 "LSAGG" 1522209 NIL LSAGG (NIL T) -9 NIL 1522287 NIL) (-663 1513511 1514435 1515648 "LSAGG-" 1515653 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-662 1511110 1512655 1512904 "LPOLY" 1513306 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-661 1510692 1510777 1510900 "LPEFRAC" 1511019 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-660 1509013 1509786 1510039 "LO" 1510524 NIL LO (NIL T T T) -8 NIL NIL NIL) (-659 1508665 1508777 1508805 "LOGIC" 1508916 T LOGIC (NIL) -9 NIL 1508997 NIL) (-658 1508527 1508550 1508621 "LOGIC-" 1508626 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-657 1507720 1507860 1508053 "LODOOPS" 1508383 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-656 1505143 1507636 1507702 "LODO" 1507707 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-655 1503681 1503916 1504269 "LODOF" 1504890 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-654 1499899 1502330 1502371 "LODOCAT" 1502809 NIL LODOCAT (NIL T) -9 NIL 1503020 NIL) (-653 1499632 1499690 1499817 "LODOCAT-" 1499822 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-652 1496952 1499473 1499591 "LODO2" 1499596 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-651 1494387 1496889 1496934 "LODO1" 1496939 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-650 1493268 1493433 1493738 "LODEEF" 1494210 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-649 1488507 1491398 1491439 "LNAGG" 1492386 NIL LNAGG (NIL T) -9 NIL 1492830 NIL) (-648 1487654 1487868 1488210 "LNAGG-" 1488215 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-647 1483790 1484579 1485218 "LMOPS" 1487069 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-646 1483193 1483581 1483622 "LMODULE" 1483627 NIL LMODULE (NIL T) -9 NIL 1483653 NIL) (-645 1480391 1482838 1482961 "LMDICT" 1483103 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-644 1479797 1480018 1480059 "LLINSET" 1480250 NIL LLINSET (NIL T) -9 NIL 1480341 NIL) (-643 1479496 1479705 1479765 "LITERAL" 1479770 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-642 1472679 1478442 1478740 "LIST" 1479231 NIL LIST (NIL T) -8 NIL NIL NIL) (-641 1472204 1472278 1472417 "LIST3" 1472599 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-640 1471211 1471389 1471617 "LIST2" 1472022 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-639 1469345 1469657 1470056 "LIST2MAP" 1470858 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-638 1468941 1469178 1469219 "LINSET" 1469224 NIL LINSET (NIL T) -9 NIL 1469258 NIL) (-637 1467602 1468272 1468313 "LINEXP" 1468568 NIL LINEXP (NIL T) -9 NIL 1468717 NIL) (-636 1466249 1466509 1466806 "LINDEP" 1467354 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1463016 1463735 1464512 "LIMITRF" 1465504 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1461319 1461615 1462024 "LIMITPS" 1462711 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1455747 1460830 1461058 "LIE" 1461140 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1454695 1455164 1455204 "LIECAT" 1455344 NIL LIECAT (NIL T) -9 NIL 1455495 NIL) (-631 1454536 1454563 1454651 "LIECAT-" 1454656 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1447032 1453985 1454150 "LIB" 1454391 T LIB (NIL) -8 NIL NIL NIL) (-629 1442667 1443550 1444485 "LGROBP" 1446149 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1440665 1440939 1441289 "LF" 1442388 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1439505 1440197 1440225 "LFCAT" 1440432 T LFCAT (NIL) -9 NIL 1440571 NIL) (-626 1436407 1437037 1437725 "LEXTRIPK" 1438869 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1433151 1433977 1434480 "LEXP" 1435987 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1432627 1432872 1432964 "LETAST" 1433079 T LETAST (NIL) -8 NIL NIL NIL) (-623 1431025 1431338 1431739 "LEADCDET" 1432309 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1430215 1430289 1430518 "LAZM3PK" 1430946 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1425132 1428292 1428830 "LAUPOL" 1429727 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1424711 1424755 1424916 "LAPLACE" 1425082 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1422650 1423812 1424063 "LA" 1424544 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1421644 1422228 1422269 "LALG" 1422331 NIL LALG (NIL T) -9 NIL 1422390 NIL) (-617 1421358 1421417 1421553 "LALG-" 1421558 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1421193 1421217 1421258 "KVTFROM" 1421320 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1420116 1420560 1420745 "KTVLOGIC" 1421028 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1419951 1419975 1420016 "KRCFROM" 1420078 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1418855 1419042 1419341 "KOVACIC" 1419751 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1418690 1418714 1418755 "KONVERT" 1418817 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1418525 1418549 1418590 "KOERCE" 1418652 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1416207 1416995 1417396 "KERNEL" 1418157 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1415703 1415784 1415916 "KERNEL2" 1416121 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1409473 1414242 1414296 "KDAGG" 1414673 NIL KDAGG (NIL T T) -9 NIL 1414879 NIL) (-607 1409002 1409126 1409331 "KDAGG-" 1409336 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1402150 1408663 1408818 "KAFILE" 1408880 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1396578 1401661 1401889 "JORDAN" 1401971 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1395957 1396227 1396348 "JOINAST" 1396477 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1395803 1395862 1395917 "JAVACODE" 1395922 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1392055 1394008 1394062 "IXAGG" 1394991 NIL IXAGG (NIL T T) -9 NIL 1395450 NIL) (-601 1390974 1391280 1391699 "IXAGG-" 1391704 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386504 1390896 1390955 "IVECTOR" 1390960 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1385270 1385507 1385773 "ITUPLE" 1386271 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1383772 1383949 1384244 "ITRIGMNP" 1385092 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1382517 1382721 1383004 "ITFUN3" 1383548 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1382149 1382206 1382315 "ITFUN2" 1382454 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1379951 1381011 1381310 "ITAYLOR" 1381883 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1368896 1374088 1375251 "ISUPS" 1378821 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1368000 1368140 1368376 "ISUMP" 1368743 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1363214 1367801 1367880 "ISTRING" 1367953 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1362690 1362935 1363027 "ISAST" 1363142 T ISAST (NIL) -8 NIL NIL NIL) (-590 1361899 1361981 1362197 "IRURPK" 1362604 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1360835 1361036 1361276 "IRSN" 1361679 T IRSN (NIL) -7 NIL NIL NIL) (-588 1358906 1359261 1359690 "IRRF2F" 1360473 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1358653 1358691 1358767 "IRREDFFX" 1358862 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1357268 1357527 1357826 "IROOT" 1358386 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1353872 1354952 1355644 "IR" 1356608 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1351485 1351980 1352546 "IR2" 1353350 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1350585 1350698 1350912 "IR2F" 1351368 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1350376 1350410 1350470 "IPRNTPK" 1350545 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1346956 1350265 1350334 "IPF" 1350339 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1345283 1346881 1346938 "IPADIC" 1346943 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1344595 1344843 1344973 "IP4ADDR" 1345173 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1344068 1344299 1344409 "IOMODE" 1344505 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1343141 1343665 1343792 "IOBFILE" 1343961 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1342629 1343045 1343073 "IOBCON" 1343078 T IOBCON (NIL) -9 NIL 1343099 NIL) (-575 1342140 1342198 1342381 "INVLAPLA" 1342565 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1331788 1334142 1336528 "INTTR" 1339804 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1328123 1328865 1329730 "INTTOOLS" 1330973 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1327709 1327800 1327917 "INTSLPE" 1328026 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1325663 1327632 1327691 "INTRVL" 1327696 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1323265 1323777 1324352 "INTRF" 1325148 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1322676 1322773 1322915 "INTRET" 1323163 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1320673 1321062 1321532 "INTRAT" 1322284 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1317936 1318519 1319138 "INTPM" 1320158 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1314680 1315280 1316018 "INTPAF" 1317322 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1309859 1310821 1311872 "INTPACK" 1313649 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1306739 1309588 1309715 "INT" 1309752 T INT (NIL) -8 NIL NIL NIL) (-563 1305991 1306143 1306351 "INTHERTR" 1306581 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1305430 1305510 1305698 "INTHERAL" 1305905 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1303276 1303719 1304176 "INTHEORY" 1304993 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1294682 1296303 1298075 "INTG0" 1301628 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1275255 1280045 1284855 "INTFTBL" 1289892 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1274504 1274642 1274815 "INTFACT" 1275114 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1271931 1272377 1272934 "INTEF" 1274058 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1270298 1271037 1271065 "INTDOM" 1271366 T INTDOM (NIL) -9 NIL 1271573 NIL) (-555 1269667 1269841 1270083 "INTDOM-" 1270088 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1266055 1267983 1268037 "INTCAT" 1268836 NIL INTCAT (NIL T) -9 NIL 1269157 NIL) (-553 1265527 1265630 1265758 "INTBIT" 1265947 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1264226 1264380 1264687 "INTALG" 1265372 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1263709 1263799 1263956 "INTAF" 1264130 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1257052 1263519 1263659 "INTABL" 1263664 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1256393 1256859 1256924 "INT8" 1256958 T INT8 (NIL) -8 NIL NIL 1257003) (-548 1255733 1256199 1256264 "INT64" 1256298 T INT64 (NIL) -8 NIL NIL 1256343) (-547 1255073 1255539 1255604 "INT32" 1255638 T INT32 (NIL) -8 NIL NIL 1255683) (-546 1254413 1254879 1254944 "INT16" 1254978 T INT16 (NIL) -8 NIL NIL 1255023) (-545 1249323 1252036 1252064 "INS" 1252998 T INS (NIL) -9 NIL 1253663 NIL) (-544 1246563 1247334 1248308 "INS-" 1248381 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1245338 1245565 1245863 "INPSIGN" 1246316 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1244456 1244573 1244770 "INPRODPF" 1245218 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1243350 1243467 1243704 "INPRODFF" 1244336 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1242350 1242502 1242762 "INNMFACT" 1243186 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1241547 1241644 1241832 "INMODGCD" 1242249 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1240055 1240300 1240624 "INFSP" 1241292 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1239239 1239356 1239539 "INFPROD0" 1239935 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1236094 1237304 1237819 "INFORM" 1238732 T INFORM (NIL) -8 NIL NIL NIL) (-535 1235704 1235764 1235862 "INFORM1" 1236029 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1235227 1235316 1235430 "INFINITY" 1235610 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1234403 1234947 1235048 "INETCLTS" 1235146 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1233019 1233269 1233590 "INEP" 1234151 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1232268 1232916 1232981 "INDE" 1232986 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1231832 1231900 1232017 "INCRMAPS" 1232195 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1230650 1231101 1231307 "INBFILE" 1231646 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1225950 1226886 1227830 "INBFF" 1229738 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1224858 1225127 1225155 "INBCON" 1225668 T INBCON (NIL) -9 NIL 1225934 NIL) (-526 1224110 1224333 1224609 "INBCON-" 1224614 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1223589 1223834 1223925 "INAST" 1224039 T INAST (NIL) -8 NIL NIL NIL) (-524 1223016 1223268 1223374 "IMPTAST" 1223503 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1219462 1222860 1222964 "IMATRIX" 1222969 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1218174 1218297 1218612 "IMATQF" 1219318 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1216394 1216621 1216958 "IMATLIN" 1217930 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1210972 1216318 1216376 "ILIST" 1216381 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1208877 1210832 1210945 "IIARRAY2" 1210950 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1204275 1208788 1208852 "IFF" 1208857 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1203622 1203892 1204008 "IFAST" 1204179 T IFAST (NIL) -8 NIL NIL NIL) (-516 1198617 1202914 1203102 "IFARRAY" 1203479 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1197797 1198521 1198594 "IFAMON" 1198599 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1197381 1197446 1197500 "IEVALAB" 1197707 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1197056 1197124 1197284 "IEVALAB-" 1197289 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1196687 1196970 1197033 "IDPO" 1197038 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1195937 1196576 1196651 "IDPOAMS" 1196656 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1195244 1195826 1195901 "IDPOAM" 1195906 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1194303 1194579 1194632 "IDPC" 1195045 NIL IDPC (NIL T T) -9 NIL 1195194 NIL) (-508 1193772 1194195 1194268 "IDPAM" 1194273 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1193148 1193664 1193737 "IDPAG" 1193742 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1192793 1192984 1193059 "IDENT" 1193093 T IDENT (NIL) -8 NIL NIL NIL) (-505 1189048 1189896 1190791 "IDECOMP" 1191950 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1181884 1182971 1184018 "IDEAL" 1188084 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1181048 1181160 1181359 "ICDEN" 1181768 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1180119 1180528 1180675 "ICARD" 1180921 T ICARD (NIL) -8 NIL NIL NIL) (-501 1178179 1178492 1178897 "IBPTOOLS" 1179796 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1173786 1177799 1177912 "IBITS" 1178098 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1170509 1171085 1171780 "IBATOOL" 1173203 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1168288 1168750 1169283 "IBACHIN" 1170044 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1166117 1168134 1168237 "IARRAY2" 1168242 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1162223 1166043 1166100 "IARRAY1" 1166105 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1156332 1160635 1161116 "IAN" 1161762 T IAN (NIL) -8 NIL NIL NIL) (-494 1155843 1155900 1156073 "IALGFACT" 1156269 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1155371 1155484 1155512 "HYPCAT" 1155719 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1154909 1155026 1155212 "HYPCAT-" 1155217 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1154504 1154704 1154787 "HOSTNAME" 1154846 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1154349 1154386 1154427 "HOMOTOP" 1154432 NIL HOMOTOP (NIL T) -9 NIL 1154465 NIL) (-489 1150981 1152359 1152400 "HOAGG" 1153381 NIL HOAGG (NIL T) -9 NIL 1154060 NIL) (-488 1149575 1149974 1150500 "HOAGG-" 1150505 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1143579 1149170 1149319 "HEXADEC" 1149446 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1142327 1142549 1142812 "HEUGCD" 1143356 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1141403 1142164 1142294 "HELLFDIV" 1142299 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1139582 1141180 1141268 "HEAP" 1141347 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1138845 1139134 1139268 "HEADAST" 1139468 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1132711 1138760 1138822 "HDP" 1138827 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1126699 1132346 1132498 "HDMP" 1132612 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1126023 1126163 1126327 "HB" 1126555 T HB (NIL) -7 NIL NIL NIL) (-479 1119409 1125869 1125973 "HASHTBL" 1125978 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1118885 1119130 1119222 "HASAST" 1119337 T HASAST (NIL) -8 NIL NIL NIL) (-477 1116663 1118507 1118689 "HACKPI" 1118723 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1112331 1116516 1116629 "GTSET" 1116634 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1105746 1112209 1112307 "GSTBL" 1112312 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1098024 1104777 1105042 "GSERIES" 1105537 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1097165 1097582 1097610 "GROUP" 1097813 T GROUP (NIL) -9 NIL 1097947 NIL) (-472 1096531 1096690 1096941 "GROUP-" 1096946 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1094898 1095219 1095606 "GROEBSOL" 1096208 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1093812 1094100 1094151 "GRMOD" 1094680 NIL GRMOD (NIL T T) -9 NIL 1094848 NIL) (-469 1093580 1093616 1093744 "GRMOD-" 1093749 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1088870 1089934 1090934 "GRIMAGE" 1092600 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1087336 1087597 1087921 "GRDEF" 1088566 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1086780 1086896 1087037 "GRAY" 1087215 T GRAY (NIL) -7 NIL NIL NIL) (-465 1085967 1086373 1086424 "GRALG" 1086577 NIL GRALG (NIL T T) -9 NIL 1086670 NIL) (-464 1085628 1085701 1085864 "GRALG-" 1085869 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1082405 1085213 1085391 "GPOLSET" 1085535 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1081759 1081816 1082074 "GOSPER" 1082342 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1077491 1078197 1078723 "GMODPOL" 1081458 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1076496 1076680 1076918 "GHENSEL" 1077303 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1070652 1071495 1072515 "GENUPS" 1075580 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1070349 1070400 1070489 "GENUFACT" 1070595 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1069761 1069838 1070003 "GENPGCD" 1070267 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1069235 1069270 1069483 "GENMFACT" 1069720 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1067801 1068058 1068365 "GENEEZ" 1068978 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1061946 1067412 1067574 "GDMP" 1067724 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1051288 1055717 1056823 "GCNAALG" 1060929 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1049615 1050477 1050505 "GCDDOM" 1050760 T GCDDOM (NIL) -9 NIL 1050917 NIL) (-451 1049085 1049212 1049427 "GCDDOM-" 1049432 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1047757 1047942 1048246 "GB" 1048864 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1036373 1038703 1041095 "GBINTERN" 1045448 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1034210 1034502 1034923 "GBF" 1036048 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1032991 1033156 1033423 "GBEUCLID" 1034026 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1032340 1032465 1032614 "GAUSSFAC" 1032862 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1030707 1031009 1031323 "GALUTIL" 1032059 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1029015 1029289 1029613 "GALPOLYU" 1030434 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1026380 1026670 1027077 "GALFACTU" 1028712 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1018185 1019685 1021293 "GALFACT" 1024812 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1015573 1016231 1016259 "FVFUN" 1017415 T FVFUN (NIL) -9 NIL 1018135 NIL) (-440 1014839 1015021 1015049 "FVC" 1015340 T FVC (NIL) -9 NIL 1015523 NIL) (-439 1014482 1014664 1014732 "FUNDESC" 1014791 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1014097 1014279 1014360 "FUNCTION" 1014434 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1011841 1012419 1012885 "FT" 1013651 T FT (NIL) -8 NIL NIL NIL) (-436 1010632 1011142 1011345 "FTEM" 1011658 T FTEM (NIL) -8 NIL NIL NIL) (-435 1008923 1009212 1009609 "FSUPFACT" 1010323 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1007320 1007609 1007941 "FST" 1008611 T FST (NIL) -8 NIL NIL NIL) (-433 1006519 1006625 1006813 "FSRED" 1007202 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1005218 1005474 1005821 "FSPRMELT" 1006234 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 1002524 1002962 1003448 "FSPECF" 1004781 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 984162 992493 992534 "FS" 996418 NIL FS (NIL T) -9 NIL 998707 NIL) (-429 972805 975798 979855 "FS-" 980155 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 972333 972387 972557 "FSINT" 972746 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 970625 971326 971629 "FSERIES" 972112 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 969667 969783 970007 "FSCINT" 970505 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 965875 968611 968652 "FSAGG" 969022 NIL FSAGG (NIL T) -9 NIL 969281 NIL) (-424 963637 964238 965034 "FSAGG-" 965129 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 962679 962822 963049 "FSAGG2" 963490 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 960361 960641 961188 "FS2UPS" 962397 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 959995 960038 960167 "FS2" 960312 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 958873 959044 959346 "FS2EXPXP" 959820 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 958299 958414 958566 "FRUTIL" 958753 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 949712 953794 955152 "FR" 956973 NIL FR (NIL T) -8 NIL NIL NIL) (-417 944681 947355 947395 "FRNAALG" 948791 NIL FRNAALG (NIL T) -9 NIL 949398 NIL) (-416 940354 941430 942705 "FRNAALG-" 943455 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 939992 940035 940162 "FRNAAF2" 940305 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 938372 938846 939141 "FRMOD" 939804 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 936123 936755 937072 "FRIDEAL" 938163 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 935318 935405 935694 "FRIDEAL2" 936030 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 934451 934865 934906 "FRETRCT" 934911 NIL FRETRCT (NIL T) -9 NIL 935087 NIL) (-410 933563 933794 934145 "FRETRCT-" 934150 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 930651 931861 931920 "FRAMALG" 932802 NIL FRAMALG (NIL T T) -9 NIL 933094 NIL) (-408 928785 929240 929870 "FRAMALG-" 930093 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 922706 928260 928536 "FRAC" 928541 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 922342 922399 922506 "FRAC2" 922643 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 921978 922035 922142 "FR2" 922279 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 916491 919384 919412 "FPS" 920531 T FPS (NIL) -9 NIL 921088 NIL) (-403 915940 916049 916213 "FPS-" 916359 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 913242 914911 914939 "FPC" 915164 T FPC (NIL) -9 NIL 915306 NIL) (-401 913035 913075 913172 "FPC-" 913177 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 911825 912523 912564 "FPATMAB" 912569 NIL FPATMAB (NIL T) -9 NIL 912721 NIL) (-399 909498 910001 910427 "FPARFRAC" 911462 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 904891 905390 906072 "FORTRAN" 908930 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 902607 903107 903646 "FORT" 904372 T FORT (NIL) -7 NIL NIL NIL) (-396 900283 900845 900873 "FORTFN" 901933 T FORTFN (NIL) -9 NIL 902557 NIL) (-395 900047 900097 900125 "FORTCAT" 900184 T FORTCAT (NIL) -9 NIL 900246 NIL) (-394 898153 898663 899053 "FORMULA" 899677 T FORMULA (NIL) -8 NIL NIL NIL) (-393 897941 897971 898040 "FORMULA1" 898117 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 897464 897516 897689 "FORDER" 897883 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 896560 896724 896917 "FOP" 897291 T FOP (NIL) -7 NIL NIL NIL) (-390 895141 895840 896014 "FNLA" 896442 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 893870 894285 894313 "FNCAT" 894773 T FNCAT (NIL) -9 NIL 895033 NIL) (-388 893409 893829 893857 "FNAME" 893862 T FNAME (NIL) -8 NIL NIL NIL) (-387 891972 892935 892963 "FMTC" 892968 T FMTC (NIL) -9 NIL 893004 NIL) (-386 888305 889495 890124 "FMONOID" 891376 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 887497 888047 888196 "FM" 888201 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 884921 885567 885595 "FMFUN" 886739 T FMFUN (NIL) -9 NIL 887447 NIL) (-383 884190 884371 884399 "FMC" 884689 T FMC (NIL) -9 NIL 884871 NIL) (-382 881269 882129 882183 "FMCAT" 883378 NIL FMCAT (NIL T T) -9 NIL 883873 NIL) (-381 880135 881035 881135 "FM1" 881214 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 877909 878325 878819 "FLOATRP" 879686 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 871483 875638 876259 "FLOAT" 877308 T FLOAT (NIL) -8 NIL NIL NIL) (-378 868921 869421 869999 "FLOATCP" 870950 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 867661 868499 868540 "FLINEXP" 868545 NIL FLINEXP (NIL T) -9 NIL 868638 NIL) (-376 866815 867050 867378 "FLINEXP-" 867383 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 865891 866035 866259 "FLASORT" 866667 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 863007 863875 863927 "FLALG" 865154 NIL FLALG (NIL T T) -9 NIL 865621 NIL) (-373 856743 860493 860534 "FLAGG" 861796 NIL FLAGG (NIL T) -9 NIL 862448 NIL) (-372 855469 855808 856298 "FLAGG-" 856303 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 854511 854654 854881 "FLAGG2" 855322 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 851362 852370 852429 "FINRALG" 853557 NIL FINRALG (NIL T T) -9 NIL 854065 NIL) (-369 850522 850751 851090 "FINRALG-" 851095 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 849902 850141 850169 "FINITE" 850365 T FINITE (NIL) -9 NIL 850472 NIL) (-367 842259 844446 844486 "FINAALG" 848153 NIL FINAALG (NIL T) -9 NIL 849606 NIL) (-366 837591 838641 839785 "FINAALG-" 841164 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 836959 837346 837449 "FILE" 837521 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 835617 835955 836009 "FILECAT" 836693 NIL FILECAT (NIL T T) -9 NIL 836909 NIL) (-363 833333 834861 834889 "FIELD" 834929 T FIELD (NIL) -9 NIL 835009 NIL) (-362 831953 832338 832849 "FIELD-" 832854 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 829803 830588 830935 "FGROUP" 831639 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 828893 829057 829277 "FGLMICPK" 829635 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 824725 828818 828875 "FFX" 828880 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 824326 824387 824522 "FFSLPE" 824658 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 820315 821098 821894 "FFPOLY" 823562 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 819819 819855 820064 "FFPOLY2" 820273 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 815662 819738 819801 "FFP" 819806 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 811060 815573 815637 "FF" 815642 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 806186 810403 810593 "FFNBX" 810914 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 801115 805321 805579 "FFNBP" 806040 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 795748 800399 800610 "FFNB" 800948 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 794580 794778 795093 "FFINTBAS" 795545 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 790649 792869 792897 "FFIELDC" 793517 T FFIELDC (NIL) -9 NIL 793893 NIL) (-348 789311 789682 790179 "FFIELDC-" 790184 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 788880 788926 789050 "FFHOM" 789253 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 786575 787062 787579 "FFF" 788395 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 782193 786317 786418 "FFCGX" 786518 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 777814 781925 782032 "FFCGP" 782136 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 772997 777541 777649 "FFCG" 777750 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 754393 763474 763560 "FFCAT" 768725 NIL FFCAT (NIL T T T) -9 NIL 770176 NIL) (-341 749591 750638 751952 "FFCAT-" 753182 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 749002 749045 749280 "FFCAT2" 749542 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 738323 741974 743194 "FEXPR" 747854 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 737323 737758 737799 "FEVALAB" 737883 NIL FEVALAB (NIL T) -9 NIL 738144 NIL) (-337 736482 736692 737030 "FEVALAB-" 737035 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 735048 735865 736068 "FDIV" 736381 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 732068 732809 732924 "FDIVCAT" 734492 NIL FDIVCAT (NIL T T T T) -9 NIL 734929 NIL) (-334 731830 731857 732027 "FDIVCAT-" 732032 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 731050 731137 731414 "FDIV2" 731737 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 729736 729995 730284 "FCPAK1" 730781 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 728835 729236 729377 "FCOMP" 729627 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 712537 715985 719523 "FC" 725317 T FC (NIL) -8 NIL NIL NIL) (-329 704900 708928 708968 "FAXF" 710770 NIL FAXF (NIL T) -9 NIL 711462 NIL) (-328 702176 702834 703659 "FAXF-" 704124 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 697228 701552 701728 "FARRAY" 702033 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 692122 694189 694242 "FAMR" 695265 NIL FAMR (NIL T T) -9 NIL 695725 NIL) (-325 691012 691314 691749 "FAMR-" 691754 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 690181 690934 690987 "FAMONOID" 690992 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 687967 688677 688730 "FAMONC" 689671 NIL FAMONC (NIL T T) -9 NIL 690057 NIL) (-322 686632 687721 687858 "FAGROUP" 687863 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 684427 684746 685149 "FACUTIL" 686313 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 683526 683711 683933 "FACTFUNC" 684237 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 675948 682829 683028 "EXPUPXS" 683382 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 673431 673971 674557 "EXPRTUBE" 675382 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 669702 670294 671024 "EXPRODE" 672770 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 655187 668351 668780 "EXPR" 669306 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 649741 650328 651134 "EXPR2UPS" 654485 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 649373 649430 649539 "EXPR2" 649678 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 640764 648526 648816 "EXPEXPAN" 649210 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 640564 640721 640750 "EXIT" 640755 T EXIT (NIL) -8 NIL NIL NIL) (-311 640044 640288 640379 "EXITAST" 640493 T EXITAST (NIL) -8 NIL NIL NIL) (-310 639671 639733 639846 "EVALCYC" 639976 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 639212 639330 639371 "EVALAB" 639541 NIL EVALAB (NIL T) -9 NIL 639645 NIL) (-308 638693 638815 639036 "EVALAB-" 639041 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 636061 637363 637391 "EUCDOM" 637946 T EUCDOM (NIL) -9 NIL 638296 NIL) (-306 634466 634908 635498 "EUCDOM-" 635503 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 622004 624764 627514 "ESTOOLS" 631736 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 621636 621693 621802 "ESTOOLS2" 621941 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 621387 621429 621509 "ESTOOLS1" 621588 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 615424 617032 617060 "ES" 619828 T ES (NIL) -9 NIL 621238 NIL) (-301 610371 611658 613475 "ES-" 613639 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 606745 607506 608286 "ESCONT" 609611 T ESCONT (NIL) -7 NIL NIL NIL) (-299 606490 606522 606604 "ESCONT1" 606707 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 606165 606215 606315 "ES2" 606434 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 605795 605853 605962 "ES1" 606101 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 605011 605140 605316 "ERROR" 605639 T ERROR (NIL) -7 NIL NIL NIL) (-295 598403 604870 604961 "EQTBL" 604966 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 590906 593717 595166 "EQ" 596987 NIL -2089 (NIL T) -8 NIL NIL NIL) (-293 590538 590595 590704 "EQ2" 590843 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 585827 586876 587969 "EP" 589477 NIL EP (NIL T) -7 NIL NIL NIL) (-291 584427 584718 585024 "ENV" 585541 T ENV (NIL) -8 NIL NIL NIL) (-290 583521 584075 584103 "ENTIRER" 584108 T ENTIRER (NIL) -9 NIL 584154 NIL) (-289 579988 581476 581846 "EMR" 583320 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 579132 579317 579371 "ELTAGG" 579751 NIL ELTAGG (NIL T T) -9 NIL 579962 NIL) (-287 578851 578913 579054 "ELTAGG-" 579059 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 578640 578669 578723 "ELTAB" 578807 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 577766 577912 578111 "ELFUTS" 578491 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 577508 577564 577592 "ELEMFUN" 577697 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 577378 577399 577467 "ELEMFUN-" 577472 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 572222 575478 575519 "ELAGG" 576459 NIL ELAGG (NIL T) -9 NIL 576922 NIL) (-281 570507 570941 571604 "ELAGG-" 571609 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 569172 569450 569743 "ELABEXPR" 570234 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 562036 563839 564666 "EFUPXS" 568448 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 555486 557287 558097 "EFULS" 561312 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 552971 553329 553801 "EFSTRUC" 555118 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 542762 544328 545876 "EF" 551486 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 541836 542247 542396 "EAB" 542633 T EAB (NIL) -8 NIL NIL NIL) (-274 541018 541795 541823 "E04UCFA" 541828 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 540200 540977 541005 "E04NAFA" 541010 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 539382 540159 540187 "E04MBFA" 540192 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 538564 539341 539369 "E04JAFA" 539374 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 537748 538523 538551 "E04GCFA" 538556 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 536932 537707 537735 "E04FDFA" 537740 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 536114 536891 536919 "E04DGFA" 536924 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 530287 531639 533003 "E04AGNT" 534770 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 528967 529473 529513 "DVARCAT" 529988 NIL DVARCAT (NIL T) -9 NIL 530187 NIL) (-265 528171 528383 528697 "DVARCAT-" 528702 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 521308 527970 528099 "DSMP" 528104 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 516090 517253 518321 "DROPT" 520260 T DROPT (NIL) -8 NIL NIL NIL) (-262 515755 515814 515912 "DROPT1" 516025 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 510870 511996 513133 "DROPT0" 514638 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 509215 509540 509926 "DRAWPT" 510504 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 503802 504725 505804 "DRAW" 508189 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 503435 503488 503606 "DRAWHACK" 503743 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 502166 502435 502726 "DRAWCX" 503164 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 501681 501750 501901 "DRAWCURV" 502092 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 492149 494111 496226 "DRAWCFUN" 499586 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 488915 490844 490885 "DQAGG" 491514 NIL DQAGG (NIL T) -9 NIL 491787 NIL) (-253 477039 483508 483591 "DPOLCAT" 485443 NIL DPOLCAT (NIL T T T T) -9 NIL 485988 NIL) (-252 471875 473224 475182 "DPOLCAT-" 475187 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 464997 471736 471834 "DPMO" 471839 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 458022 464777 464944 "DPMM" 464949 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 457595 457941 457989 "DOMCTOR" 457994 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456863 457117 457254 "DOMAIN" 457478 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450851 456498 456650 "DMP" 456764 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450451 450507 450651 "DLP" 450789 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444273 449778 449968 "DLIST" 450293 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 441070 443126 443167 "DLAGG" 443717 NIL DLAGG (NIL T) -9 NIL 443947 NIL) (-243 439746 440410 440438 "DIVRING" 440530 T DIVRING (NIL) -9 NIL 440613 NIL) (-242 438983 439173 439473 "DIVRING-" 439478 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437085 437442 437848 "DISPLAY" 438597 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430973 436999 437062 "DIRPROD" 437067 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429821 430024 430289 "DIRPROD2" 430766 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418596 424602 424655 "DIRPCAT" 425065 NIL DIRPCAT (NIL NIL T) -9 NIL 425905 NIL) (-237 415922 416564 417445 "DIRPCAT-" 417782 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415209 415369 415555 "DIOSP" 415756 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411864 414121 414162 "DIOPS" 414596 NIL DIOPS (NIL T) -9 NIL 414825 NIL) (-234 411413 411527 411718 "DIOPS-" 411723 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410236 410864 410892 "DIFRING" 411079 T DIFRING (NIL) -9 NIL 411189 NIL) (-232 409882 409959 410111 "DIFRING-" 410116 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407618 408890 408931 "DIFEXT" 409294 NIL DIFEXT (NIL T) -9 NIL 409588 NIL) (-230 405903 406331 406997 "DIFEXT-" 407002 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403178 405435 405476 "DIAGG" 405481 NIL DIAGG (NIL T) -9 NIL 405501 NIL) (-228 402562 402719 402971 "DIAGG-" 402976 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397979 401521 401798 "DHMATRIX" 402331 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393591 394500 395510 "DFSFUN" 396989 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388669 392522 392834 "DFLOAT" 393299 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386932 387213 387602 "DFINTTLS" 388377 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383961 384953 385353 "DERHAM" 386598 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381762 383736 383825 "DEQUEUE" 383905 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 381016 381149 381332 "DEGRED" 381624 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377446 378191 379037 "DEFINTRF" 380244 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 375001 375470 376062 "DEFINTEF" 376965 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374351 374621 374736 "DEFAST" 374906 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368355 373946 374095 "DECIMAL" 374222 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365866 366325 366831 "DDFACT" 367899 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365462 365505 365656 "DBLRESP" 365817 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363334 363695 364055 "DBASE" 365229 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362576 362814 362960 "DATAARY" 363233 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361682 362535 362563 "D03FAFA" 362568 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360789 361641 361669 "D03EEFA" 361674 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358739 359205 359694 "D03AGNT" 360320 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 358028 358698 358726 "D02EJFA" 358731 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357317 357987 358015 "D02CJFA" 358020 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356606 357276 357304 "D02BHFA" 357309 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355895 356565 356593 "D02BBFA" 356598 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349092 350681 352287 "D02AGNT" 354309 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346860 347383 347929 "D01WGTS" 348566 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345927 346819 346847 "D01TRNS" 346852 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344995 345886 345914 "D01GBFA" 345919 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 344063 344954 344982 "D01FCFA" 344987 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343131 344022 344050 "D01ASFA" 344055 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342199 343090 343118 "D01AQFA" 343123 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341267 342158 342186 "D01APFA" 342191 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340335 341226 341254 "D01ANFA" 341259 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339403 340294 340322 "D01AMFA" 340327 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338471 339362 339390 "D01ALFA" 339395 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337539 338430 338458 "D01AKFA" 338463 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336607 337498 337526 "D01AJFA" 337531 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329902 331455 333016 "D01AGNT" 335066 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329239 329367 329519 "CYCLOTOM" 329770 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325974 326687 327414 "CYCLES" 328532 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325286 325420 325591 "CVMP" 325835 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323127 323385 323754 "CTRIGMNP" 325014 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322563 322921 322994 "CTOR" 323074 T CTOR (NIL) -8 NIL NIL NIL) (-186 322072 322294 322395 "CTORKIND" 322482 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321363 321679 321707 "CTORCAT" 321889 T CTORCAT (NIL) -9 NIL 322002 NIL) (-184 320961 321072 321231 "CTORCAT-" 321236 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320450 320664 320762 "CTORCALL" 320883 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319824 319923 320076 "CSTTOOLS" 320347 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315623 316280 317038 "CRFP" 319136 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315098 315344 315436 "CRCEAST" 315551 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314145 314330 314558 "CRAPACK" 314902 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313529 313630 313834 "CPMATCH" 314021 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313254 313282 313388 "CPIMA" 313495 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309602 310274 310993 "COORDSYS" 312589 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 309014 309135 309277 "CONTOUR" 309480 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304905 307017 307509 "CONTFRAC" 308554 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304785 304806 304834 "CONDUIT" 304871 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303873 304427 304455 "COMRING" 304460 T COMRING (NIL) -9 NIL 304512 NIL) (-171 302927 303231 303415 "COMPPROP" 303709 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302588 302623 302751 "COMPLPAT" 302886 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292879 302397 302506 "COMPLEX" 302511 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292515 292572 292679 "COMPLEX2" 292816 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292233 292268 292366 "COMPFACT" 292474 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276313 286307 286347 "COMPCAT" 287351 NIL COMPCAT (NIL T) -9 NIL 288699 NIL) (-165 265823 268752 272379 "COMPCAT-" 272735 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265552 265580 265683 "COMMUPC" 265789 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265346 265380 265439 "COMMONOP" 265513 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264902 265097 265184 "COMM" 265279 T COMM (NIL) -8 NIL NIL NIL) (-161 264478 264706 264781 "COMMAAST" 264847 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263727 263921 263949 "COMBOPC" 264287 T COMBOPC (NIL) -9 NIL 264462 NIL) (-159 262623 262833 263075 "COMBINAT" 263517 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 259080 259654 260281 "COMBF" 262045 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257838 258196 258431 "COLOR" 258865 T COLOR (NIL) -8 NIL NIL NIL) (-156 257314 257559 257651 "COLONAST" 257766 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256954 257001 257126 "CMPLXRT" 257261 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256402 256654 256753 "CLLCTAST" 256875 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251902 252932 254012 "CLIP" 255342 T CLIP (NIL) -7 NIL NIL NIL) (-152 250248 251008 251247 "CLIF" 251729 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246423 248394 248435 "CLAGG" 249364 NIL CLAGG (NIL T) -9 NIL 249900 NIL) (-150 244845 245302 245885 "CLAGG-" 245890 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244389 244474 244614 "CINTSLPE" 244754 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241890 242361 242909 "CHVAR" 243917 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 241064 241618 241646 "CHARZ" 241651 T CHARZ (NIL) -9 NIL 241666 NIL) (-146 240818 240858 240936 "CHARPOL" 241018 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239876 240463 240491 "CHARNZ" 240538 T CHARNZ (NIL) -9 NIL 240594 NIL) (-144 237842 238566 238901 "CHAR" 239561 T CHAR (NIL) -8 NIL NIL NIL) (-143 237568 237629 237657 "CFCAT" 237768 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236813 236924 237106 "CDEN" 237452 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232778 235966 236246 "CCLASS" 236553 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232085 232228 232391 "CATEGORY" 232635 T -10 (NIL) -8 NIL NIL NIL) (-139 231658 232004 232052 "CATCTOR" 232057 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231109 231361 231459 "CATAST" 231580 T CATAST (NIL) -8 NIL NIL NIL) (-137 230585 230830 230922 "CASEAST" 231037 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225594 226614 227367 "CARTEN" 229888 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224702 224850 225071 "CARTEN2" 225441 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 223017 223852 224109 "CARD" 224465 T CARD (NIL) -8 NIL NIL NIL) (-133 222593 222821 222896 "CAPSLAST" 222962 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222097 222305 222333 "CACHSET" 222465 T CACHSET (NIL) -9 NIL 222543 NIL) (-131 221567 221889 221917 "CABMON" 221967 T CABMON (NIL) -9 NIL 222023 NIL) (-130 221040 221271 221381 "BYTEORD" 221477 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 220019 220574 220716 "BYTE" 220879 T BYTE (NIL) -8 NIL NIL 221001) (-128 215369 219524 219696 "BYTEBUF" 219867 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212878 215061 215168 "BTREE" 215295 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210327 212526 212648 "BTOURN" 212788 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207697 209797 209838 "BTCAT" 209906 NIL BTCAT (NIL T) -9 NIL 209983 NIL) (-124 207364 207444 207593 "BTCAT-" 207598 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202629 206507 206535 "BTAGG" 206757 T BTAGG (NIL) -9 NIL 206918 NIL) (-122 202119 202244 202450 "BTAGG-" 202455 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199114 201397 201612 "BSTREE" 201936 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198252 198378 198562 "BRILL" 198970 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194904 196978 197019 "BRAGG" 197668 NIL BRAGG (NIL T) -9 NIL 197926 NIL) (-118 193433 193839 194394 "BRAGG-" 194399 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186662 192779 192963 "BPADICRT" 193281 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184977 186599 186644 "BPADIC" 186649 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184675 184705 184819 "BOUNDZRO" 184941 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179903 181101 182013 "BOP" 183783 T BOP (NIL) -8 NIL NIL NIL) (-113 177684 178088 178563 "BOP1" 179461 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176509 177258 177407 "BOOLEAN" 177555 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175788 176192 176246 "BMODULE" 176251 NIL BMODULE (NIL T T) -9 NIL 176316 NIL) (-110 171589 175586 175659 "BITS" 175735 T BITS (NIL) -8 NIL NIL NIL) (-109 171010 171129 171269 "BINDING" 171469 T BINDING (NIL) -8 NIL NIL NIL) (-108 165017 170607 170755 "BINARY" 170882 T BINARY (NIL) -8 NIL NIL NIL) (-107 162797 164272 164313 "BGAGG" 164573 NIL BGAGG (NIL T) -9 NIL 164710 NIL) (-106 162628 162660 162751 "BGAGG-" 162756 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161699 162012 162217 "BFUNCT" 162443 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160389 160567 160855 "BEZOUT" 161523 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156858 159241 159571 "BBTREE" 160092 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156592 156645 156673 "BASTYPE" 156792 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156444 156473 156546 "BASTYPE-" 156551 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155878 155954 156106 "BALFACT" 156355 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154734 155293 155479 "AUTOMOR" 155723 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154460 154465 154491 "ATTREG" 154496 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152712 153157 153509 "ATTRBUT" 154126 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152320 152540 152606 "ATTRAST" 152664 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151856 151969 151995 "ATRIG" 152196 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151665 151706 151793 "ATRIG-" 151798 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151310 151496 151522 "ASTCAT" 151527 T ASTCAT (NIL) -9 NIL 151557 NIL) (-92 151037 151096 151215 "ASTCAT-" 151220 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149186 150813 150901 "ASTACK" 150980 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147691 147988 148353 "ASSOCEQ" 148868 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146723 147350 147474 "ASP9" 147598 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146486 146671 146710 "ASP8" 146715 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145354 146091 146233 "ASP80" 146375 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144252 144989 145121 "ASP7" 145253 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143206 143929 144047 "ASP78" 144165 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142175 142886 143003 "ASP77" 143120 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141087 141813 141944 "ASP74" 142075 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139987 140722 140854 "ASP73" 140986 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139091 139813 139913 "ASP6" 139918 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 138035 138768 138886 "ASP55" 139004 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136984 137709 137828 "ASP50" 137947 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 136072 136685 136795 "ASP4" 136905 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135160 135773 135883 "ASP49" 135993 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133944 134699 134867 "ASP42" 135049 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132720 133477 133647 "ASP41" 133831 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131670 132397 132515 "ASP35" 132633 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131435 131618 131657 "ASP34" 131662 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131172 131239 131315 "ASP33" 131390 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 130065 130807 130939 "ASP31" 131071 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129830 130013 130052 "ASP30" 130057 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129565 129634 129710 "ASP29" 129785 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129330 129513 129552 "ASP28" 129557 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129095 129278 129317 "ASP27" 129322 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128179 128793 128904 "ASP24" 129015 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127255 127981 128093 "ASP20" 128098 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126343 126956 127066 "ASP1" 127176 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125285 126017 126136 "ASP19" 126255 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 125022 125089 125165 "ASP12" 125240 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123874 124621 124765 "ASP10" 124909 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121725 123718 123809 "ARRAY2" 123814 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117490 121373 121487 "ARRAY1" 121642 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116522 116695 116916 "ARRAY12" 117313 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110834 112752 112827 "ARR2CAT" 115457 NIL ARR2CAT (NIL T T T) -9 NIL 116215 NIL) (-56 108268 109012 109966 "ARR2CAT-" 109971 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107585 107895 108020 "ARITY" 108161 T ARITY (NIL) -8 NIL NIL NIL) (-54 106361 106513 106812 "APPRULE" 107421 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 106012 106060 106179 "APPLYORE" 106307 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104959 105277 105472 "ANY" 105835 T ANY (NIL) -8 NIL NIL NIL) (-51 104237 104360 104517 "ANY1" 104833 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101767 102674 103001 "ANTISYM" 103961 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101259 101474 101570 "ANON" 101689 T ANON (NIL) -8 NIL NIL NIL) (-48 95508 99798 100252 "AN" 100823 T AN (NIL) -8 NIL NIL NIL) (-47 91406 92794 92845 "AMR" 93593 NIL AMR (NIL T T) -9 NIL 94193 NIL) (-46 90518 90739 91102 "AMR-" 91107 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74957 90435 90496 "ALIST" 90501 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71759 74551 74720 "ALGSC" 74875 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68314 68869 69476 "ALGPKG" 71199 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67591 67692 67876 "ALGMFACT" 68200 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64149 64767 "ALGMANIP" 67151 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 1ce621af..52cd6623 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,89 +1,222 @@ -(731999 . 3452782370) -(((*1 *2 *1) (-12 (-5 *2 (-1267)) (-5 *1 (-819))))) -(((*1 *2 *3) (-12 (-5 *3 (-1155)) (-5 *2 (-1267)) (-5 *1 (-436))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-430 *3) (-1000))) (-5 *1 (-276 *3 *2)) - (-4 *3 (-556))))) -(((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-192)))) - ((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-300)))) - ((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-305))))) -(((*1 *1 *2) (-12 (-5 *2 (-642 *3)) (-4 *3 (-1212)) (-4 *1 (-107 *3))))) -(((*1 *2 *1 *1) - (-12 +(731999 . 3452796870) +(((*1 *1) (-5 *1 (-578))) + ((*1 *2 *3) (-12 (-5 *3 (-1155)) (-5 *2 (-1267)) (-5 *1 (-861)))) + ((*1 *2 *3) (-12 (-5 *3 (-860)) (-5 *2 (-1267)) (-5 *1 (-861)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 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"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| + (-3 (|:| |str| (-1153 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2913 + (-3 (|:| |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")))))))) + (-5 *1 (-559))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-642 (-862 *5))) (-14 *5 (-642 (-1173))) (-4 *6 (-452)) + (-5 *2 + (-2 (|:| |dpolys| (-642 (-247 *5 *6))) + (|:| |coords| (-642 (-564))))) + (-5 *1 (-471 *5 *6 *7)) (-5 *3 (-642 (-247 *5 *6))) (-4 *7 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((*1 *1 *1 *1) (|partial| -5 *1 (-134))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-848) - (-10 -8 (-15 -4368 ((-1155) $ (-1173))) (-15 -1664 ((-1267) $)) - (-15 -1937 ((-1267) $))))))) + (-10 -8 (-15 -4370 ((-1155) $ (-1173))) (-15 -1674 ((-1267) $)) + (-15 -1375 ((-1267) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1212)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-294 *2)) (-4 *2 (-21)) (-4 *2 (-1212)))) ((*1 *1 *1 *1) @@ -8670,66 +7671,61 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-941 (-225))) (-5 *1 (-1208)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1260 *2)) (-4 *2 (-1212)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1260 *2)) (-4 *2 (-1212)) (-4 *2 (-21))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) (-5 *2 (-1033)) (-5 *1 (-756))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1262 (-316 (-225)))) - (-5 *2 - (-2 (|:| |additions| (-564)) (|:| |multiplications| (-564)) - (|:| |exponentiations| (-564)) (|:| |functionCalls| (-564)))) - (-5 *1 (-305))))) -(((*1 *2 *1) - (-12 (-5 *2 (-642 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(-4 *3 (-1097))))) +(((*1 *2 *3) (-12 (-5 *3 (-1173)) (-5 *2 (-1267)) (-5 *1 (-1176)))) + ((*1 *2 *1) (-12 (-5 *2 (-1267)) (-5 *1 (-1177))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-642 (-1173))) (-5 *1 (-536))))) +(((*1 *1 *1) (-4 *1 (-627))) + ((*1 *2 *2) + (-12 (-4 *3 (-556)) (-5 *1 (-628 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1000) (-1197)))))) +(((*1 *2 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545))))) +(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) + (-12 (-5 *3 (-919)) (-5 *4 (-225)) (-5 *5 (-564)) (-5 *6 (-872)) + (-5 *2 (-1267)) (-5 *1 (-1263))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-556) (-147))) (-5 *1 (-1232 *3 *2)) + (-4 *2 (-1238 *3))))) (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-157))) ((*1 *1 *1 *1) (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-848) - (-10 -8 (-15 -4368 ((-1155) $ (-1173))) (-15 -1664 ((-1267) $)) - (-15 -1937 ((-1267) $))))))) + (-10 -8 (-15 -4370 ((-1155) $ (-1173))) (-15 -1674 ((-1267) $)) + (-15 -1375 ((-1267) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 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(|:| |localSymbols| (-1177)) (|:| -3146 (-642 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1177)) (|:| -3214 (-642 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-642 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1262 (-697))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1177)) (|:| -3146 (-642 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1177)) (|:| -3214 (-642 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-642 (-330))) (-4 *1 (-441)))) @@ -12303,7 +11116,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-642 (-2 (|:| -4378 *3) (|:| -3214 *4)))) + (-12 (-5 *2 (-642 (-2 (|:| -3089 *3) (|:| -1921 *4)))) (-4 *3 (-1047)) (-4 *4 (-724)) (-5 *1 (-733 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-761)))) ((*1 *1 *2) @@ -12312,25 +11125,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225))) - (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225)) + (|:| -2913 (-1091 (-841 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -3894 (-642 (-1091 (-841 (-225))))) + (|:| -2913 (-642 (-1091 (-841 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-767)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -3894 (-642 (-1091 (-841 (-225))))) (|:| |abserr| (-225)) + (|:| -2913 (-642 (-1091 (-841 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-767)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225))) - (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225)) + (|:| -2913 (-1091 (-841 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-767)))) ((*1 *2 *3) (-12 (-5 *2 (-772)) (-5 *1 (-771 *3)) (-4 *3 (-1212)))) @@ -12348,23 +11161,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3366 (-642 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3927 (-642 (-225))) (|:| |lb| (-642 (-841 (-225)))) (|:| |cf| (-642 (-316 (-225)))) (|:| |ub| (-642 (-841 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-642 (-316 (-225)))) - (|:| -3366 (-642 (-225))))))) + (|:| -3927 (-642 (-225))))))) (-5 *1 (-839)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-642 (-316 (-225)))) (|:| -3366 (-642 (-225))))) + (-2 (|:| |lfn| (-642 (-316 (-225)))) (|:| -3927 (-642 (-225))))) (-5 *1 (-839)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3366 (-642 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3927 (-642 (-225))) (|:| |lb| (-642 (-841 (-225)))) (|:| |cf| (-642 (-316 (-225)))) (|:| |ub| (-642 (-841 (-225)))))) (-5 *1 (-839)))) @@ -12465,106 +11278,349 @@ ((*1 *1 *2) (-12 (-5 *2 (-662 *3 *4)) (-4 *3 (-848)) (-4 *4 (-172)) (-5 *1 (-1282 *3 *4))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1062 *2 *3 *4)) (-4 *2 (-1047)) (-4 *3 (-791)) + (-4 *4 (-848)))) + ((*1 *2 *2 *1) + (-12 (-4 *1 (-1205 *3 *4 *5 *2)) (-4 *3 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*5) (-12 (-5 *3 (-294 *7)) (-5 *4 (-114)) (-5 *5 (-1173)) (-4 *7 (-13 (-29 *6) (-1197) (-957))) (-4 *6 (-13 (-307) (-1036 (-564)) (-637 (-564)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -4263 (-642 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -2318 (-642 *7))) *7 "failed")) (-5 *1 (-800 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-114)) (-5 *5 (-1173)) (-4 *6 (-13 (-307) (-1036 (-564)) (-637 (-564)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -4263 (-642 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -2318 (-642 *3))) *3 "failed")) (-5 *1 (-800 *6 *3)) (-4 *3 (-13 (-29 *6) (-1197) (-957))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-294 *2)) (-5 *4 (-114)) (-5 *5 (-642 *2)) @@ -15759,10 +17126,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -4263 (-642 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -2318 (-642 *6))) "failed") *7 *6)) (-4 *6 (-363)) (-4 *7 (-654 *6)) - (-5 *2 (-2 (|:| |particular| (-1262 *6)) (|:| 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\ No newline at end of file |