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-rw-r--r--src/ChangeLog22
-rw-r--r--src/algebra/strap/CHAR.lsp220
-rw-r--r--src/algebra/string.spad.pamphlet27
-rw-r--r--src/interp/g-opt.boot2
-rw-r--r--src/interp/g-util.boot25
-rw-r--r--src/interp/spad.lisp1
-rw-r--r--src/interp/sys-macros.lisp10
-rw-r--r--src/share/algebra/browse.daase1284
-rw-r--r--src/share/algebra/category.daase1578
-rw-r--r--src/share/algebra/compress.daase1347
-rw-r--r--src/share/algebra/interp.daase9190
-rw-r--r--src/share/algebra/operation.daase31719
12 files changed, 22790 insertions, 22635 deletions
diff --git a/src/ChangeLog b/src/ChangeLog
index c8e633a3..c0d548c0 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,25 @@
+2010-11-16 Gabriel Dos Reis <gdr@cs.tamu.edu>
+
+ * interp/g-opt.boot ($VMsideEffectFreeOperators): Include %s2c
+ builtin.
+ * interp/g-util.boot (stringToChar): New.
+ (expandCst): Use it.
+ (expandS2c): Likewise. New.
+ * interp/spad.lisp (|$Newline): Move to interp/sys-macros.lisp.
+ * interp/sys-macros.lisp (|$Backspace): New.
+ (|$HorizontalTab|): Likewise.
+ (|$VerticalTab|): Likewise.
+ (|$FormFeed|): Likewise.
+ (|$CarriageReturn|): Likewise.
+ * algebra/string.spad.pamphlet (Character) [newline]: New.
+ [carriageReturn]: Likewise.
+ [linefeed]: Likewise.
+ [formfeed]: Likewise.
+ [backspace]: Likewise.
+ [horizontalTab]: Likewise.
+ [verticalTab]: Likewise.
+ [char]: Tidy.
+
2010-11-04 Gabriel Dos Reis <gdr@cs.tamu.edu>
* interp/Makefile.pamphlet: Remove.
diff --git a/src/algebra/strap/CHAR.lsp b/src/algebra/strap/CHAR.lsp
index 15a63aa1..bb9f017d 100644
--- a/src/algebra/strap/CHAR.lsp
+++ b/src/algebra/strap/CHAR.lsp
@@ -61,44 +61,79 @@
(PUT '|CHAR;escape;$;14| '|SPADreplace| '(XLAM NIL (|%ccst| "_")))
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;newline;$;15|))
+
+(PUT '|CHAR;newline;$;15| '|SPADreplace| '(XLAM NIL (|%ccst| "\\n")))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|)
+ |CHAR;carriageReturn;$;16|))
+
+(PUT '|CHAR;carriageReturn;$;16| '|SPADreplace|
+ '(XLAM NIL (|%ccst| "\\r")))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;linefeed;$;17|))
+
+(PUT '|CHAR;linefeed;$;17| '|SPADreplace| '(XLAM NIL (|%i2c| 10)))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;formfeed;$;18|))
+
+(PUT '|CHAR;formfeed;$;18| '|SPADreplace| '(XLAM NIL (|%ccst| "\\f")))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;backspace;$;19|))
+
+(PUT '|CHAR;backspace;$;19| '|SPADreplace| '(XLAM NIL (|%ccst| "\\b")))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|)
+ |CHAR;horizontalTab;$;20|))
+
+(PUT '|CHAR;horizontalTab;$;20| '|SPADreplace|
+ '(XLAM NIL (|%ccst| "\\t")))
+
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Char|) |CHAR;verticalTab;$;21|))
+
+(PUT '|CHAR;verticalTab;$;21| '|SPADreplace|
+ '(XLAM NIL (|%ccst| "\\v")))
+
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Thing|)
- |CHAR;coerce;$Of;15|))
+ |CHAR;coerce;$Of;22|))
-(PUT '|CHAR;coerce;$Of;15| '|SPADreplace| '(XLAM (|c|) |c|))
+(PUT '|CHAR;coerce;$Of;22| '|SPADreplace| '(XLAM (|c|) |c|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;digit?;$B;16|))
+ |CHAR;digit?;$B;23|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;hexDigit?;$B;17|))
+ |CHAR;hexDigit?;$B;24|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;upperCase?;$B;18|))
+ |CHAR;upperCase?;$B;25|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;lowerCase?;$B;19|))
+ |CHAR;lowerCase?;$B;26|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;alphabetic?;$B;20|))
+ |CHAR;alphabetic?;$B;27|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Boolean|)
- |CHAR;alphanumeric?;$B;21|))
+ |CHAR;alphanumeric?;$B;28|))
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%String|)
- |CHAR;latex;$S;22|))
+ |CHAR;latex;$S;29|))
(DECLAIM (FTYPE (FUNCTION (|%String| |%Shell|) |%Char|)
- |CHAR;char;S$;23|))
+ |CHAR;char;S$;30|))
+
+(PUT '|CHAR;char;S$;30| '|SPADreplace| '|%s2c|)
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Char|)
- |CHAR;upperCase;2$;24|))
+ |CHAR;upperCase;2$;31|))
-(PUT '|CHAR;upperCase;2$;24| '|SPADreplace| 'CHAR-UPCASE)
+(PUT '|CHAR;upperCase;2$;31| '|SPADreplace| 'CHAR-UPCASE)
(DECLAIM (FTYPE (FUNCTION (|%Char| |%Shell|) |%Char|)
- |CHAR;lowerCase;2$;25|))
+ |CHAR;lowerCase;2$;32|))
-(PUT '|CHAR;lowerCase;2$;25| '|SPADreplace| 'CHAR-DOWNCASE)
+(PUT '|CHAR;lowerCase;2$;32| '|SPADreplace| 'CHAR-DOWNCASE)
(DEFUN |CHAR;=;2$B;1| (|a| |b| $)
(DECLARE (IGNORE $))
@@ -123,12 +158,12 @@
(DEFUN |CHAR;size;Nni;6| ($) (DECLARE (IGNORE $)) 256)
(DEFUN |CHAR;index;Pi$;7| (|n| $)
- (CODE-CHAR (LET ((#0=#:G1380 (- |n| 1)))
+ (CODE-CHAR (LET ((#0=#:G1379 (- |n| 1)))
(|check-subtype| (NOT (MINUSP #0#))
'(|NonNegativeInteger|) #0#))))
(DEFUN |CHAR;lookup;$Pi;8| (|c| $)
- (LET ((#0=#:G1382 (+ 1 (CHAR-CODE |c|))))
+ (LET ((#0=#:G1381 (+ 1 (CHAR-CODE |c|))))
(|check-subtype| (PLUSP #0#) '(|PositiveInteger|) #0#)))
(DEFUN |CHAR;char;Nni$;9| (|n| $)
@@ -147,47 +182,58 @@
(DEFUN |CHAR;escape;$;14| ($) (DECLARE (IGNORE $)) #\_)
-(DEFUN |CHAR;coerce;$Of;15| (|c| $) (DECLARE (IGNORE $)) |c|)
+(DEFUN |CHAR;newline;$;15| ($) (DECLARE (IGNORE $)) #\Newline)
-(DEFUN |CHAR;digit?;$B;16| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 32) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;carriageReturn;$;16| ($) (DECLARE (IGNORE $)) #\Return)
-(DEFUN |CHAR;hexDigit?;$B;17| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 36) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;linefeed;$;17| ($) (DECLARE (IGNORE $)) (CODE-CHAR 10))
-(DEFUN |CHAR;upperCase?;$B;18| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 38) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;formfeed;$;18| ($) (DECLARE (IGNORE $)) #\Page)
-(DEFUN |CHAR;lowerCase?;$B;19| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 40) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;backspace;$;19| ($) (DECLARE (IGNORE $)) #\Backspace)
-(DEFUN |CHAR;alphabetic?;$B;20| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 42) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;horizontalTab;$;20| ($) (DECLARE (IGNORE $)) #\Tab)
-(DEFUN |CHAR;alphanumeric?;$B;21| (|c| $)
- (SPADCALL |c| (|spadConstant| $ 44) (|getShellEntry| $ 34)))
+(DEFUN |CHAR;verticalTab;$;21| ($) (DECLARE (IGNORE $)) #\^K)
-(DEFUN |CHAR;latex;$S;22| (|c| $)
+(DEFUN |CHAR;coerce;$Of;22| (|c| $) (DECLARE (IGNORE $)) |c|)
+
+(DEFUN |CHAR;digit?;$B;23| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 39) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;hexDigit?;$B;24| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 43) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;upperCase?;$B;25| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 45) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;lowerCase?;$B;26| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 47) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;alphabetic?;$B;27| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 49) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;alphanumeric?;$B;28| (|c| $)
+ (SPADCALL |c| (|spadConstant| $ 51) (|getShellEntry| $ 41)))
+
+(DEFUN |CHAR;latex;$S;29| (|c| $)
(STRCONC "\\mbox{`" (STRCONC (MAKE-FULL-CVEC 1 |c|) "'}")))
-(DEFUN |CHAR;char;S$;23| (|s| $)
- (COND
- ((EQL (QCSIZE |s|) 1)
- (SPADCALL |s| (SPADCALL |s| (|getShellEntry| $ 52))
- (|getShellEntry| $ 53)))
- (T (|userError| "String is not a single character"))))
+(DEFUN |CHAR;char;S$;30| (|s| $)
+ (DECLARE (IGNORE $))
+ (|stringToChar| |s|))
-(DEFUN |CHAR;upperCase;2$;24| (|c| $)
+(DEFUN |CHAR;upperCase;2$;31| (|c| $)
(DECLARE (IGNORE $))
(CHAR-UPCASE |c|))
-(DEFUN |CHAR;lowerCase;2$;25| (|c| $)
+(DEFUN |CHAR;lowerCase;2$;32| (|c| $)
(DECLARE (IGNORE $))
(CHAR-DOWNCASE |c|))
(DEFUN |Character| ()
(DECLARE (SPECIAL |$ConstructorCache|))
- (PROG (#0=#:G1402)
+ (PROG (#0=#:G1407)
(RETURN
(COND
((SETQ #0# (HGET |$ConstructorCache| '|Character|))
@@ -202,7 +248,7 @@
(DEFUN |Character;| ()
(DECLARE (SPECIAL |$ConstructorCache|))
- (LET ((|dv$| (LIST '|Character|)) ($ (|newShell| 58))
+ (LET ((|dv$| (LIST '|Character|)) ($ (|newShell| 61))
(|pv$| (|buildPredVector| 0 0 NIL)))
(|setShellEntry| $ 0 |dv$|)
(|setShellEntry| $ 3 |pv$|)
@@ -224,25 +270,49 @@
(FUNCALL (|dispatchFunction| |CHAR;quote;$;13|) $))
(CONS IDENTITY
(FUNCALL (|dispatchFunction| |CHAR;escape;$;14|) $))
- (|OutputForm|) |CHAR;coerce;$Of;15| (|CharacterClass|)
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction| |CHAR;newline;$;15|) $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction|
+ |CHAR;carriageReturn;$;16|)
+ $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction| |CHAR;linefeed;$;17|)
+ $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction| |CHAR;formfeed;$;18|)
+ $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction| |CHAR;backspace;$;19|)
+ $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction|
+ |CHAR;horizontalTab;$;20|)
+ $))
+ (CONS IDENTITY
+ (FUNCALL (|dispatchFunction|
+ |CHAR;verticalTab;$;21|)
+ $))
+ (|OutputForm|) |CHAR;coerce;$Of;22| (|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;$S;22| (67 . |#|)
- (72 . |one?|) (77 . |minIndex|) (82 . |elt|)
- |CHAR;char;S$;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
- |index| 165 |hexDigit?| 170 |hash| 175 |escape| 180
- |digit?| 184 |coerce| 189 |char| 194 |before?| 204
- |alphanumeric?| 210 |alphabetic?| 215 >= 220 > 226 = 232
- <= 238 < 244)
+ |CHAR;digit?;$B;23| (35 . |hexDigit|)
+ |CHAR;hexDigit?;$B;24| (39 . |upperCase|)
+ |CHAR;upperCase?;$B;25| (43 . |lowerCase|)
+ |CHAR;lowerCase?;$B;26| (47 . |alphabetic|)
+ |CHAR;alphabetic?;$B;27| (51 . |alphanumeric|)
+ |CHAR;alphanumeric?;$B;28| (|String|) (55 . |new|)
+ (61 . |concat|) |CHAR;latex;$S;29| |CHAR;char;S$;30|
+ |CHAR;upperCase;2$;31| |CHAR;lowerCase;2$;32|
+ (|SingleInteger|))
+ '#(~= 67 |verticalTab| 73 |upperCase?| 77 |upperCase| 82
+ |space| 87 |size| 91 |random| 95 |quote| 99 |ord| 103
+ |newline| 108 |min| 112 |max| 122 |lowerCase?| 132
+ |lowerCase| 137 |lookup| 142 |linefeed| 147 |latex| 151
+ |index| 156 |horizontalTab| 161 |hexDigit?| 165 |hash| 170
+ |formfeed| 175 |escape| 179 |digit?| 183 |coerce| 188
+ |char| 193 |carriageReturn| 203 |before?| 207 |backspace|
+ 213 |alphanumeric?| 217 |alphabetic?| 222 >= 227 > 233 =
+ 239 <= 245 < 251)
'NIL
(CONS (|makeByteWordVec2| 1 '(0 0 0 0 0 0 0 0))
(CONS '#(NIL NIL NIL |SetCategory&| |OrderedType&|
@@ -250,24 +320,24 @@
(CONS '#((|OrderedFinite|) (|OrderedSet|)
(|Finite|) (|SetCategory|)
(|OrderedType|) (|BasicType|) (|Type|)
- (|CoercibleTo| 29))
- (|makeByteWordVec2| 57
+ (|CoercibleTo| 36))
+ (|makeByteWordVec2| 60
'(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)))))
+ 12 0 0 0 22 1 12 0 0 24 0 38 0 39 2
+ 38 6 40 0 41 0 38 0 43 0 38 0 45 0 38
+ 0 47 0 38 0 49 0 38 0 51 2 53 0 12 40
+ 54 2 53 0 0 0 55 2 0 6 0 0 1 0 0 0 35
+ 1 0 6 0 46 1 0 0 0 58 0 0 0 26 0 0 12
+ 13 0 0 0 25 0 0 0 27 1 0 12 0 21 0 0
+ 0 29 0 0 0 1 2 0 0 0 0 1 0 0 0 1 2 0
+ 0 0 0 1 1 0 6 0 48 1 0 0 0 59 1 0 14
+ 0 23 0 0 0 31 1 0 53 0 56 1 0 0 14 20
+ 0 0 0 34 1 0 6 0 44 1 0 60 0 1 0 0 0
+ 32 0 0 0 28 1 0 6 0 42 1 0 36 0 37 1
+ 0 0 53 57 1 0 0 12 19 0 0 0 30 2 0 6
+ 0 0 1 0 0 0 33 1 0 6 0 52 1 0 6 0 50
+ 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/string.spad.pamphlet b/src/algebra/string.spad.pamphlet
index 9f2e5883..9ea5e74f 100644
--- a/src/algebra/string.spad.pamphlet
+++ b/src/algebra/string.spad.pamphlet
@@ -42,6 +42,20 @@ Character: OrderedFinite() with
++ \spad{escape} provides the escape character, \spad{_}, which
++ is used to allow quotes and other characters {\em within}
++ strings.
+ newline: %
+ ++ \spad{newline} designates the new line character.
+ carriageReturn: %
+ ++ \spad{carriageReturn} designates carriage return.
+ linefeed: %
+ ++ \spad{linefeed} designates the line feed character.
+ formfeed: %
+ ++ \spad{formfeed} designates the form feed character.
+ backspace: %
+ ++ \spad{backspace} designates the backspace character.
+ horizontalTab: %
+ ++ \spad{horizontalTab} designates horizontal tab.
+ verticalTab: %
+ ++ \spad{verticalTab} designates vertical tab.
upperCase: % -> %
++ upperCase(c) converts a lower case letter to the corresponding
++ upper case letter. If c is not a lower case letter, then
@@ -83,6 +97,7 @@ Character: OrderedFinite() with
import %c2i: % -> NNI from Foreign Builtin
import %i2c: NNI -> % from Foreign Builtin
import %ccst: String -> % from Foreign Builtin
+ import %s2c: String -> % from Foreign Builtin
a = b == %ceq(a,b)
a < b == %clt(a,b)
@@ -98,6 +113,13 @@ Character: OrderedFinite() with
space == %ccst " "
quote == %ccst "_""
escape == %ccst "__"
+ newline == %ccst "\n"
+ carriageReturn == %ccst "\r"
+ linefeed == %i2c 10
+ formfeed == %ccst "\f"
+ backspace == %ccst "\b"
+ horizontalTab == %ccst "\t"
+ verticalTab == %ccst "\v"
coerce(c:%):OutputForm == c : OutputForm
digit? c == member?(c, digit())
hexDigit? c == member?(c, hexDigit())
@@ -109,9 +131,8 @@ Character: OrderedFinite() with
latex c ==
concat("\mbox{`", concat(new(1,c)$String, "'}")$String)$String
- char(s:String) ==
- one?(#s) => s(minIndex s)
- userError "String is not a single character"
+ char(s: String) ==
+ %s2c s
upperCase c ==
CHAR_-UPCASE(c)$Lisp : %
diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot
index 1c45d60f..4e909d60 100644
--- a/src/interp/g-opt.boot
+++ b/src/interp/g-opt.boot
@@ -450,7 +450,7 @@ $VMsideEffectFreeOperators ==
%fsinh %fcosh %ftanh %fcsch %fcoth %fsech %fasinh %facsch
%nil %pair? %lconcat %llength %lfirst %lsecond %lthird
%lreverse %lempty? %hash %ismall? %string? %f2s
- %ccst %ceq %clt %cle %cgt %cge %c2i %i2c %sname
+ %ccst %ceq %clt %cle %cgt %cge %c2i %i2c %s2c %sname
%vref %vlength %before?)
++ List of simple VM operators
diff --git a/src/interp/g-util.boot b/src/interp/g-util.boot
index 96bbe1fd..e8fe239c 100644
--- a/src/interp/g-util.boot
+++ b/src/interp/g-util.boot
@@ -61,6 +61,19 @@ usedSymbol?(s,x) ==
usedSymbol?(s,body)
or/[usedSymbol?(s,x') for x' in x]
+
+++ Return the character designated by the string `s'.
+stringToChar: %String -> %Char
+stringToChar s ==
+ #s = 1 => char s
+ s = '"\a" => $Bell
+ s = '"\n" => $Newline
+ s = '"\f" => $FormFeed
+ s = '"\r" => $CarriageReturn
+ s = '"\b" => $Backspace
+ s = '"\t" => $HorizontalTab
+ s = '"\v" => $VerticalTab
+ error strconc("invalid character designator: ", s)
--% VM forms
@@ -253,9 +266,14 @@ expandBcompl ['%bcompl,x] ==
-- Character operations
expandCcst ['%ccst,s] ==
+ -- FIXME: this expander should return forms, instead of character constants
not string? s => error "operand is not a string constant"
- #s ~= 1 => error "string constant must contain exactly one character"
- char s
+ stringToChar s
+
+++ string-to-character conversion.
+expandS2c ['%s2c, x] ==
+ string? x => expandCcst ['%ccst, x]
+ ['stringToChar, x]
-- Integer operations
expandIneg ['%ineg,x] ==
@@ -364,7 +382,7 @@ for x in [
['%and, :'AND],
['%or, :'OR],
- -- character binary operations
+ -- character operations
['%ceq, :'CHAR_=],
['%clt, :'CHAR_<],
['%cle, :'CHAR_<_=],
@@ -479,6 +497,7 @@ for x in [
['%bcompl, :function expandBcompl],
['%ccst, :function expandCcst],
+ ['%s2c, :function expandS2c],
['%ieq, :function expandIeq],
['%igt, :function expandIgt],
diff --git a/src/interp/spad.lisp b/src/interp/spad.lisp
index 4342ca96..8410f52e 100644
--- a/src/interp/spad.lisp
+++ b/src/interp/spad.lisp
@@ -42,7 +42,6 @@
;;; Common Block
-(defconstant |$Newline| #\Newline)
(defvar |$preserveSystemLisplib| t "if nil finalizeLisplib does MA REP")
(defvar |$reportInstantiations| nil)
(defvar |$reportEachInstantiation| nil)
diff --git a/src/interp/sys-macros.lisp b/src/interp/sys-macros.lisp
index 0979262e..fac17612 100644
--- a/src/interp/sys-macros.lisp
+++ b/src/interp/sys-macros.lisp
@@ -42,6 +42,16 @@
;; -*- Charcters and Strings -*-
;;
+;; Special character constants
+(defconstant |$Bell| (code-char 7))
+(defconstant |$Backspace| #\Backspace)
+(defconstant |$HorizontalTab| #\Tab)
+(defconstant |$Newline| #\Newline)
+(defconstant |$VerticalTab| (code-char 11))
+(defconstant |$FormFeed| #\Page)
+(defconstant |$CarriageReturn| #\Return)
+
+
(defmacro |char| (arg)
(cond ((stringp arg)
(character arg))
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index f8919e2d..dc9722a4 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(2300174 . 3497194935)
+(2300691 . 3498909339)
(-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
NIL
(-19 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.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}")))
@@ -38,7 +38,7 @@ NIL
NIL
(-27)
((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-28 S R)
((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
@@ -46,7 +46,7 @@ NIL
NIL
(-29 R)
((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4497 . T) (-4495 . T) (-4494 . T) ((-4502 "*") . T) (-4493 . T) (-4498 . T) (-4492 . T))
+((-4504 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4500 . T) (-4505 . T) (-4499 . T))
NIL
(-30)
((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted.")))
@@ -56,14 +56,14 @@ 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 -2155)
+(-32 R -2174)
((|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 -1069) (QUOTE (-578)))))
(-33 S)
((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4500)))
+((|HasAttribute| |#1| (QUOTE -4507)))
(-34)
((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects.")))
NIL
@@ -74,7 +74,7 @@ NIL
NIL
(-36 |Key| |Entry|)
((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}.")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
@@ -82,17 +82,17 @@ NIL
NIL
(-38 R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-39 UP)
((|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 -2155 UP UPUP -3724)
+(-40 -2174 UP UPUP -2027)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
-((-4493 |has| (-421 |#2|) (-376)) (-4498 |has| (-421 |#2|) (-376)) (-4492 |has| (-421 |#2|) (-376)) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2230 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2230 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2230 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2230 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2230 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2230 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))))
-(-41 R -2155)
+((-4500 |has| (-421 |#2|) (-376)) (-4505 |has| (-421 |#2|) (-376)) (-4499 |has| (-421 |#2|) (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2225 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))))
+(-41 R -2174)
((|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| $)) $) "\\spad{numer(x)} \\undocumented")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -444) (|devaluate| |#1|)))))
@@ -106,23 +106,23 @@ NIL
((|HasCategory| |#1| (QUOTE (-319))))
(-44 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra.")))
-((-4497 |has| |#1| (-570)) (-4495 . T) (-4494 . T))
+((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T))
((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570))))
(-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.")))
-((-4500 . T) (-4501 . T))
-((-2230 (-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|))))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-871))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))))
+((-4507 . T) (-4508 . T))
+((-2225 (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|))))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))))
(-46 S R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}.")))
@@ -130,7 +130,7 @@ NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-51 S)
((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}.")))
@@ -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 -2155)
+(-54 |Base| R -2174)
((|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
@@ -158,7 +158,7 @@ NIL
NIL
(-57 R |Row| |Col|)
((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-58 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")))
@@ -166,65 +166,65 @@ NIL
NIL
(-59 S)
((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
-(-61 -4107)
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+(-61 -2178)
((|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 -4107)
+(-62 -2178)
((|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 -4107)
+(-63 -2178)
((|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 -4107)
+(-64 -2178)
((|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 -4107)
+(-65 -2178)
((|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 -4107)
+(-66 -2178)
((|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 -4107)
+(-67 -2178)
((|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 -4107)
+(-68 -2178)
((|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 -4107)
+(-69 -2178)
((|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 -4107)
+(-70 -2178)
((|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 -4107)
+(-71 -2178)
((|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 -4107)
+(-72 -2178)
((|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 -4107)
+(-73 -2178)
((|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 -4107)
+(-74 -2178)
((|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 -4107)
+(-77 -2178)
((|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 -4107)
+(-78 -2178)
((|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 -4107)
+(-79 -2178)
((|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 -4107)
+(-80 -2178)
((|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 -4107)
+(-81 -2178)
((|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 -4107)
+(-82 -2178)
((|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 -4107)
+(-83 -2178)
((|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 -4107)
+(-84 -2178)
((|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 -4107)
+(-85 -2178)
((|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 -4107)
+(-86 -2178)
((|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 -4107)
+(-87 -2178)
((|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 -4107)
+(-88 -2178)
((|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 -4107)
+(-89 -2178)
((|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
@@ -294,8 +294,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-376))))
(-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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-92 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
NIL
@@ -318,15 +318,15 @@ NIL
NIL
(-97)
((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")))
-((-4500 . T))
+((-4507 . T))
NIL
(-98)
((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements.")))
-((-4500 . T) ((-4502 "*") . T) (-4501 . T) (-4497 . T) (-4495 . T) (-4494 . T) (-4493 . T) (-4498 . T) (-4492 . T) (-4491 . T) (-4490 . T) (-4489 . T) (-4488 . T) (-4496 . T) (-4499 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4487 . T))
+((-4507 . T) ((-4509 "*") . T) (-4508 . T) (-4504 . T) (-4502 . T) (-4501 . T) (-4500 . T) (-4505 . T) (-4499 . T) (-4498 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4503 . T) (-4506 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4494 . T))
NIL
(-99 R)
((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-100 R UP)
((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}.")))
@@ -342,15 +342,15 @@ NIL
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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-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
-((|HasAttribute| |#1| (QUOTE (-4502 "*"))))
+((|HasAttribute| |#1| (QUOTE (-4509 "*"))))
(-105)
((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table")))
-((-4500 . T))
+((-4507 . T))
NIL
(-106 A S)
((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed.")))
@@ -358,23 +358,23 @@ NIL
NIL
(-107 S)
((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed.")))
-((-4501 . T))
+((-4508 . T))
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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2230 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
(-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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
NIL
NIL
(-110)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -321) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-112) (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-112) (QUOTE (-102))))
(-111 R S)
((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-112)
((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")))
@@ -396,22 +396,22 @@ NIL
((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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
-(-117 -2155 UP)
+(-117 -2174 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
(-118 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-119 |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}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-118 |#1|) (QUOTE (-938))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-118 |#1|) (QUOTE (-1053))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2230 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (|HasCategory| (-118 |#1|) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-118 |#1|) (QUOTE (-938))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-118 |#1|) (QUOTE (-1053))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2225 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-938)))) (|HasCategory| (-118 |#1|) (QUOTE (-147)))))
(-120 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| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)))
+((|HasAttribute| |#1| (QUOTE -4508)))
(-121 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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
@@ -422,15 +422,15 @@ NIL
NIL
(-123 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")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-124 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
NIL
NIL
(-125)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-126 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -438,20 +438,20 @@ NIL
NIL
(-127 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-128 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-129 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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-130)
((|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.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) (-2230 (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-131) (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-131) (QUOTE (-871))) (-2230 (|HasCategory| (-131) (QUOTE (-102))) (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-131) (QUOTE (-102))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131)))))) (-2225 (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-131) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-131) (QUOTE (-871))) (-2225 (|HasCategory| (-131) (QUOTE (-102))) (|HasCategory| (-131) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-131) (QUOTE (-102))) (-12 (|HasCategory| (-131) (QUOTE (-1131))) (|HasCategory| (-131) (LIST (QUOTE -321) (QUOTE (-131))))))
(-131)
((|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
@@ -474,13 +474,13 @@ NIL
NIL
(-136)
((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")))
-(((-4502 "*") . T))
+(((-4509 "*") . T))
NIL
-(-137 |minix| -3755 S T$)
+(-137 |minix| -2591 S T$)
((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}.")))
NIL
NIL
-(-138 |minix| -3755 R)
+(-138 |minix| -2591 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $) "\\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
@@ -502,8 +502,8 @@ NIL
NIL
(-143)
((|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}.")))
-((-4500 . T) (-4490 . T) (-4501 . T))
-((-2230 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
+((-4507 . T) (-4497 . T) (-4508 . T))
+((-2225 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
(-144 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{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{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
@@ -513,12 +513,12 @@ NIL
NIL
NIL
(-146)
-((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape} provides the escape character,{} \\spad{_},{} which is used to allow quotes and other characters {\\em within} strings.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}.")))
+((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|verticalTab| (($) "\\spad{verticalTab} designates vertical tab.")) (|horizontalTab| (($) "\\spad{horizontalTab} designates horizontal tab.")) (|backspace| (($) "\\spad{backspace} designates the backspace character.")) (|formfeed| (($) "\\spad{formfeed} designates the form feed character.")) (|linefeed| (($) "\\spad{linefeed} designates the line feed character.")) (|carriageReturn| (($) "\\spad{carriageReturn} designates carriage return.")) (|newline| (($) "\\spad{newline} designates the new line character.")) (|escape| (($) "\\spad{escape} provides the escape character,{} \\spad{_},{} which is used to allow quotes and other characters {\\em within} strings.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}.")))
NIL
NIL
(-147)
((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-148 R)
((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}.")))
@@ -526,9 +526,9 @@ NIL
NIL
(-149)
((|constructor| (NIL "Rings of Characteristic Zero.")))
-((-4497 . T))
+((-4504 . T))
NIL
-(-150 -2155 UP UPUP)
+(-150 -2174 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
@@ -539,14 +539,14 @@ NIL
(-152 A S)
((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasAttribute| |#1| (QUOTE -4500)))
+((|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasAttribute| |#1| (QUOTE -4507)))
(-153 S)
((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List.")))
NIL
NIL
(-154 |n| K Q)
((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element.")))
-((-4495 . T) (-4494 . T) (-4497 . T))
+((-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-155)
((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function.")))
@@ -568,7 +568,7 @@ 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
-(-160 R -2155)
+(-160 R -2174)
((|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
@@ -599,10 +599,10 @@ NIL
(-167 S R)
((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})")))
NIL
-((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4496)) (|HasAttribute| |#2| (QUOTE -4499)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570))))
+((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570))))
(-168 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})")))
-((-4493 -2230 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4496 |has| |#1| (-6 -4496)) (-4499 |has| |#1| (-6 -4499)) (-3921 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 -2225 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4503 |has| |#1| (-6 -4503)) (-4506 |has| |#1| (-6 -4506)) (-1924 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-169 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.")))
@@ -618,8 +618,8 @@ NIL
NIL
(-172 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}.")))
-((-4493 -2230 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4496 |has| |#1| (-6 -4496)) (-4499 |has| |#1| (-6 -4499)) (-3921 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
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+((-4500 -2225 (|has| |#1| (-570)) (-12 (|has| |#1| (-319)) (|has| |#1| (-938)))) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4503 |has| |#1| (-6 -4503)) (-4506 |has| |#1| (-6 -4506)) (-1924 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
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(-173 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
@@ -630,7 +630,7 @@ NIL
NIL
(-175)
((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative.")))
-(((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-176)
((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations.")))
@@ -638,7 +638,7 @@ NIL
NIL
(-177 R)
((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}.")))
-(((-4502 "*") . T) (-4493 . T) (-4498 . T) (-4492 . T) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") . T) (-4500 . T) (-4505 . T) (-4499 . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-178)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}.")))
@@ -692,7 +692,7 @@ NIL
((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-191 R -2155)
+(-191 R -2174)
((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels.")))
NIL
NIL
@@ -804,23 +804,23 @@ NIL
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis.")))
NIL
NIL
-(-219 -2155 UP UPUP R)
+(-219 -2174 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
-(-220 -2155 FP)
+(-220 -2174 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
(-221)
((|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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2230 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
(-222)
((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-223 R -2155)
+(-223 R -2174)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
@@ -834,19 +834,19 @@ NIL
NIL
(-226 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-227 |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}.")))
-((-4497 . T))
+((-4504 . T))
NIL
-(-228 R -2155)
+(-228 R -2174)
((|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
(-229)
((|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}.")))
-((-3909 . T) (-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-230)
((|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{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * 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*\\%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*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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)}.}")))
@@ -854,19 +854,19 @@ NIL
NIL
(-231 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}")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4502 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-232 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
NIL
(-233 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.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-234 R)
((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-235 S T$)
((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}.")))
@@ -878,7 +878,7 @@ NIL
NIL
(-237 R)
((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-238 S)
((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")))
@@ -890,36 +890,36 @@ NIL
NIL
(-240)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")))
-((-4497 . T))
+((-4504 . T))
NIL
(-241 A S)
((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4500)))
+((|HasAttribute| |#1| (QUOTE -4507)))
(-242 S)
((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-243)
((|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
-(-244 S -3755 R)
+(-244 S -2591 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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
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+((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4504)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1131))))
+(-245 -2591 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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")))
-((-4494 |has| |#2| (-1080)) (-4495 |has| |#2| (-1080)) (-4497 |has| |#2| (-6 -4497)) (-4500 . T))
+((-4501 |has| |#2| (-1080)) (-4502 |has| |#2| (-1080)) (-4504 |has| |#2| (-6 -4504)) (-4507 . T))
NIL
-(-246 -3755 A B)
+(-246 -2591 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
-(-247 -3755 R)
+(-247 -2591 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.")))
-((-4494 |has| |#2| (-1080)) (-4495 |has| |#2| (-1080)) (-4497 |has| |#2| (-6 -4497)) (-4500 . T))
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(-248)
((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type.")))
NIL
@@ -930,7 +930,7 @@ NIL
NIL
(-250)
((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")))
-((-4493 . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-251 S)
((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")))
@@ -938,20 +938,20 @@ NIL
NIL
(-252 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}")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-253 M)
((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}")))
NIL
NIL
(-254 R)
((|constructor| (NIL "Category of modules that extend differential rings. \\blankline")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-255 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial")))
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(-256)
((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\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| (|DomainConstructor|)) $) "\\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'}.")))
NIL
@@ -966,23 +966,23 @@ NIL
NIL
(-259 |n| R M S)
((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
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(-260 |n| R S)
((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view.")))
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(QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#3| (QUOTE (-376))) (-2225 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1080)))) (-2225 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-815))) (-2225 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871)))) (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (QUOTE (-381))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578)))))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (|HasCategory| |#3| (QUOTE (-240))) (-2225 (|HasCategory| |#3| (QUOTE (-240))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080))))) (-2225 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#3| (QUOTE (-1131))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-21)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-175)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-240)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-376)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-381)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-748)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-815)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-871)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1131))))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| (-578) (QUOTE (-871))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578))))) (-2225 (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207)))))) (-2225 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080))))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-2225 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1131)))) (-2225 (|HasAttribute| |#3| (QUOTE -4504)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))))
(-261 A R S V E)
((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.")))
NIL
((|HasCategory| |#2| (QUOTE (-240))))
(-262 R S V E)
((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-263 S)
((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}.")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-264)
((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
@@ -1030,8 +1030,8 @@ NIL
NIL
(-275 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")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
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+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
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(-276 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}.")) (|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
@@ -1076,11 +1076,11 @@ 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
-(-287 R -2155)
+(-287 R -2174)
((|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{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
-(-288 R -2155)
+(-288 R -2174)
((|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{ki} was rewritten as \\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
@@ -1106,7 +1106,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))))
(-294 S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-295 S)
((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}.")))
@@ -1127,18 +1127,18 @@ NIL
(-299 S |Dom| |Im|)
((|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!| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2|) "\\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| ((|#3| $ |#2| |#3|) "\\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
-((|HasAttribute| |#1| (QUOTE -4501)))
+((|HasAttribute| |#1| (QUOTE -4508)))
(-300 |Dom| |Im|)
((|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
-(-301 S R |Mod| -3108 -2026 |exactQuo|)
+(-301 S R |Mod| -1606 -3949 |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}")) (|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| $) "\\spad{modulus(x)} \\undocumented")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-302)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-4493 . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-303)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment")))
@@ -1154,21 +1154,21 @@ NIL
NIL
(-306 S)
((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation.")))
-((-4497 -2230 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4494 |has| |#1| (-1080)) (-4495 |has| |#1| (-1080)))
-((|HasCategory| |#1| (QUOTE (-376))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2230 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-314))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2230 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2230 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748))))
+((-4504 -2225 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4501 |has| |#1| (-1080)) (-4502 |has| |#1| (-1080)))
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(-307 |Key| |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))))
(-308)
((|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
-(-309 -2155 S)
+(-309 -2174 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
-(-310 E -2155)
+(-310 E -2174)
((|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
@@ -1206,7 +1206,7 @@ NIL
NIL
(-319)
((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-320 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
@@ -1216,7 +1216,7 @@ 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
-(-322 -2155)
+(-322 -2174)
((|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
@@ -1230,8 +1230,8 @@ NIL
NIL
(-325 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))}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
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+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
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(-326 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
@@ -1242,9 +1242,9 @@ NIL
NIL
(-328 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.")))
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-(-329 R -2155)
+((-4504 -2225 (-12 (|has| |#1| (-570)) (-2225 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) ((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-570)) (-4499 |has| |#1| (-570)))
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+(-329 R -2174)
((|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{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + 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
@@ -1254,8 +1254,8 @@ NIL
NIL
(-331 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.")))
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(-332 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
@@ -1266,7 +1266,7 @@ NIL
NIL
(-334 S)
((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-814))))
(-335 S E)
((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
@@ -1282,19 +1282,19 @@ NIL
((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))))
(-338 R E)
((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-339 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.")))
-((-4501 . T) (-4500 . T))
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-(-340 S -2155)
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+(-340 S -2174)
((|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 (-381))))
-(-341 -2155)
+(-341 -2174)
((|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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-342)
((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")))
@@ -1316,15 +1316,15 @@ 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
-(-347 S -2155 UP UPUP R)
+(-347 S -2174 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
-(-348 -2155 UP UPUP R)
+(-348 -2174 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
-(-349 -2155 UP UPUP R)
+(-349 -2174 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
@@ -1338,32 +1338,32 @@ NIL
NIL
(-352 |basicSymbols| |subscriptedSymbols| R)
((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-392)))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578)))))
(-353 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}.")))
NIL
NIL
-(-354 S -2155 UP UPUP)
+(-354 S -2174 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(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 (-381))) (|HasCategory| |#2| (QUOTE (-376))))
-(-355 -2155 UP UPUP)
+(-355 -2174 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(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.")))
-((-4493 |has| (-421 |#2|) (-376)) (-4498 |has| (-421 |#2|) (-376)) (-4492 |has| (-421 |#2|) (-376)) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 |has| (-421 |#2|) (-376)) (-4505 |has| (-421 |#2|) (-376)) (-4499 |has| (-421 |#2|) (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-356 |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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
(-357 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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
(-358 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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
(-359 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
@@ -1378,33 +1378,33 @@ NIL
NIL
(-362)
((|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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
-(-363 R UP -2155)
+(-363 R UP -2174)
((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
(-364 |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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
(-365 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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
(-366 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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
(-367 |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}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| (-939 |#1|) (QUOTE (-147))) (|HasCategory| (-939 |#1|) (QUOTE (-381)))) (|HasCategory| (-939 |#1|) (QUOTE (-149))) (|HasCategory| (-939 |#1|) (QUOTE (-381))) (|HasCategory| (-939 |#1|) (QUOTE (-147))))
(-368 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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
-(-369 -2155 GF)
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+(-369 -2174 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
@@ -1412,21 +1412,21 @@ 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
-(-371 -2155 FP FPP)
+(-371 -2174 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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
(-372 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}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147))))
(-373 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
NIL
(-374 S)
((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-375 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
@@ -1434,7 +1434,7 @@ NIL
NIL
(-376)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-377 |Name| S)
((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input.")))
@@ -1450,7 +1450,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-570))))
(-380 R)
((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-4497 |has| |#1| (-570)) (-4495 . T) (-4494 . T))
+((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T))
NIL
(-381)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set.")))
@@ -1462,7 +1462,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376))))
(-383 R UP)
((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-384 S A R B)
((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain.")))
@@ -1471,14 +1471,14 @@ NIL
(-385 A S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))))
+((|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))))
(-386 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-4500 . T))
+((-4507 . T))
NIL
(-387 |VarSet| R)
((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4495 . T) (-4494 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4502 . T) (-4501 . T))
NIL
(-388 S V)
((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm.")))
@@ -1498,7 +1498,7 @@ NIL
NIL
(-392)
((|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{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}.")))
-((-4483 . T) (-4491 . T) (-3909 . T) (-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4490 . T) (-4498 . T) (-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-393 |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}.")))
@@ -1506,11 +1506,11 @@ NIL
NIL
(-394 R S)
((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((|HasCategory| |#1| (QUOTE (-175))))
(-395 R |Basis|)
((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-396)
((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}.")))
@@ -1522,7 +1522,7 @@ NIL
NIL
(-398 R S)
((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))))
(-399 S)
((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
@@ -1534,7 +1534,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-871))))
(-401)
((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-402)
((|constructor| (NIL "This domain provides an interface to names in the file system.")))
@@ -1546,13 +1546,13 @@ NIL
NIL
(-404 |n| |class| R)
((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-405)
((|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
-(-406 -2155 UP UPUP R)
+(-406 -2174 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
@@ -1576,11 +1576,11 @@ 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
-(-412 -4107 |returnType| -4086 |symbols|)
+(-412 -2178 |returnType| -3588 |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
-(-413 -2155 UP)
+(-413 -2174 UP)
((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 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.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
@@ -1594,15 +1594,15 @@ NIL
NIL
(-416)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-417 S)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\".")))
NIL
-((|HasAttribute| |#1| (QUOTE -4483)) (|HasAttribute| |#1| (QUOTE -4491)))
+((|HasAttribute| |#1| (QUOTE -4490)) (|HasAttribute| |#1| (QUOTE -4498)))
(-418)
((|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\".")))
-((-3909 . T) (-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-419 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.")))
@@ -1614,15 +1614,15 @@ NIL
NIL
(-421 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.")))
-((-4487 -12 (|has| |#1| (-6 -4498)) (|has| |#1| (-466)) (|has| |#1| (-6 -4487))) (-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
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(-422 S R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
NIL
(-423 R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-424 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
@@ -1636,11 +1636,11 @@ NIL
((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}")))
NIL
NIL
-(-427 R -2155 UP A)
+(-427 R -2174 UP A)
((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}.")))
-((-4497 . T))
+((-4504 . T))
NIL
-(-428 R -2155 UP A |ibasis|)
+(-428 R -2174 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")))
NIL
((|HasCategory| |#4| (LIST (QUOTE -1069) (|devaluate| |#2|))))
@@ -1654,12 +1654,12 @@ NIL
((|HasCategory| |#2| (QUOTE (-376))))
(-431 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4497 |has| |#1| (-570)) (-4495 . T) (-4494 . T))
+((-4504 |has| |#1| (-570)) (-4502 . T) (-4501 . T))
NIL
(-432 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.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2230 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466))))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466))))
(-433 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
@@ -1686,17 +1686,17 @@ NIL
((|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381))))
(-439 S)
((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-4500 . T) (-4490 . T) (-4501 . T))
+((-4507 . T) (-4497 . T) (-4508 . T))
NIL
-(-440 R -2155)
+(-440 R -2174)
((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")))
NIL
NIL
(-441 R E)
((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series")))
-((-4487 -12 (|has| |#1| (-6 -4487)) (|has| |#2| (-6 -4487))) (-4494 . T) (-4495 . T) (-4497 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -4487)) (|HasAttribute| |#2| (QUOTE -4487))))
-(-442 R -2155)
+((-4494 -12 (|has| |#1| (-6 -4494)) (|has| |#2| (-6 -4494))) (-4501 . T) (-4502 . T) (-4504 . T))
+((-12 (|HasAttribute| |#1| (QUOTE -4494)) (|HasAttribute| |#2| (QUOTE -4494))))
+(-442 R -2174)
((|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
@@ -1706,17 +1706,17 @@ NIL
((|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))))
(-444 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}.")))
-((-4497 -2230 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) ((-4502 "*") |has| |#1| (-570)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-570)) (-4492 |has| |#1| (-570)))
+((-4504 -2225 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) ((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-570)) (-4499 |has| |#1| (-570)))
NIL
-(-445 R -2155)
+(-445 R -2174)
((|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
-(-446 R -2155)
+(-446 R -2174)
((|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{ai = 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{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.")))
NIL
((|HasCategory| |#2| (QUOTE (-27))))
-(-447 R -2155)
+(-447 R -2174)
((|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
@@ -1724,7 +1724,7 @@ 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
-(-449 R -2155 UP)
+(-449 R -2174 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 -1069) (QUOTE (-48)))))
@@ -1756,7 +1756,7 @@ 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
-(-457 R UP -2155)
+(-457 R UP -2174)
((|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
@@ -1794,16 +1794,16 @@ NIL
NIL
(-466)
((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-467 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed")))
-((-4497 |has| (-421 (-981 |#1|)) (-570)) (-4495 . T) (-4494 . T))
+((-4504 |has| (-421 (-981 |#1|)) (-570)) (-4502 . T) (-4501 . T))
((|HasCategory| (-421 (-981 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| (-421 (-981 |#1|)) (QUOTE (-570))))
(-468 |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")))
-(((-4502 "*") |has| |#2| (-175)) (-4493 |has| |#2| (-570)) (-4498 |has| |#2| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#2| (QUOTE (-938))) (-2230 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2230 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4498)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
+(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-938))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
(-469 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
@@ -1830,7 +1830,7 @@ NIL
NIL
(-475 |vl| R IS E |ff| P)
((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-476 E V R P Q)
((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
@@ -1838,7 +1838,7 @@ NIL
NIL
(-477 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102))))
(-478 S R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}.")))
@@ -1868,7 +1868,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-485 |lv| -2155 R)
+(-485 |lv| -2174 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
@@ -1878,23 +1878,23 @@ NIL
NIL
(-487)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-488 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
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+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1369) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
(-489 |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.")))
-((-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))))
+((-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))))
(-490 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)}")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102))))
(-491)
((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-492)
((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'.")))
@@ -1902,29 +1902,29 @@ NIL
NIL
(-493 |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.")))
-((-4500 . T) (-4501 . T))
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+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))))
(-494)
((|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
NIL
(-495 |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")))
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-(-496 -3755 S)
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+(-496 -2591 S)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-4494 |has| |#2| (-1080)) (-4495 |has| |#2| (-1080)) (-4497 |has| |#2| (-6 -4497)) (-4500 . T))
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(-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1080)))) (-2230 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE 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(-497)
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NIL
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(-498 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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
-(-499 -2155 UP UPUP R)
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+(-499 -2174 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
@@ -1934,12 +1934,12 @@ NIL
NIL
(-501)
((|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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2230 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
(-502 A S)
((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4500)) (|HasAttribute| |#1| (QUOTE -4501)) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))
+((|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))
(-503 S)
((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
@@ -1960,33 +1960,33 @@ NIL
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-508 -2155 UP |AlExt| |AlPol|)
+(-508 -2174 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
(-509)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-578)))))
(-510 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-511 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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-512 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
-(-513 R UP -2155)
+(-513 R UP -2174)
((|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{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\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{mi} is given by \\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{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{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
(-514 |mn|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -321) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-112) (QUOTE (-871))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-112) (QUOTE (-1131))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-112) (QUOTE (-102))))
(-515 K R UP L)
((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.")))
@@ -2000,7 +2000,7 @@ 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{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{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
-(-518 -2155 |Expon| |VarSet| |DPoly|)
+(-518 -2174 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}.")))
NIL
((|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-1207)))))
@@ -2050,36 +2050,36 @@ NIL
((|HasCategory| |#2| (QUOTE (-814))))
(-530 S |mn|)
((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-531)
((|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
NIL
(-532 |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}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((-2225 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147))))
(-533 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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-534 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.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-535 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
-((|HasAttribute| |#3| (QUOTE -4501)))
+((|HasAttribute| |#3| (QUOTE -4508)))
(-536 R |Row| |Col| M QF |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "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. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field.")))
NIL
-((|HasAttribute| |#7| (QUOTE -4501)))
+((|HasAttribute| |#7| (QUOTE -4508)))
(-537 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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4502 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-538)
((|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
@@ -2112,7 +2112,7 @@ 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
((-12 (|HasCategory| (-793) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131)))))
-(-546 K -2155 |Par|)
+(-546 K -2174 |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
@@ -2136,7 +2136,7 @@ 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
-(-552 K -2155 |Par|)
+(-552 K -2174 |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
@@ -2166,7 +2166,7 @@ NIL
NIL
(-559)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
-((-4498 . T) (-4499 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-560)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits.")))
@@ -2186,13 +2186,13 @@ NIL
NIL
(-564 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))))
-(-565 R -2155)
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))))
+(-565 R -2174)
((|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
-(-566 R0 -2155 UP UPUP R)
+(-566 R0 -2174 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
@@ -2202,7 +2202,7 @@ NIL
NIL
(-568 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.")))
-((-3909 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-1915 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-569 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.")))
@@ -2210,9 +2210,9 @@ NIL
NIL
(-570)
((|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.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
-(-571 R -2155)
+(-571 R -2174)
((|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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(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
@@ -2224,7 +2224,7 @@ 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
-(-574 R -2155 L)
+(-574 R -2174 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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 -678) (|devaluate| |#2|))))
@@ -2232,31 +2232,31 @@ 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
-(-576 -2155 UP UPUP R)
+(-576 -2174 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
-(-577 -2155 UP)
+(-577 -2174 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
(-578)
((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")))
-((-4482 . T) (-4488 . T) (-4492 . T) (-4487 . T) (-4498 . T) (-4499 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4489 . T) (-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-579)
((|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
-(-580 R -2155 L)
+(-580 R -2174 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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 -678) (|devaluate| |#2|))))
-(-581 R -2155)
+(-581 R -2174)
((|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 -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-648)))))
-(-582 -2155 UP)
+(-582 -2174 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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(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
@@ -2264,27 +2264,27 @@ 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
-(-584 -2155)
+(-584 -2174)
((|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, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(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
(-585 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.")))
-((-3909 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-1915 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-586)
((|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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
-(-587 R -2155)
+(-587 R -2174)
((|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 -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-648))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-570))))
-(-588 -2155 UP)
+(-588 -2174 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' + +/[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(+,[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(+,[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
-(-589 R -2155)
+(-589 R -2174)
((|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
@@ -2306,21 +2306,21 @@ NIL
NIL
(-594 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-595 |p|)
((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381))))
(-596)
((|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
-(-597 R -2155)
+(-597 R -2174)
((|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
-(-598 E -2155)
+(-598 E -2174)
((|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
@@ -2328,9 +2328,9 @@ NIL
((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}")))
NIL
NIL
-(-600 -2155)
+(-600 -2174)
((|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}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207)))))
(-601 I)
((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise")))
@@ -2358,19 +2358,19 @@ NIL
NIL
(-607 |mn|)
((|constructor| (NIL "This domain implements low-level strings")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2230 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2230 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2225 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2225 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
(-608 E V R P)
((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}.")))
NIL
NIL
(-609 |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}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|)))) (|HasCategory| (-578) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -2411) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|)))) (|HasCategory| (-578) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-578))))))
(-610 |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}.")) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}")))
-(((-4502 "*") |has| |#1| (-570)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-570)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-570))))
(-611)
((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context")))
@@ -2384,7 +2384,7 @@ 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
-(-614 R -2155 FG)
+(-614 R -2174 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{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{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
@@ -2394,12 +2394,12 @@ NIL
NIL
(-616 R |mn|)
((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-617 S |Index| |Entry|)
((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)) (|HasCategory| |#2| (QUOTE (-871))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#3| (QUOTE (-1131))))
+((|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-871))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#3| (QUOTE (-1131))))
(-618 |Index| |Entry|)
((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
NIL
@@ -2410,8 +2410,8 @@ NIL
NIL
(-620 R A)
((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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).")))
-((-4497 -2230 (-2320 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4495 . T) (-4494 . T))
-((-2230 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))))
+((-4504 -2225 (-3534 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4502 . T) (-4501 . T))
+((-2225 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))))
(-621)
((|constructor| (NIL "This is the datatype for the \\spad{JVM} bytecodes.")))
NIL
@@ -2438,15 +2438,15 @@ NIL
NIL
(-627 |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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (QUOTE (-102))))
(-628 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
NIL
(-629 |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| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-630 R S)
((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented")))
@@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-634 -2155 UP)
+(-634 -2174 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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
@@ -2486,19 +2486,19 @@ NIL
NIL
(-639 R)
((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-640 A R S)
((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-870))))
-(-641 R -2155)
+(-641 R -2174)
((|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
(-642 R UP)
((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented")))
-((-4495 . T) (-4494 . T) ((-4502 "*") . T) (-4493 . T) (-4497 . T))
+((-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4500 . T) (-4504 . T))
((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))
(-643 R E V P TS ST)
((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional.")))
@@ -2514,7 +2514,7 @@ NIL
NIL
(-646 |VarSet| R |Order|)
((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-647 R |ls|)
((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}.")))
@@ -2524,30 +2524,30 @@ NIL
((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}.")))
NIL
NIL
-(-649 R -2155)
+(-649 R -2174)
((|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{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\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
-(-650 |lv| -2155)
+(-650 |lv| -2174)
((|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
(-651)
((|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}.")) (|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.")))
-((-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2754) (QUOTE (-52))))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 (-1189)) (|:| -2754 (-52))) (QUOTE (-1131))))
+((-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -2078) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1189)) (|:| -2078 (-52))) (QUOTE (-1131))))
(-652 S R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
NIL
((|HasCategory| |#2| (QUOTE (-376))))
(-653 R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4495 . T) (-4494 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4502 . T) (-4501 . T))
NIL
(-654 R A)
((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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).")))
-((-4497 -2230 (-2320 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4495 . T) (-4494 . T))
-((-2230 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))))
+((-4504 -2225 (-3534 (|has| |#2| (-380 |#1|)) (|has| |#1| (-570))) (-12 (|has| |#2| (-431 |#1|)) (|has| |#1| (-570)))) (-4502 . T) (-4501 . T))
+((-2225 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -431) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))))
(-655 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
@@ -2563,10 +2563,10 @@ NIL
(-658 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
-((-2309 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376))))
+((-3523 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376))))
(-659 K B)
((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((-12 (|HasCategory| (-657 |#2|) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-1131)))))
(-660 R)
((|constructor| (NIL "An extension of left-module 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}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}.")))
@@ -2574,7 +2574,7 @@ NIL
NIL
(-661 K B)
((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-662 S)
((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet.")))
@@ -2594,8 +2594,8 @@ NIL
NIL
(-666 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} is the empty list.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-667 T$)
((|constructor| (NIL "This domain represents AST for Spad literals.")))
NIL
@@ -2606,8 +2606,8 @@ NIL
NIL
(-669 S)
((|substitute| (($ |#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.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-670 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
@@ -2619,22 +2619,22 @@ NIL
(-672 A S)
((|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| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\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}..) )}.") (($ |#2| $ (|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,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\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|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)))
+((|HasAttribute| |#1| (QUOTE -4508)))
(-673 S)
((|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,{}..))}.")) (|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
-(-674 R -2155 L)
+(-674 R -2174 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
(-675 A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376))))
(-676 A M)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376))))
(-677 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}.")))
@@ -2642,15 +2642,15 @@ NIL
((|HasCategory| |#2| (QUOTE (-376))))
(-678 A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
-(-679 -2155 UP)
+(-679 -2174 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))))
-(-680 A -4254)
+(-680 A -3370)
((|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}}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376))))
(-681 A L)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")))
@@ -2666,7 +2666,7 @@ NIL
NIL
(-684 M R S)
((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
((|HasCategory| |#1| (QUOTE (-813))))
(-685 R)
((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists.")))
@@ -2674,7 +2674,7 @@ NIL
NIL
(-686 |VarSet| R)
((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4495 . T) (-4494 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4502 . T) (-4501 . T))
((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175))))
(-687 A S)
((|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| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}.")))
@@ -2682,13 +2682,13 @@ NIL
NIL
(-688 S)
((|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}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
-(-689 -2155)
+(-689 -2174)
((|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
-(-690 -2155 |Row| |Col| M)
+(-690 -2174 |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
@@ -2698,8 +2698,8 @@ NIL
NIL
(-692 |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.")))
-((-4497 . T) (-4500 . T) (-4494 . T) (-4495 . T))
-((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4502 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))) (-2230 (|HasAttribute| |#2| (QUOTE (-4502 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175))))
+((-4504 . T) (-4507 . T) (-4501 . T) (-4502 . T))
+((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))) (-2225 (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175))))
(-693)
((|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
@@ -2719,7 +2719,7 @@ NIL
(-697 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
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-698)
((|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
@@ -2763,10 +2763,10 @@ NIL
(-708 S R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
NIL
-((|HasAttribute| |#2| (QUOTE (-4502 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))))
+((|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-570))))
(-709 R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-710 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")))
@@ -2774,8 +2774,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))))
(-711 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.")))
-((-4500 . T) (-4501 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4502 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4507 . T) (-4508 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-570))) (|HasAttribute| |#1| (QUOTE (-4509 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-712 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
@@ -2784,7 +2784,7 @@ 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
-(-714 S -2155 FLAF FLAS)
+(-714 S -2174 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
@@ -2794,11 +2794,11 @@ NIL
NIL
(-716)
((|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")))
-((-4493 . T) (-4498 |has| (-721) (-376)) (-4492 |has| (-721) (-376)) (-3921 . T) (-4499 |has| (-721) (-6 -4499)) (-4496 |has| (-721) (-6 -4496)) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
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+((-4500 . T) (-4505 |has| (-721) (-376)) (-4499 |has| (-721) (-376)) (-1924 . T) (-4506 |has| (-721) (-6 -4506)) (-4503 |has| (-721) (-6 -4503)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2225 (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2225 (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207))))) (-2225 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (LIST (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (-2225 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-362)))) (|HasCategory| (-721) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-721) (QUOTE (-1053))) (|HasCategory| (-721) (QUOTE (-1233))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1233)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-938)))) (-12 (|HasCategory| (-721) (QUOTE (-362))) (|HasCategory| (-721) (QUOTE (-938))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1233)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2225 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-570)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-721) (QUOTE (-570))) (|HasAttribute| (-721) (QUOTE -4506)) (|HasAttribute| (-721) (QUOTE -4503)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-938)))) (|HasCategory| (-721) (QUOTE (-362)))))
(-717 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}.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-718 U)
((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}.")))
@@ -2808,13 +2808,13 @@ 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
-(-720 OV E -2155 PG)
+(-720 OV E -2174 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
(-721)
((|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}")))
-((-3909 . T) (-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-1915 . T) (-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-722 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.")))
@@ -2822,7 +2822,7 @@ NIL
NIL
(-723)
((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}")))
-((-4499 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4506 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-724 S D1 D2 I)
((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function")))
@@ -2840,7 +2840,7 @@ 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
-(-728 S -1676 I)
+(-728 S -4247 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
@@ -2850,7 +2850,7 @@ NIL
NIL
(-730 R)
((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-731 R1 UP1 UPUP1 R2 UP2 UPUP2)
((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}.")))
@@ -2860,25 +2860,25 @@ 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
-(-733 R |Mod| -3108 -2026 |exactQuo|)
+(-733 R |Mod| -1606 -3949 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-734 R |Rep|)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4496 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4498)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4503 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
(-735 IS E |ff|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
(-736 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) (-4497 . T))
+((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))))
-(-737 R |Mod| -3108 -2026 |exactQuo|)
+(-737 R |Mod| -1606 -3949 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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")))
-((-4497 . T))
+((-4504 . T))
NIL
(-738 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
@@ -2886,11 +2886,11 @@ NIL
NIL
(-739 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
-(-740 -2155)
+(-740 -2174)
((|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]]}.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-741 S)
((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation.")))
@@ -2914,7 +2914,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381))))
(-746 R UP)
((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain.")))
-((-4493 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 |has| |#1| (-376)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-747 S)
((|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.")))
@@ -2924,7 +2924,7 @@ 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
-(-749 -2155 UP)
+(-749 -2174 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
@@ -2942,8 +2942,8 @@ NIL
NIL
(-753 |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.")))
-(((-4502 "*") |has| |#2| (-175)) (-4493 |has| |#2| (-570)) (-4498 |has| |#2| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
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+(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-938))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
(-754 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
@@ -2958,15 +2958,15 @@ NIL
NIL
(-757 R M)
((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}.")))
-((-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) (-4497 . T))
+((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T))
((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-871))))
(-758 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-4490 . T) (-4501 . T))
+((-4497 . T) (-4508 . T))
NIL
(-759 S)
((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}.")))
-((-4500 . T) (-4490 . T) (-4501 . T))
+((-4507 . T) (-4497 . T) (-4508 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-760)
((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned.")))
@@ -2978,7 +2978,7 @@ NIL
NIL
(-762 |Coef| |Var|)
((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4495 . T) (-4494 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-763 OV E R P)
((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")))
@@ -2994,7 +2994,7 @@ NIL
NIL
(-766 R)
((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-767)
((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}.")))
@@ -3076,11 +3076,11 @@ 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
-(-787 -2155)
+(-787 -2174)
((|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
-(-788 P -2155)
+(-788 P -2174)
((|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
@@ -3088,7 +3088,7 @@ NIL
NIL
NIL
NIL
-(-790 UP -2155)
+(-790 UP -2174)
((|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{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{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{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{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{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{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
@@ -3102,9 +3102,9 @@ NIL
NIL
(-793)
((|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.")))
-(((-4502 "*") . T))
+(((-4509 "*") . T))
NIL
-(-794 R -2155)
+(-794 R -2174)
((|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
@@ -3124,7 +3124,7 @@ 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
-(-799 -2155 |ExtF| |SUEx| |ExtP| |n|)
+(-799 -2174 |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
@@ -3138,23 +3138,23 @@ NIL
NIL
(-802 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.")))
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(-803 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
(-804 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)}")))
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+((|HasCategory| |#1| (QUOTE (-938))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
(-805 R)
((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented")))
NIL
((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))
(-806 R E V P)
((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-807 S)
((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.")))
@@ -3206,25 +3206,25 @@ NIL
((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381))))
(-819 R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
-(-820 -2230 R OS S)
+(-820 -2225 R OS S)
((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}.")))
NIL
NIL
(-821 R)
((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
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+((-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2225 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1030 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))))
(-822)
((|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
-(-823 R -2155 L)
+(-823 R -2174 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{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}.")))
NIL
NIL
-(-824 R -2155)
+(-824 R -2174)
((|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
@@ -3232,7 +3232,7 @@ 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
-(-826 R -2155)
+(-826 R -2174)
((|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
@@ -3240,11 +3240,11 @@ 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
-(-828 -2155 UP UPUP R)
+(-828 -2174 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
-(-829 -2155 UP L LQ)
+(-829 -2174 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
@@ -3252,41 +3252,41 @@ 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
-(-831 -2155 UP L LQ)
+(-831 -2174 UP L LQ)
((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^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{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{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 ai}} is \\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
-(-832 -2155 UP)
+(-832 -2174 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
-(-833 -2155 L UP A LO)
+(-833 -2174 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
-(-834 -2155 UP)
+(-834 -2174 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{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 ai}} is \\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))))
-(-835 -2155 LO)
+(-835 -2174 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
-(-836 -2155 LODO)
+(-836 -2174 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(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(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.")))
NIL
NIL
-(-837 -3755 S |f|)
+(-837 -2591 S |f|)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-4494 |has| |#2| (-1080)) (-4495 |has| |#2| (-1080)) (-4497 |has| |#2| (-6 -4497)) (-4500 . T))
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(QUOTE (-376)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-381)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-871)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-1131))))) (-2225 (-12 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) 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(|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| (-578) (QUOTE (-871))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207))))) (-2225 (|HasCategory| |#2| (QUOTE (-1080))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-1131)))) (|HasAttribute| |#2| (QUOTE -4504)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))))
(-838 R)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
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(-839 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")))
-(((-4502 "*") |has| |#2| (-376)) (-4493 |has| |#2| (-376)) (-4498 |has| |#2| (-376)) (-4492 |has| |#2| (-376)) (-4497 . T) (-4495 . T) (-4494 . T))
+(((-4509 "*") |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4505 |has| |#2| (-376)) (-4499 |has| |#2| (-376)) (-4504 . T) (-4502 . T) (-4501 . T))
((|HasCategory| |#2| (QUOTE (-376))))
(-840 S)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u})).")))
@@ -3298,7 +3298,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-871))))
(-842)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-843)
((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}")))
@@ -3326,7 +3326,7 @@ NIL
NIL
(-849 P R)
((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240))))
(-850)
((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object.")))
@@ -3338,7 +3338,7 @@ NIL
NIL
(-852 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-4500 . T) (-4490 . T) (-4501 . T))
+((-4507 . T) (-4497 . T) (-4508 . T))
NIL
(-853)
((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object.")))
@@ -3350,8 +3350,8 @@ NIL
NIL
(-855 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.")))
-((-4497 |has| |#1| (-870)))
-((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2230 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2230 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559))))
+((-4504 |has| |#1| (-870)))
+((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559))))
(-856 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
@@ -3362,7 +3362,7 @@ NIL
NIL
(-858 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) (-4497 . T))
+((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))))
(-859)
((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages).")))
@@ -3390,13 +3390,13 @@ NIL
NIL
(-865 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| (($) "\\spad{plusInfinity()} returns +infinity.")))
-((-4497 |has| |#1| (-870)))
-((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2230 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2230 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559))))
+((-4504 |has| |#1| (-870)))
+((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2225 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-559))))
(-866)
((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%.")))
NIL
NIL
-(-867 -3755 S)
+(-867 -2591 S)
((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering.")))
NIL
NIL
@@ -3410,7 +3410,7 @@ NIL
NIL
(-870)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-871)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")))
@@ -3434,19 +3434,19 @@ NIL
((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))))
(-876 R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-877 R C)
((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use.")))
NIL
((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570))))
-(-878 R |sigma| -2956)
+(-878 R |sigma| -4147)
((|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.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376))))
-(-879 |x| R |sigma| -2956)
+(-879 |x| R |sigma| -4147)
((|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}.")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376))))
(-880 R)
((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")))
@@ -3490,7 +3490,7 @@ NIL
NIL
(-890 R |vl| |wl| |wtlevel|)
((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")))
-((-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) (-4497 . T))
+((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))))
(-891 R PS UP)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")))
@@ -3502,24 +3502,24 @@ NIL
NIL
(-893 |p|)
((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-894 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1).")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-895 |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).")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-894 |#1|) (QUOTE (-938))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-894 |#1|) (QUOTE (-1053))) (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871))) (-2230 (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-1183))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -894) (|devaluate| |#1|)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (|HasCategory| (-894 |#1|) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-894 |#1|) (QUOTE (-938))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-149))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-894 |#1|) (QUOTE (-1053))) (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871))) (-2225 (|HasCategory| (-894 |#1|) (QUOTE (-842))) (|HasCategory| (-894 |#1|) (QUOTE (-871)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-1183))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| (-894 |#1|) (QUOTE (-239))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (QUOTE (-240))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -894) (|devaluate| |#1|)) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| (-894 |#1|) (QUOTE (-319))) (|HasCategory| (-894 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-894 |#1|) (QUOTE (-938)))) (|HasCategory| (-894 |#1|) (QUOTE (-147)))))
(-896 |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)}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2230 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2225 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
(-897 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 (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))))
(-898)
((|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
@@ -3579,7 +3579,7 @@ NIL
(-912 |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 (-2309 (|HasCategory| |#2| (QUOTE (-1080)))) (-2309 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-2309 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))
+((-12 (-3523 (|HasCategory| |#2| (QUOTE (-1080)))) (-3523 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-3523 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))
(-913 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
@@ -3588,7 +3588,7 @@ 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
-(-915 R -1676)
+(-915 R -4247)
((|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
@@ -3620,7 +3620,7 @@ 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
-(-923 UP -2155)
+(-923 UP -2174)
((|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
@@ -3634,11 +3634,11 @@ NIL
NIL
(-926 R S)
((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-927 S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-4497 . T))
+((-4504 . T))
NIL
(-928 A S)
((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.")))
@@ -3651,14 +3651,14 @@ NIL
(-930 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 (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-931 |n| R)
((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}")))
NIL
NIL
(-932 S)
((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.")))
-((-4497 . T))
+((-4504 . T))
NIL
(-933 S)
((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}.")))
@@ -3666,8 +3666,8 @@ NIL
NIL
(-934 S)
((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|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.")))
-((-4497 . T))
-((-2230 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871))))
+((-4504 . T))
+((-2225 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871))))
(-935 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 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
@@ -3682,13 +3682,13 @@ NIL
((|HasCategory| |#1| (QUOTE (-147))))
(-938)
((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-939 |p|)
((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381))))
-(-940 R0 -2155 UP UPUP R)
+(-940 R0 -2174 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
@@ -3702,7 +3702,7 @@ NIL
NIL
(-943 R)
((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-944 R)
((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var.")))
@@ -3716,7 +3716,7 @@ 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(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em 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(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em 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 ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,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(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,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
-(-947 -2155)
+(-947 -2174)
((|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
@@ -3726,17 +3726,17 @@ NIL
NIL
(-949)
((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-950)
((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}.")))
-(((-4502 "*") . T))
+(((-4509 "*") . T))
NIL
-(-951 -2155 P)
+(-951 -2174 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented")))
NIL
NIL
-(-952 |xx| -2155)
+(-952 |xx| -2174)
((|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
@@ -3760,7 +3760,7 @@ NIL
((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented")))
NIL
NIL
-(-958 R -2155)
+(-958 R -2174)
((|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
@@ -3772,7 +3772,7 @@ 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
-(-961 S R -2155)
+(-961 S R -2174)
((|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
@@ -3792,11 +3792,11 @@ 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 -911) (|devaluate| |#1|))))
-(-966 R -2155 -1676)
+(-966 R -2174 -4247)
((|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
-(-967 -1676)
+(-967 -4247)
((|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
@@ -3818,8 +3818,8 @@ NIL
NIL
(-972 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-973 |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
@@ -3839,12 +3839,12 @@ NIL
(-977 S R E |VarSet|)
((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-938))) (|HasAttribute| |#2| (QUOTE -4498)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))))
+((|HasCategory| |#2| (QUOTE (-938))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#4| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))))
(-978 R E |VarSet|)
((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
-(-979 E V R P -2155)
+(-979 E V R P -2174)
((|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
@@ -3854,9 +3854,9 @@ NIL
NIL
(-981 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}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-938))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4498)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
-(-982 E V R P -2155)
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
+(-982 E V R P -2174)
((|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| $) "\\spad{numer(x)} \\undocumented")))
NIL
((|HasCategory| |#3| (QUOTE (-466))))
@@ -3878,13 +3878,13 @@ NIL
NIL
(-987 S)
((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed")))
-((-4501 . T) (-4500 . T))
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+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-988)
((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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
-(-989 -2155)
+(-989 -2174)
((|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{ai = 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{ai = 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
@@ -3898,12 +3898,12 @@ NIL
NIL
(-992 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}")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4494 . T) (-4495 . T) (-4497 . T))
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(-993 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")))
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(-994)
((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
NIL
@@ -3926,7 +3926,7 @@ NIL
NIL
(-999 S)
((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}.")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-1000 R |polR|)
((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")))
@@ -3946,7 +3946,7 @@ NIL
NIL
(-1004 |Coef| |Expon| |Var|)
((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1005)
((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
@@ -3958,7 +3958,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-570))))
(-1007 R E |VarSet| P)
((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
-((-4500 . T))
+((-4507 . T))
NIL
(-1008 R E V P)
((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor.")))
@@ -3974,7 +3974,7 @@ NIL
NIL
(-1011 R)
((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1012 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented")))
@@ -3992,7 +3992,7 @@ 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
-(-1016 K R UP -2155)
+(-1016 K R UP -2174)
((|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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")))
NIL
NIL
@@ -4022,7 +4022,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-1183))))
(-1023 S)
((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1024 |n| K)
((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}.")))
@@ -4034,7 +4034,7 @@ NIL
NIL
(-1026 S)
((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end.")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-1027 S R)
((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
@@ -4042,7 +4042,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-302))))
(-1028 R)
((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
-((-4493 |has| |#1| (-302)) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 |has| |#1| (-302)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1029 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
@@ -4050,12 +4050,12 @@ NIL
NIL
(-1030 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.}")))
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+((-4500 |has| |#1| (-302)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))))
(-1031 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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-1032 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
@@ -4064,14 +4064,14 @@ NIL
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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
-(-1034 -2155 UP UPUP |radicnd| |n|)
+(-1034 -2174 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
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+((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-362))) (-2225 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-362)))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-362))))) (-2225 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))))
(-1035 |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.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2230 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-578) (QUOTE (-938))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-149))) (|HasCategory| (-578) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-1053))) (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871))) (-2225 (|HasCategory| (-578) (QUOTE (-842))) (|HasCategory| (-578) (QUOTE (-871)))) (|HasCategory| (-578) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-1183))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| (-578) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| (-578) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| (-578) (QUOTE (-239))) (|HasCategory| (-578) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-578) (QUOTE (-240))) (|HasCategory| (-578) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-578) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -321) (QUOTE (-578)))) (|HasCategory| (-578) (LIST (QUOTE -298) (QUOTE (-578)) (QUOTE (-578)))) (|HasCategory| (-578) (QUOTE (-319))) (|HasCategory| (-578) (QUOTE (-559))) (|HasCategory| (-578) (LIST (QUOTE -660) (QUOTE (-578)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-578) (QUOTE (-938)))) (|HasCategory| (-578) (QUOTE (-147)))))
(-1036)
((|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
@@ -4091,7 +4091,7 @@ NIL
(-1040 A S)
((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)) (|HasCategory| |#2| (QUOTE (-1131))))
+((|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-1131))))
(-1041 S)
((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}.")))
NIL
@@ -4102,21 +4102,21 @@ NIL
NIL
(-1043)
((|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}}")))
-((-4493 . T) (-4498 . T) (-4492 . T) (-4495 . T) (-4494 . T) ((-4502 "*") . T) (-4497 . T))
+((-4500 . T) (-4505 . T) (-4499 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4504 . T))
NIL
-(-1044 R -2155)
+(-1044 R -2174)
((|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
-(-1045 R -2155)
+(-1045 R -2174)
((|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
-(-1046 -2155 UP)
+(-1046 -2174 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
-(-1047 -2155 UP)
+(-1047 -2174 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
@@ -4150,9 +4150,9 @@ NIL
NIL
(-1055 |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")))
-((-4493 . T) (-4498 . T) (-4492 . T) (-4495 . T) (-4494 . T) ((-4502 "*") . T) (-4497 . T))
-((-2230 (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))))
-(-1056 -2155 L)
+((-4500 . T) (-4505 . T) (-4499 . T) (-4502 . T) (-4501 . T) ((-4509 "*") . T) (-4504 . T))
+((-2225 (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-421 (-578)) (LIST (QUOTE -1069) (QUOTE (-578)))))
+(-1056 -2174 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{fi} must satisfy \\spad{op 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
@@ -4162,12 +4162,12 @@ NIL
((|HasCategory| |#1| (QUOTE (-1131))))
(-1058 R E V P)
((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102))))
(-1059 R)
((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.")))
NIL
-((|HasAttribute| |#1| (QUOTE (-4502 "*"))))
+((|HasAttribute| |#1| (QUOTE (-4509 "*"))))
(-1060 R)
((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis.")))
NIL
@@ -4188,14 +4188,14 @@ 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
-(-1065 -2155 |Expon| |VarSet| |FPol| |LFPol|)
+(-1065 -2174 |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")))
-(((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1066)
((|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.}")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2754) (QUOTE (-52))))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2078) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))))
(-1067)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
NIL
@@ -4238,7 +4238,7 @@ NIL
NIL
(-1077 R |ls|)
((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1131))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -802) (|devaluate| |#1|) (LIST (QUOTE -888) (|devaluate| |#2|)))))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| (-888 |#2|) (QUOTE (-381))) (|HasCategory| (-802 |#1| (-888 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-802 |#1| (-888 |#2|)) (QUOTE (-102))))
(-1078)
((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented")))
@@ -4250,9 +4250,9 @@ NIL
NIL
(-1080)
((|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.")))
-((-4497 . T))
+((-4504 . T))
NIL
-(-1081 |xx| -2155)
+(-1081 |xx| -2174)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
@@ -4266,12 +4266,12 @@ NIL
((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-570))) (|HasCategory| |#4| (QUOTE (-175))))
(-1084 |m| |n| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite")))
-((-4500 . T) (-4495 . T) (-4494 . T))
+((-4507 . T) (-4502 . T) (-4501 . T))
NIL
(-1085 |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}.")))
-((-4500 . T) (-4495 . T) (-4494 . T))
-((|HasCategory| |#3| (QUOTE (-175))) (-2230 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-570))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886)))))
+((-4507 . T) (-4502 . T) (-4501 . T))
+((|HasCategory| |#3| (QUOTE (-175))) (-2225 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-570))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886)))))
(-1086 |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
@@ -4294,7 +4294,7 @@ NIL
NIL
(-1091)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1092 |TheField| |ThePolDom|)
((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
@@ -4302,19 +4302,19 @@ NIL
NIL
(-1093)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")))
-((-4488 . T) (-4492 . T) (-4487 . T) (-4498 . T) (-4499 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1094)
((|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}")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2754) (QUOTE (-52))))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -2078) (QUOTE (-52))))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| (-52) (QUOTE (-1131))) (|HasCategory| (-52) (LIST (QUOTE -321) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-1131))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-52) (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (QUOTE (-102))))
(-1095 S R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
NIL
((|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1023) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-1207)))))
(-1096 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-1097)
((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'.")))
@@ -4338,7 +4338,7 @@ NIL
NIL
(-1102 R E V P)
((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1103 R E V P TS)
((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\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}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
@@ -4356,11 +4356,11 @@ NIL
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-1107 |Base| R -2155)
+(-1107 |Base| R -2174)
((|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
-(-1108 |Base| R -2155)
+(-1108 |Base| R -2174)
((|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
@@ -4374,8 +4374,8 @@ NIL
NIL
(-1111 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.")))
-((-4493 |has| |#1| (-376)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))))
+((-4500 |has| |#1| (-376)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-362))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))))
(-1112 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
@@ -4402,8 +4402,8 @@ NIL
NIL
(-1118 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")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-938))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4498)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-938))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-938)))) (|HasCategory| |#1| (QUOTE (-147)))))
(-1119 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
@@ -4446,7 +4446,7 @@ NIL
NIL
(-1129 S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
-((-4490 . T))
+((-4497 . T))
NIL
(-1130 S)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
@@ -4462,8 +4462,8 @@ NIL
NIL
(-1133 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)}}")))
-((-4500 . T) (-4490 . T) (-4501 . T))
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+((-4507 . T) (-4497 . T) (-4508 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-1134 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|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 \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers.")))
NIL
@@ -4490,7 +4490,7 @@ NIL
NIL
(-1140 R E V P)
((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\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}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1141)
((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber.")))
@@ -4506,8 +4506,8 @@ NIL
NIL
(-1144 |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}.")))
-((-4494 |has| |#3| (-1080)) (-4495 |has| |#3| (-1080)) (-4497 |has| |#3| (-6 -4497)) (-4500 . T))
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(QUOTE (-376)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-381)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-748)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-815)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-871)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1131))))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (|HasCategory| (-578) (QUOTE (-871))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207))))) (-2225 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578)))))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#3| (QUOTE (-1131)))) (|HasAttribute| |#3| (QUOTE -4504)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1131))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))))
(-1145 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
@@ -4516,7 +4516,7 @@ 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
-(-1147 R -2155)
+(-1147 R -2174)
((|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
@@ -4534,19 +4534,19 @@ NIL
NIL
(-1151)
((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality.")))
-((-4488 . T) (-4492 . T) (-4487 . T) (-4498 . T) (-4499 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4495 . T) (-4499 . T) (-4494 . T) (-4505 . T) (-4506 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1152 S)
((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-4500 . T) (-4501 . T))
+((-4507 . T) (-4508 . T))
NIL
(-1153 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")))
NIL
-((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4502 "*"))) (|HasCategory| |#3| (QUOTE (-175))))
+((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4509 "*"))) (|HasCategory| |#3| (QUOTE (-175))))
(-1154 |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")))
-((-4500 . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4507 . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1155 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}.")))
@@ -4554,17 +4554,17 @@ NIL
NIL
(-1156 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.")))
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(-1157 |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}.")))
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(-1158 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}")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
-(-1159 UP -2155)
+(-1159 UP -2174)
((|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
@@ -4618,19 +4618,19 @@ NIL
NIL
(-1172 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-4500 . T) (-4501 . T))
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+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))) (-2225 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131)))) (-2225 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1131))))) (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))))
(-1173 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}.")))
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+((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-376))) (-2225 (|HasAttribute| |#2| (QUOTE (-4509 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175))))
(-1174 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
(-1175)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1176 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
@@ -4638,12 +4638,12 @@ NIL
NIL
(-1177 R E V P)
((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102))))
(-1178 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}.")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-1179 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
@@ -4654,8 +4654,8 @@ NIL
NIL
(-1181 |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.")))
-((-4501 . T))
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+((-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))))
(-1182)
((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}.")))
NIL
@@ -4682,16 +4682,16 @@ NIL
NIL
(-1188 S)
((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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.")))
-((-4501 . T))
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+((-4508 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-1189)
((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2230 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2230 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2225 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-146) (QUOTE (-871))) (-2225 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1131))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))))
(-1190 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-4500 . T) (-4501 . T))
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+((-4507 . T) (-4508 . T))
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(-1191 A)
((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|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,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
@@ -4722,9 +4722,9 @@ NIL
NIL
(-1198 |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.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series.")))
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+(-1199 R -2174)
((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n}).")))
NIL
NIL
@@ -4742,16 +4742,16 @@ NIL
NIL
(-1203 R)
((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable.")))
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(-1204 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} 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{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\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.")))
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(-1205 |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.")) (|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}.")))
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+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1369) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
(-1206)
((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}")))
NIL
@@ -4766,8 +4766,8 @@ NIL
NIL
(-1209 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-6 -4498)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2230 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasAttribute| |#1| (QUOTE -4498)))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-6 -4505)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2225 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasAttribute| |#1| (QUOTE -4505)))
(-1210)
((|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
@@ -4810,8 +4810,8 @@ NIL
NIL
(-1220 |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}")))
-((-4500 . T) (-4501 . T))
-((-12 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3172) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2754) (|devaluate| |#2|)))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2230 (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (QUOTE (-102))))
+((-4507 . T) (-4508 . T))
+((-12 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2338) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2078) (|devaluate| |#2|)))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1131)))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -633) (QUOTE (-550)))) (-12 (|HasCategory| |#2| (QUOTE (-1131))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1131))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886))))) (-2225 (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (QUOTE (-102))))
(-1221 S)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}.")))
NIL
@@ -4826,7 +4826,7 @@ NIL
NIL
(-1224 |Key| |Entry|)
((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}.")))
-((-4501 . T))
+((-4508 . T))
NIL
(-1225 |Key| |Entry|)
((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table.")))
@@ -4866,8 +4866,8 @@ NIL
NIL
(-1234 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-4501 . T) (-4500 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
+((-4508 . T) (-4507 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1131))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1131)))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))))
(-1235 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
@@ -4876,7 +4876,7 @@ NIL
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1237 R -2155)
+(-1237 R -2174)
((|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
@@ -4884,7 +4884,7 @@ 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
-(-1239 R -2155)
+(-1239 R -2174)
((|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 -633) (LIST (QUOTE -917) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -911) (|devaluate| |#1|)))))
@@ -4894,12 +4894,12 @@ NIL
((|HasCategory| |#4| (QUOTE (-381))))
(-1241 R E V P)
((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1242 |Coef|)
((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-376))))
(-1243 |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
@@ -4912,7 +4912,7 @@ 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 (-1131))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))))
-(-1246 -2155)
+(-1246 -2174)
((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")))
NIL
NIL
@@ -4938,7 +4938,7 @@ NIL
NIL
(-1252)
((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1253)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits.")))
@@ -4962,7 +4962,7 @@ NIL
NIL
(-1258 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1259 S |Coef| UTS)
((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}.")))
@@ -4970,16 +4970,16 @@ NIL
((|HasCategory| |#2| (QUOTE (-376))))
(-1260 |Coef| UTS)
((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1261 |Coef| UTS)
((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
-((-2230 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-871)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (-2230 (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147))))) (-2230 (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-149))))) (-2230 (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2230 (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-240)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-578)) (|devaluate| |#1|))))) (|HasCategory| (-578) (QUOTE (-1143))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-938)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| 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(-1263 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
@@ -5014,8 +5014,8 @@ NIL
NIL
(-1271 |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}")))
-(((-4502 "*") |has| |#2| (-175)) (-4493 |has| |#2| (-570)) (-4496 |has| |#2| (-376)) (-4498 |has| |#2| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2230 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2230 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2230 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4498)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2230 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
+(((-4509 "*") |has| |#2| (-175)) (-4500 |has| |#2| (-570)) (-4503 |has| |#2| (-376)) (-4505 |has| |#2| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-938))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-570)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-392)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-392))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-578)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-578))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-392)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -917) (QUOTE (-578)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-578)))) (-2225 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (-2225 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (-2225 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-938)))) (|HasCategory| |#2| (QUOTE (-147)))))
(-1272 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
@@ -5026,15 +5026,15 @@ NIL
((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1183))))
(-1274 R)
((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4496 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4495 . T) (-4494 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4503 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-1275 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}.")) (|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 -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2411) (LIST (|devaluate| |#2|) (QUOTE (-1207))))))
+((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2863) (LIST (|devaluate| |#2|) (QUOTE (-1207))))))
(-1276 |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}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1277 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
@@ -5046,7 +5046,7 @@ NIL
NIL
(-1279 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1280 S |Coef| ULS)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}.")))
@@ -5054,24 +5054,24 @@ NIL
NIL
(-1281 |Coef| ULS)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1282 |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)}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2411) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2230 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -3044) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2948) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1369) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))))
(-1283 |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.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4498 |has| |#1| (-376)) (-4492 |has| |#1| (-376)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2230 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2411) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2230 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -3044) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2948) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4505 |has| |#1| (-376)) (-4499 |has| |#1| (-376)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#1| (QUOTE (-175))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-578)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-2225 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-570)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-578)))))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1369) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
(-1284 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))}.")))
-(((-4502 "*") |has| (-1283 |#2| |#3| |#4|) (-175)) (-4493 |has| (-1283 |#2| |#3| |#4|) (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-175))) (-2230 (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-570))))
+(((-4509 "*") |has| (-1283 |#2| |#3| |#4|) (-175)) (-4500 |has| (-1283 |#2| |#3| |#4|) (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-175))) (-2225 (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578)))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| (-1283 |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-578)))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1283 |#2| |#3| |#4|) (QUOTE (-570))))
(-1285 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4501)))
+((|HasAttribute| |#1| (QUOTE -4508)))
(-1286 S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
@@ -5083,20 +5083,20 @@ NIL
(-1288 S |Coef|)
((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-578)))) (|HasCategory| |#2| (QUOTE (-988))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -2948) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3044) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))))
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#2| (QUOTE (-988))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1369) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#2| (QUOTE (-376))))
(-1289 |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.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1290 |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|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|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))}.}")) (|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}.")))
-(((-4502 "*") |has| |#1| (-175)) (-4493 |has| |#1| (-570)) (-4494 . T) (-4495 . T) (-4497 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2230 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2411) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2230 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -3044) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2948) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
+(((-4509 "*") |has| |#1| (-175)) (-4500 |has| |#1| (-570)) (-4501 . T) (-4502 . T) (-4504 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasCategory| |#1| (QUOTE (-570))) (-2225 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2225 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-578)))) (|HasCategory| |#1| (QUOTE (-988))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasSignature| |#1| (LIST (QUOTE -1369) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -1880) (LIST (LIST (QUOTE -666) (QUOTE (-1207))) (|devaluate| |#1|)))))))
(-1291 |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
-(-1292 -2155 UP L UTS)
+(-1292 -2174 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 (-570))))
@@ -5114,7 +5114,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
(-1296 R)
((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
NIL
(-1297 A B)
((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
@@ -5122,8 +5122,8 @@ NIL
NIL
(-1298 R)
((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-4501 . T) (-4500 . T))
-((-2230 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2230 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2230 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2230 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
+((-4508 . T) (-4507 . T))
+((-2225 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2225 (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-550)))) (-2225 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| |#1| (QUOTE (-871))) (-2225 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131)))) (|HasCategory| (-578) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1131))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))))
(-1299)
((|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,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{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\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(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc.")))
NIL
@@ -5150,13 +5150,13 @@ NIL
NIL
(-1305 S)
((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}.")))
-((-4495 . T) (-4494 . T))
+((-4502 . T) (-4501 . T))
NIL
(-1306 R)
((|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
-(-1307 K R UP -2155)
+(-1307 K R UP -2174)
((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}.")))
NIL
NIL
@@ -5170,56 +5170,56 @@ NIL
NIL
(-1310 R |VarSet| E P |vl| |wl| |wtlevel|)
((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")))
-((-4495 |has| |#1| (-175)) (-4494 |has| |#1| (-175)) (-4497 . T))
+((-4502 |has| |#1| (-175)) (-4501 |has| |#1| (-175)) (-4504 . T))
((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))))
(-1311 R E V P)
((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}.")))
-((-4501 . T) (-4500 . T))
+((-4508 . T) (-4507 . T))
((-12 (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#4| (LIST (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -633) (QUOTE (-550)))) (|HasCategory| |#4| (QUOTE (-1131))) (|HasCategory| |#1| (QUOTE (-570))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-886)))) (|HasCategory| |#4| (QUOTE (-102))))
(-1312 R)
((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")))
-((-4494 . T) (-4495 . T) (-4497 . T))
+((-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1313 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute.")))
-((-4497 . T) (-4493 |has| |#2| (-6 -4493)) (-4495 . T) (-4494 . T))
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4493)))
+((-4504 . T) (-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T))
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4500)))
(-1314 R |VarSet| XPOLY)
((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")))
NIL
NIL
(-1315 |vl| R)
((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-4493 |has| |#2| (-6 -4493)) (-4495 . T) (-4494 . T) (-4497 . T))
+((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
-(-1316 S -2155)
+(-1316 S -2174)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))))
-(-1317 -2155)
+(-1317 -2174)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
-((-4492 . T) (-4498 . T) (-4493 . T) ((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+((-4499 . T) (-4505 . T) (-4500 . T) ((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
(-1318 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}.")))
-((-4493 |has| |#2| (-6 -4493)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -739) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasAttribute| |#2| (QUOTE -4493)))
+((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -739) (LIST (QUOTE -421) (QUOTE (-578))))) (|HasAttribute| |#2| (QUOTE -4500)))
(-1319 |vl| R)
((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-4493 |has| |#2| (-6 -4493)) (-4495 . T) (-4494 . T) (-4497 . T))
+((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T))
NIL
(-1320 R)
((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute.")))
-((-4493 |has| |#1| (-6 -4493)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4493)))
+((-4500 |has| |#1| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4500)))
(-1321 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}.")))
-((-4497 . T) (-4498 |has| |#1| (-6 -4498)) (-4493 |has| |#1| (-6 -4493)) (-4495 . T) (-4494 . T))
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#1| (QUOTE -4498)) (|HasAttribute| |#1| (QUOTE -4493)))
+((-4504 . T) (-4505 |has| |#1| (-6 -4505)) (-4500 |has| |#1| (-6 -4500)) (-4502 . T) (-4501 . T))
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4500)))
(-1322 |VarSet| R)
((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form.")))
-((-4493 |has| |#2| (-6 -4493)) (-4495 . T) (-4494 . T) (-4497 . T))
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4493)))
+((-4500 |has| |#2| (-6 -4500)) (-4502 . T) (-4501 . T) (-4504 . T))
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4500)))
(-1323)
((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}")))
NIL
@@ -5238,7 +5238,7 @@ NIL
NIL
(-1327 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-4502 "*") . T) (-4494 . T) (-4495 . T) (-4497 . T))
+(((-4509 "*") . T) (-4501 . T) (-4502 . T) (-4504 . T))
NIL
NIL
NIL
@@ -5256,4 +5256,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 2300154 2300159 2300164 2300169) (-2 NIL 2300134 2300139 2300144 2300149) (-1 NIL 2300114 2300119 2300124 2300129) (0 NIL 2300094 2300099 2300104 2300109) (-1327 "ZMOD.spad" 2299903 2299916 2300032 2300089) (-1326 "ZLINDEP.spad" 2298969 2298980 2299893 2299898) (-1325 "ZDSOLVE.spad" 2288913 2288935 2298959 2298964) (-1324 "YSTREAM.spad" 2288408 2288419 2288903 2288908) (-1323 "YDIAGRAM.spad" 2288042 2288051 2288398 2288403) (-1322 "XRPOLY.spad" 2287262 2287282 2287898 2287967) (-1321 "XPR.spad" 2285057 2285070 2286980 2287079) (-1320 "XPOLY.spad" 2284612 2284623 2284913 2284982) (-1319 "XPOLYC.spad" 2283931 2283947 2284538 2284607) (-1318 "XPBWPOLY.spad" 2282368 2282388 2283711 2283780) (-1317 "XF.spad" 2280831 2280846 2282270 2282363) (-1316 "XF.spad" 2279274 2279291 2280715 2280720) (-1315 "XFALG.spad" 2276322 2276338 2279200 2279269) (-1314 "XEXPPKG.spad" 2275573 2275599 2276312 2276317) (-1313 "XDPOLY.spad" 2275187 2275203 2275429 2275498) (-1312 "XALG.spad" 2274847 2274858 2275143 2275182) (-1311 "WUTSET.spad" 2270650 2270667 2274457 2274484) (-1310 "WP.spad" 2269849 2269893 2270508 2270575) (-1309 "WHILEAST.spad" 2269647 2269656 2269839 2269844) (-1308 "WHEREAST.spad" 2269318 2269327 2269637 2269642) (-1307 "WFFINTBS.spad" 2266981 2267003 2269308 2269313) (-1306 "WEIER.spad" 2265203 2265214 2266971 2266976) (-1305 "VSPACE.spad" 2264876 2264887 2265171 2265198) (-1304 "VSPACE.spad" 2264569 2264582 2264866 2264871) (-1303 "VOID.spad" 2264246 2264255 2264559 2264564) (-1302 "VIEW.spad" 2261926 2261935 2264236 2264241) (-1301 "VIEWDEF.spad" 2257127 2257136 2261916 2261921) (-1300 "VIEW3D.spad" 2241088 2241097 2257117 2257122) (-1299 "VIEW2D.spad" 2228979 2228988 2241078 2241083) (-1298 "VECTOR.spad" 2227500 2227511 2227751 2227778) (-1297 "VECTOR2.spad" 2226139 2226152 2227490 2227495) (-1296 "VECTCAT.spad" 2224043 2224054 2226107 2226134) (-1295 "VECTCAT.spad" 2221754 2221767 2223820 2223825) (-1294 "VARIABLE.spad" 2221534 2221549 2221744 2221749) (-1293 "UTYPE.spad" 2221178 2221187 2221524 2221529) (-1292 "UTSODETL.spad" 2220473 2220497 2221134 2221139) (-1291 "UTSODE.spad" 2218689 2218709 2220463 2220468) (-1290 "UTS.spad" 2213636 2213664 2217156 2217253) (-1289 "UTSCAT.spad" 2211115 2211131 2213534 2213631) (-1288 "UTSCAT.spad" 2208238 2208256 2210659 2210664) (-1287 "UTS2.spad" 2207833 2207868 2208228 2208233) (-1286 "URAGG.spad" 2202506 2202517 2207823 2207828) (-1285 "URAGG.spad" 2197143 2197156 2202462 2202467) (-1284 "UPXSSING.spad" 2194788 2194814 2196224 2196357) (-1283 "UPXS.spad" 2192084 2192112 2192920 2193069) (-1282 "UPXSCONS.spad" 2189843 2189863 2190216 2190365) (-1281 "UPXSCCA.spad" 2188414 2188434 2189689 2189838) (-1280 "UPXSCCA.spad" 2187127 2187149 2188404 2188409) (-1279 "UPXSCAT.spad" 2185716 2185732 2186973 2187122) (-1278 "UPXS2.spad" 2185259 2185312 2185706 2185711) (-1277 "UPSQFREE.spad" 2183673 2183687 2185249 2185254) (-1276 "UPSCAT.spad" 2181460 2181484 2183571 2183668) (-1275 "UPSCAT.spad" 2178953 2178979 2181066 2181071) (-1274 "UPOLYC.spad" 2173993 2174004 2178795 2178948) (-1273 "UPOLYC.spad" 2168925 2168938 2173729 2173734) (-1272 "UPOLYC2.spad" 2168396 2168415 2168915 2168920) (-1271 "UP.spad" 2165502 2165517 2165889 2166042) (-1270 "UPMP.spad" 2164402 2164415 2165492 2165497) (-1269 "UPDIVP.spad" 2163967 2163981 2164392 2164397) (-1268 "UPDECOMP.spad" 2162212 2162226 2163957 2163962) (-1267 "UPCDEN.spad" 2161421 2161437 2162202 2162207) (-1266 "UP2.spad" 2160785 2160806 2161411 2161416) (-1265 "UNISEG.spad" 2160138 2160149 2160704 2160709) (-1264 "UNISEG2.spad" 2159635 2159648 2160094 2160099) (-1263 "UNIFACT.spad" 2158738 2158750 2159625 2159630) (-1262 "ULS.spad" 2148522 2148550 2149467 2149896) (-1261 "ULSCONS.spad" 2139656 2139676 2140026 2140175) (-1260 "ULSCCAT.spad" 2137393 2137413 2139502 2139651) (-1259 "ULSCCAT.spad" 2135238 2135260 2137349 2137354) (-1258 "ULSCAT.spad" 2133470 2133486 2135084 2135233) (-1257 "ULS2.spad" 2132984 2133037 2133460 2133465) (-1256 "UINT8.spad" 2132861 2132870 2132974 2132979) (-1255 "UINT64.spad" 2132737 2132746 2132851 2132856) (-1254 "UINT32.spad" 2132613 2132622 2132727 2132732) (-1253 "UINT16.spad" 2132489 2132498 2132603 2132608) (-1252 "UFD.spad" 2131554 2131563 2132415 2132484) (-1251 "UFD.spad" 2130681 2130692 2131544 2131549) (-1250 "UDVO.spad" 2129562 2129571 2130671 2130676) (-1249 "UDPO.spad" 2127055 2127066 2129518 2129523) (-1248 "TYPE.spad" 2126987 2126996 2127045 2127050) (-1247 "TYPEAST.spad" 2126906 2126915 2126977 2126982) (-1246 "TWOFACT.spad" 2125558 2125573 2126896 2126901) (-1245 "TUPLE.spad" 2125044 2125055 2125457 2125462) (-1244 "TUBETOOL.spad" 2121911 2121920 2125034 2125039) (-1243 "TUBE.spad" 2120558 2120575 2121901 2121906) (-1242 "TS.spad" 2119157 2119173 2120123 2120220) (-1241 "TSETCAT.spad" 2106284 2106301 2119125 2119152) (-1240 "TSETCAT.spad" 2093397 2093416 2106240 2106245) (-1239 "TRMANIP.spad" 2087763 2087780 2093103 2093108) (-1238 "TRIMAT.spad" 2086726 2086751 2087753 2087758) (-1237 "TRIGMNIP.spad" 2085253 2085270 2086716 2086721) (-1236 "TRIGCAT.spad" 2084765 2084774 2085243 2085248) (-1235 "TRIGCAT.spad" 2084275 2084286 2084755 2084760) (-1234 "TREE.spad" 2082733 2082744 2083765 2083792) (-1233 "TRANFUN.spad" 2082572 2082581 2082723 2082728) (-1232 "TRANFUN.spad" 2082409 2082420 2082562 2082567) (-1231 "TOPSP.spad" 2082083 2082092 2082399 2082404) (-1230 "TOOLSIGN.spad" 2081746 2081757 2082073 2082078) (-1229 "TEXTFILE.spad" 2080307 2080316 2081736 2081741) (-1228 "TEX.spad" 2077453 2077462 2080297 2080302) (-1227 "TEX1.spad" 2077009 2077020 2077443 2077448) (-1226 "TEMUTL.spad" 2076564 2076573 2076999 2077004) (-1225 "TBCMPPK.spad" 2074657 2074680 2076554 2076559) (-1224 "TBAGG.spad" 2073707 2073730 2074637 2074652) (-1223 "TBAGG.spad" 2072765 2072790 2073697 2073702) (-1222 "TANEXP.spad" 2072173 2072184 2072755 2072760) (-1221 "TALGOP.spad" 2071897 2071908 2072163 2072168) (-1220 "TABLE.spad" 2069866 2069889 2070136 2070163) (-1219 "TABLEAU.spad" 2069347 2069358 2069856 2069861) (-1218 "TABLBUMP.spad" 2066150 2066161 2069337 2069342) (-1217 "SYSTEM.spad" 2065378 2065387 2066140 2066145) (-1216 "SYSSOLP.spad" 2062861 2062872 2065368 2065373) (-1215 "SYSPTR.spad" 2062760 2062769 2062851 2062856) (-1214 "SYSNNI.spad" 2061951 2061962 2062750 2062755) (-1213 "SYSINT.spad" 2061355 2061366 2061941 2061946) (-1212 "SYNTAX.spad" 2057561 2057570 2061345 2061350) (-1211 "SYMTAB.spad" 2055629 2055638 2057551 2057556) (-1210 "SYMS.spad" 2051652 2051661 2055619 2055624) (-1209 "SYMPOLY.spad" 2050658 2050669 2050740 2050867) (-1208 "SYMFUNC.spad" 2050159 2050170 2050648 2050653) (-1207 "SYMBOL.spad" 2047662 2047671 2050149 2050154) (-1206 "SWITCH.spad" 2044433 2044442 2047652 2047657) (-1205 "SUTS.spad" 2041481 2041509 2042900 2042997) (-1204 "SUPXS.spad" 2038764 2038792 2039613 2039762) (-1203 "SUP.spad" 2035484 2035495 2036257 2036410) (-1202 "SUPFRACF.spad" 2034589 2034607 2035474 2035479) (-1201 "SUP2.spad" 2033981 2033994 2034579 2034584) (-1200 "SUMRF.spad" 2032955 2032966 2033971 2033976) (-1199 "SUMFS.spad" 2032592 2032609 2032945 2032950) (-1198 "SULS.spad" 2022363 2022391 2023321 2023750) (-1197 "SUCHTAST.spad" 2022132 2022141 2022353 2022358) (-1196 "SUCH.spad" 2021814 2021829 2022122 2022127) (-1195 "SUBSPACE.spad" 2013929 2013944 2021804 2021809) (-1194 "SUBRESP.spad" 2013099 2013113 2013885 2013890) (-1193 "STTF.spad" 2009198 2009214 2013089 2013094) (-1192 "STTFNC.spad" 2005666 2005682 2009188 2009193) (-1191 "STTAYLOR.spad" 1998301 1998312 2005547 2005552) (-1190 "STRTBL.spad" 1996352 1996369 1996501 1996528) (-1189 "STRING.spad" 1995139 1995148 1995360 1995387) (-1188 "STREAM.spad" 1991940 1991951 1994547 1994562) (-1187 "STREAM3.spad" 1991513 1991528 1991930 1991935) (-1186 "STREAM2.spad" 1990641 1990654 1991503 1991508) (-1185 "STREAM1.spad" 1990347 1990358 1990631 1990636) (-1184 "STINPROD.spad" 1989283 1989299 1990337 1990342) (-1183 "STEP.spad" 1988484 1988493 1989273 1989278) (-1182 "STEPAST.spad" 1987718 1987727 1988474 1988479) (-1181 "STBL.spad" 1985802 1985830 1985969 1985984) (-1180 "STAGG.spad" 1984877 1984888 1985792 1985797) (-1179 "STAGG.spad" 1983950 1983963 1984867 1984872) (-1178 "STACK.spad" 1983190 1983201 1983440 1983467) (-1177 "SREGSET.spad" 1980858 1980875 1982800 1982827) (-1176 "SRDCMPK.spad" 1979419 1979439 1980848 1980853) (-1175 "SRAGG.spad" 1974562 1974571 1979387 1979414) (-1174 "SRAGG.spad" 1969725 1969736 1974552 1974557) (-1173 "SQMATRIX.spad" 1967268 1967286 1968184 1968271) (-1172 "SPLTREE.spad" 1961664 1961677 1966548 1966575) (-1171 "SPLNODE.spad" 1958252 1958265 1961654 1961659) (-1170 "SPFCAT.spad" 1957061 1957070 1958242 1958247) (-1169 "SPECOUT.spad" 1955613 1955622 1957051 1957056) (-1168 "SPADXPT.spad" 1947208 1947217 1955603 1955608) (-1167 "spad-parser.spad" 1946673 1946682 1947198 1947203) (-1166 "SPADAST.spad" 1946374 1946383 1946663 1946668) (-1165 "SPACEC.spad" 1930573 1930584 1946364 1946369) (-1164 "SPACE3.spad" 1930349 1930360 1930563 1930568) (-1163 "SORTPAK.spad" 1929898 1929911 1930305 1930310) (-1162 "SOLVETRA.spad" 1927661 1927672 1929888 1929893) (-1161 "SOLVESER.spad" 1926189 1926200 1927651 1927656) (-1160 "SOLVERAD.spad" 1922215 1922226 1926179 1926184) (-1159 "SOLVEFOR.spad" 1920677 1920695 1922205 1922210) (-1158 "SNTSCAT.spad" 1920277 1920294 1920645 1920672) (-1157 "SMTS.spad" 1918549 1918575 1919842 1919939) (-1156 "SMP.spad" 1916024 1916044 1916414 1916541) (-1155 "SMITH.spad" 1914869 1914894 1916014 1916019) (-1154 "SMATCAT.spad" 1912979 1913009 1914813 1914864) (-1153 "SMATCAT.spad" 1911021 1911053 1912857 1912862) (-1152 "SKAGG.spad" 1909984 1909995 1910989 1911016) (-1151 "SINT.spad" 1908924 1908933 1909850 1909979) (-1150 "SIMPAN.spad" 1908652 1908661 1908914 1908919) (-1149 "SIG.spad" 1907982 1907991 1908642 1908647) (-1148 "SIGNRF.spad" 1907100 1907111 1907972 1907977) (-1147 "SIGNEF.spad" 1906379 1906396 1907090 1907095) (-1146 "SIGAST.spad" 1905764 1905773 1906369 1906374) (-1145 "SHP.spad" 1903692 1903707 1905720 1905725) (-1144 "SHDP.spad" 1891370 1891397 1891879 1891978) (-1143 "SGROUP.spad" 1890978 1890987 1891360 1891365) (-1142 "SGROUP.spad" 1890584 1890595 1890968 1890973) (-1141 "SGCF.spad" 1883723 1883732 1890574 1890579) (-1140 "SFRTCAT.spad" 1882653 1882670 1883691 1883718) (-1139 "SFRGCD.spad" 1881716 1881736 1882643 1882648) (-1138 "SFQCMPK.spad" 1876353 1876373 1881706 1881711) (-1137 "SFORT.spad" 1875792 1875806 1876343 1876348) (-1136 "SEXOF.spad" 1875635 1875675 1875782 1875787) (-1135 "SEX.spad" 1875527 1875536 1875625 1875630) (-1134 "SEXCAT.spad" 1873299 1873339 1875517 1875522) (-1133 "SET.spad" 1871587 1871598 1872684 1872723) (-1132 "SETMN.spad" 1870037 1870054 1871577 1871582) (-1131 "SETCAT.spad" 1869522 1869531 1870027 1870032) (-1130 "SETCAT.spad" 1869005 1869016 1869512 1869517) (-1129 "SETAGG.spad" 1865554 1865565 1868985 1869000) (-1128 "SETAGG.spad" 1862111 1862124 1865544 1865549) (-1127 "SEQAST.spad" 1861814 1861823 1862101 1862106) (-1126 "SEGXCAT.spad" 1860970 1860983 1861804 1861809) (-1125 "SEG.spad" 1860783 1860794 1860889 1860894) (-1124 "SEGCAT.spad" 1859708 1859719 1860773 1860778) (-1123 "SEGBIND.spad" 1859466 1859477 1859655 1859660) (-1122 "SEGBIND2.spad" 1859164 1859177 1859456 1859461) (-1121 "SEGAST.spad" 1858878 1858887 1859154 1859159) (-1120 "SEG2.spad" 1858313 1858326 1858834 1858839) (-1119 "SDVAR.spad" 1857589 1857600 1858303 1858308) (-1118 "SDPOL.spad" 1854922 1854933 1855213 1855340) (-1117 "SCPKG.spad" 1853011 1853022 1854912 1854917) (-1116 "SCOPE.spad" 1852164 1852173 1853001 1853006) (-1115 "SCACHE.spad" 1850860 1850871 1852154 1852159) (-1114 "SASTCAT.spad" 1850769 1850778 1850850 1850855) (-1113 "SAOS.spad" 1850641 1850650 1850759 1850764) (-1112 "SAERFFC.spad" 1850354 1850374 1850631 1850636) (-1111 "SAE.spad" 1847824 1847840 1848435 1848570) (-1110 "SAEFACT.spad" 1847525 1847545 1847814 1847819) (-1109 "RURPK.spad" 1845184 1845200 1847515 1847520) (-1108 "RULESET.spad" 1844637 1844661 1845174 1845179) (-1107 "RULE.spad" 1842877 1842901 1844627 1844632) (-1106 "RULECOLD.spad" 1842729 1842742 1842867 1842872) (-1105 "RTVALUE.spad" 1842464 1842473 1842719 1842724) (-1104 "RSTRCAST.spad" 1842181 1842190 1842454 1842459) (-1103 "RSETGCD.spad" 1838559 1838579 1842171 1842176) (-1102 "RSETCAT.spad" 1828495 1828512 1838527 1838554) (-1101 "RSETCAT.spad" 1818451 1818470 1828485 1828490) (-1100 "RSDCMPK.spad" 1816903 1816923 1818441 1818446) (-1099 "RRCC.spad" 1815287 1815317 1816893 1816898) (-1098 "RRCC.spad" 1813669 1813701 1815277 1815282) (-1097 "RPTAST.spad" 1813371 1813380 1813659 1813664) (-1096 "RPOLCAT.spad" 1792731 1792746 1813239 1813366) (-1095 "RPOLCAT.spad" 1771804 1771821 1792314 1792319) (-1094 "ROUTINE.spad" 1767225 1767234 1769989 1770016) (-1093 "ROMAN.spad" 1766553 1766562 1767091 1767220) (-1092 "ROIRC.spad" 1765633 1765665 1766543 1766548) (-1091 "RNS.spad" 1764536 1764545 1765535 1765628) (-1090 "RNS.spad" 1763525 1763536 1764526 1764531) (-1089 "RNG.spad" 1763260 1763269 1763515 1763520) (-1088 "RNGBIND.spad" 1762420 1762434 1763215 1763220) (-1087 "RMODULE.spad" 1762185 1762196 1762410 1762415) (-1086 "RMCAT2.spad" 1761605 1761662 1762175 1762180) (-1085 "RMATRIX.spad" 1760393 1760412 1760736 1760775) (-1084 "RMATCAT.spad" 1755972 1756003 1760349 1760388) (-1083 "RMATCAT.spad" 1751441 1751474 1755820 1755825) (-1082 "RLINSET.spad" 1751145 1751156 1751431 1751436) (-1081 "RINTERP.spad" 1751033 1751053 1751135 1751140) (-1080 "RING.spad" 1750503 1750512 1751013 1751028) (-1079 "RING.spad" 1749981 1749992 1750493 1750498) (-1078 "RIDIST.spad" 1749373 1749382 1749971 1749976) (-1077 "RGCHAIN.spad" 1747901 1747917 1748803 1748830) (-1076 "RGBCSPC.spad" 1747682 1747694 1747891 1747896) (-1075 "RGBCMDL.spad" 1747212 1747224 1747672 1747677) (-1074 "RF.spad" 1744854 1744865 1747202 1747207) (-1073 "RFFACTOR.spad" 1744316 1744327 1744844 1744849) (-1072 "RFFACT.spad" 1744051 1744063 1744306 1744311) (-1071 "RFDIST.spad" 1743047 1743056 1744041 1744046) (-1070 "RETSOL.spad" 1742466 1742479 1743037 1743042) (-1069 "RETRACT.spad" 1741894 1741905 1742456 1742461) (-1068 "RETRACT.spad" 1741320 1741333 1741884 1741889) (-1067 "RETAST.spad" 1741132 1741141 1741310 1741315) (-1066 "RESULT.spad" 1738730 1738739 1739317 1739344) (-1065 "RESRING.spad" 1738077 1738124 1738668 1738725) (-1064 "RESLATC.spad" 1737401 1737412 1738067 1738072) (-1063 "REPSQ.spad" 1737132 1737143 1737391 1737396) (-1062 "REP.spad" 1734686 1734695 1737122 1737127) (-1061 "REPDB.spad" 1734393 1734404 1734676 1734681) (-1060 "REP2.spad" 1724051 1724062 1734235 1734240) (-1059 "REP1.spad" 1718247 1718258 1724001 1724006) (-1058 "REGSET.spad" 1716008 1716025 1717857 1717884) (-1057 "REF.spad" 1715343 1715354 1715963 1715968) (-1056 "REDORDER.spad" 1714549 1714566 1715333 1715338) (-1055 "RECLOS.spad" 1713332 1713352 1714036 1714129) (-1054 "REALSOLV.spad" 1712472 1712481 1713322 1713327) (-1053 "REAL.spad" 1712344 1712353 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"GPOLSET.spad" 780001 780024 780229 780256) (-476 "GOSPER.spad" 779270 779288 779991 779996) (-475 "GMODPOL.spad" 778418 778445 779238 779265) (-474 "GHENSEL.spad" 777501 777515 778408 778413) (-473 "GENUPS.spad" 773794 773807 777491 777496) (-472 "GENUFACT.spad" 773371 773381 773784 773789) (-471 "GENPGCD.spad" 772957 772974 773361 773366) (-470 "GENMFACT.spad" 772409 772428 772947 772952) (-469 "GENEEZ.spad" 770360 770373 772399 772404) (-468 "GDMP.spad" 767416 767433 768190 768317) (-467 "GCNAALG.spad" 761339 761366 767210 767277) (-466 "GCDDOM.spad" 760515 760523 761265 761334) (-465 "GCDDOM.spad" 759753 759763 760505 760510) (-464 "GB.spad" 757279 757317 759709 759714) (-463 "GBINTERN.spad" 753299 753337 757269 757274) (-462 "GBF.spad" 749066 749104 753289 753294) (-461 "GBEUCLID.spad" 746948 746986 749056 749061) (-460 "GAUSSFAC.spad" 746261 746269 746938 746943) (-459 "GALUTIL.spad" 744587 744597 746217 746222) (-458 "GALPOLYU.spad" 743041 743054 744577 744582) (-457 "GALFACTU.spad" 741214 741233 743031 743036) (-456 "GALFACT.spad" 731403 731414 741204 741209) (-455 "FVFUN.spad" 728426 728434 731393 731398) (-454 "FVC.spad" 727478 727486 728416 728421) (-453 "FUNDESC.spad" 727156 727164 727468 727473) (-452 "FUNCTION.spad" 727005 727017 727146 727151) (-451 "FT.spad" 725302 725310 726995 727000) (-450 "FTEM.spad" 724467 724475 725292 725297) (-449 "FSUPFACT.spad" 723367 723386 724403 724408) (-448 "FST.spad" 721453 721461 723357 723362) (-447 "FSRED.spad" 720933 720949 721443 721448) (-446 "FSPRMELT.spad" 719815 719831 720890 720895) (-445 "FSPECF.spad" 717906 717922 719805 719810) (-444 "FS.spad" 712174 712184 717681 717901) (-443 "FS.spad" 706220 706232 711729 711734) (-442 "FSINT.spad" 705880 705896 706210 706215) (-441 "FSERIES.spad" 705071 705083 705700 705799) (-440 "FSCINT.spad" 704388 704404 705061 705066) (-439 "FSAGG.spad" 703505 703515 704344 704383) (-438 "FSAGG.spad" 702584 702596 703425 703430) (-437 "FSAGG2.spad" 701327 701343 702574 702579) (-436 "FS2UPS.spad" 695818 695852 701317 701322) (-435 "FS2.spad" 695465 695481 695808 695813) (-434 "FS2EXPXP.spad" 694590 694613 695455 695460) (-433 "FRUTIL.spad" 693544 693554 694580 694585) (-432 "FR.spad" 687167 687177 692475 692544) (-431 "FRNAALG.spad" 682436 682446 687109 687162) (-430 "FRNAALG.spad" 677717 677729 682392 682397) (-429 "FRNAAF2.spad" 677173 677191 677707 677712) (-428 "FRMOD.spad" 676583 676613 677104 677109) (-427 "FRIDEAL.spad" 675808 675829 676563 676578) (-426 "FRIDEAL2.spad" 675412 675444 675798 675803) (-425 "FRETRCT.spad" 674923 674933 675402 675407) (-424 "FRETRCT.spad" 674300 674312 674781 674786) (-423 "FRAMALG.spad" 672648 672661 674256 674295) (-422 "FRAMALG.spad" 671028 671043 672638 672643) (-421 "FRAC.spad" 668034 668044 668437 668610) (-420 "FRAC2.spad" 667639 667651 668024 668029) (-419 "FR2.spad" 666975 666987 667629 667634) (-418 "FPS.spad" 663790 663798 666865 666970) (-417 "FPS.spad" 660633 660643 663710 663715) (-416 "FPC.spad" 659679 659687 660535 660628) (-415 "FPC.spad" 658811 658821 659669 659674) (-414 "FPATMAB.spad" 658573 658583 658801 658806) (-413 "FPARFRAC.spad" 657423 657440 658563 658568) (-412 "FORTRAN.spad" 655929 655972 657413 657418) (-411 "FORT.spad" 654878 654886 655919 655924) (-410 "FORTFN.spad" 652048 652056 654868 654873) (-409 "FORTCAT.spad" 651732 651740 652038 652043) (-408 "FORMULA.spad" 649206 649214 651722 651727) (-407 "FORMULA1.spad" 648685 648695 649196 649201) (-406 "FORDER.spad" 648376 648400 648675 648680) (-405 "FOP.spad" 647577 647585 648366 648371) (-404 "FNLA.spad" 647001 647023 647545 647572) (-403 "FNCAT.spad" 645596 645604 646991 646996) (-402 "FNAME.spad" 645488 645496 645586 645591) (-401 "FMTC.spad" 645286 645294 645414 645483) (-400 "FMONOID.spad" 644951 644961 645242 645247) (-399 "FMONCAT.spad" 642104 642114 644941 644946) (-398 "FM.spad" 641719 641731 641958 641985) (-397 "FMFUN.spad" 638749 638757 641709 641714) (-396 "FMC.spad" 637801 637809 638739 638744) (-395 "FMCAT.spad" 635469 635487 637769 637796) (-394 "FM1.spad" 634826 634838 635403 635430) (-393 "FLOATRP.spad" 632561 632575 634816 634821) (-392 "FLOAT.spad" 625875 625883 632427 632556) (-391 "FLOATCP.spad" 623306 623320 625865 625870) (-390 "FLINEXP.spad" 623028 623038 623296 623301) (-389 "FLINEXP.spad" 622694 622706 622964 622969) (-388 "FLASORT.spad" 622020 622032 622684 622689) (-387 "FLALG.spad" 619666 619685 621946 622015) (-386 "FLAGG.spad" 616708 616718 619646 619661) (-385 "FLAGG.spad" 613651 613663 616591 616596) (-384 "FLAGG2.spad" 612376 612392 613641 613646) (-383 "FINRALG.spad" 610437 610450 612332 612371) (-382 "FINRALG.spad" 608424 608439 610321 610326) (-381 "FINITE.spad" 607576 607584 608414 608419) (-380 "FINAALG.spad" 596697 596707 607518 607571) (-379 "FINAALG.spad" 585830 585842 596653 596658) (-378 "FILE.spad" 585413 585423 585820 585825) (-377 "FILECAT.spad" 583939 583956 585403 585408) (-376 "FIELD.spad" 583345 583353 583841 583934) (-375 "FIELD.spad" 582837 582847 583335 583340) (-374 "FGROUP.spad" 581484 581494 582817 582832) (-373 "FGLMICPK.spad" 580271 580286 581474 581479) (-372 "FFX.spad" 579646 579661 579987 580080) (-371 "FFSLPE.spad" 579149 579170 579636 579641) (-370 "FFPOLY.spad" 570411 570422 579139 579144) (-369 "FFPOLY2.spad" 569471 569488 570401 570406) (-368 "FFP.spad" 568868 568888 569187 569280) (-367 "FF.spad" 568316 568332 568549 568642) (-366 "FFNBX.spad" 566828 566848 568032 568125) (-365 "FFNBP.spad" 565341 565358 566544 566637) (-364 "FFNB.spad" 563806 563827 565022 565115) (-363 "FFINTBAS.spad" 561320 561339 563796 563801) (-362 "FFIELDC.spad" 558897 558905 561222 561315) (-361 "FFIELDC.spad" 556560 556570 558887 558892) (-360 "FFHOM.spad" 555308 555325 556550 556555) (-359 "FFF.spad" 552743 552754 555298 555303) (-358 "FFCGX.spad" 551590 551610 552459 552552) (-357 "FFCGP.spad" 550479 550499 551306 551399) (-356 "FFCG.spad" 549271 549292 550160 550253) (-355 "FFCAT.spad" 542444 542466 549110 549266) (-354 "FFCAT.spad" 535696 535720 542364 542369) (-353 "FFCAT2.spad" 535443 535483 535686 535691) (-352 "FEXPR.spad" 527160 527206 535199 535238) (-351 "FEVALAB.spad" 526868 526878 527150 527155) (-350 "FEVALAB.spad" 526361 526373 526645 526650) (-349 "FDIV.spad" 525803 525827 526351 526356) (-348 "FDIVCAT.spad" 523867 523891 525793 525798) (-347 "FDIVCAT.spad" 521929 521955 523857 523862) (-346 "FDIV2.spad" 521585 521625 521919 521924) (-345 "FCTRDATA.spad" 520593 520601 521575 521580) (-344 "FCPAK1.spad" 519160 519168 520583 520588) (-343 "FCOMP.spad" 518539 518549 519150 519155) (-342 "FC.spad" 508546 508554 518529 518534) (-341 "FAXF.spad" 501517 501531 508448 508541) (-340 "FAXF.spad" 494540 494556 501473 501478) (-339 "FARRAY.spad" 492537 492547 493570 493597) (-338 "FAMR.spad" 490673 490685 492435 492532) (-337 "FAMR.spad" 488793 488807 490557 490562) (-336 "FAMONOID.spad" 488461 488471 488747 488752) (-335 "FAMONC.spad" 486757 486769 488451 488456) (-334 "FAGROUP.spad" 486381 486391 486653 486680) (-333 "FACUTIL.spad" 484585 484602 486371 486376) (-332 "FACTFUNC.spad" 483779 483789 484575 484580) (-331 "EXPUPXS.spad" 480612 480635 481911 482060) (-330 "EXPRTUBE.spad" 477900 477908 480602 480607) (-329 "EXPRODE.spad" 475060 475076 477890 477895) (-328 "EXPR.spad" 470235 470245 470949 471244) (-327 "EXPR2UPS.spad" 466357 466370 470225 470230) (-326 "EXPR2.spad" 466062 466074 466347 466352) (-325 "EXPEXPAN.spad" 462863 462888 463495 463588) (-324 "EXIT.spad" 462534 462542 462853 462858) (-323 "EXITAST.spad" 462270 462278 462524 462529) (-322 "EVALCYC.spad" 461730 461744 462260 462265) (-321 "EVALAB.spad" 461302 461312 461720 461725) (-320 "EVALAB.spad" 460872 460884 461292 461297) (-319 "EUCDOM.spad" 458446 458454 460798 460867) (-318 "EUCDOM.spad" 456082 456092 458436 458441) (-317 "ESTOOLS.spad" 447928 447936 456072 456077) (-316 "ESTOOLS2.spad" 447531 447545 447918 447923) (-315 "ESTOOLS1.spad" 447216 447227 447521 447526) (-314 "ES.spad" 440031 440039 447206 447211) (-313 "ES.spad" 432752 432762 439929 439934) (-312 "ESCONT.spad" 429545 429553 432742 432747) (-311 "ESCONT1.spad" 429294 429306 429535 429540) (-310 "ES2.spad" 428799 428815 429284 429289) (-309 "ES1.spad" 428369 428385 428789 428794) (-308 "ERROR.spad" 425696 425704 428359 428364) (-307 "EQTBL.spad" 423726 423748 423935 423962) (-306 "EQ.spad" 418531 418541 421318 421430) (-305 "EQ2.spad" 418249 418261 418521 418526) (-304 "EP.spad" 414575 414585 418239 418244) (-303 "ENV.spad" 413253 413261 414565 414570) (-302 "ENTIRER.spad" 412921 412929 413197 413248) (-301 "EMR.spad" 412209 412250 412847 412916) (-300 "ELTAGG.spad" 410463 410482 412199 412204) (-299 "ELTAGG.spad" 408681 408702 410419 410424) (-298 "ELTAB.spad" 408156 408169 408671 408676) (-297 "ELFUTS.spad" 407543 407562 408146 408151) (-296 "ELEMFUN.spad" 407232 407240 407533 407538) (-295 "ELEMFUN.spad" 406919 406929 407222 407227) (-294 "ELAGG.spad" 404890 404900 406899 406914) (-293 "ELAGG.spad" 402798 402810 404809 404814) (-292 "ELABOR.spad" 402144 402152 402788 402793) (-291 "ELABEXPR.spad" 401076 401084 402134 402139) (-290 "EFUPXS.spad" 397852 397882 401032 401037) (-289 "EFULS.spad" 394688 394711 397808 397813) (-288 "EFSTRUC.spad" 392703 392719 394678 394683) (-287 "EF.spad" 387479 387495 392693 392698) (-286 "EAB.spad" 385755 385763 387469 387474) (-285 "E04UCFA.spad" 385291 385299 385745 385750) (-284 "E04NAFA.spad" 384868 384876 385281 385286) (-283 "E04MBFA.spad" 384448 384456 384858 384863) (-282 "E04JAFA.spad" 383984 383992 384438 384443) (-281 "E04GCFA.spad" 383520 383528 383974 383979) (-280 "E04FDFA.spad" 383056 383064 383510 383515) (-279 "E04DGFA.spad" 382592 382600 383046 383051) (-278 "E04AGNT.spad" 378442 378450 382582 382587) (-277 "DVARCAT.spad" 375332 375342 378432 378437) (-276 "DVARCAT.spad" 372220 372232 375322 375327) (-275 "DSMP.spad" 369594 369608 369899 370026) (-274 "DSEXT.spad" 368896 368906 369584 369589) (-273 "DSEXT.spad" 368105 368117 368795 368800) (-272 "DROPT.spad" 362064 362072 368095 368100) (-271 "DROPT1.spad" 361729 361739 362054 362059) (-270 "DROPT0.spad" 356586 356594 361719 361724) (-269 "DRAWPT.spad" 354759 354767 356576 356581) (-268 "DRAW.spad" 347635 347648 354749 354754) (-267 "DRAWHACK.spad" 346943 346953 347625 347630) (-266 "DRAWCX.spad" 344413 344421 346933 346938) (-265 "DRAWCURV.spad" 343960 343975 344403 344408) (-264 "DRAWCFUN.spad" 333492 333500 343950 343955) (-263 "DQAGG.spad" 331670 331680 333460 333487) (-262 "DPOLCAT.spad" 327019 327035 331538 331665) (-261 "DPOLCAT.spad" 322454 322472 326975 326980) (-260 "DPMO.spad" 314214 314230 314352 314565) (-259 "DPMM.spad" 305987 306005 306112 306325) (-258 "DOMTMPLT.spad" 305758 305766 305977 305982) (-257 "DOMCTOR.spad" 305513 305521 305748 305753) (-256 "DOMAIN.spad" 304600 304608 305503 305508) (-255 "DMP.spad" 301860 301875 302430 302557) (-254 "DMEXT.spad" 301727 301737 301828 301855) (-253 "DLP.spad" 301079 301089 301717 301722) (-252 "DLIST.spad" 299505 299515 300109 300136) (-251 "DLAGG.spad" 297922 297932 299495 299500) (-250 "DIVRING.spad" 297464 297472 297866 297917) (-249 "DIVRING.spad" 297050 297060 297454 297459) (-248 "DISPLAY.spad" 295240 295248 297040 297045) (-247 "DIRPROD.spad" 282787 282803 283427 283526) (-246 "DIRPROD2.spad" 281605 281623 282777 282782) (-245 "DIRPCAT.spad" 280798 280814 281501 281600) (-244 "DIRPCAT.spad" 279618 279636 280323 280328) (-243 "DIOSP.spad" 278443 278451 279608 279613) (-242 "DIOPS.spad" 277439 277449 278423 278438) (-241 "DIOPS.spad" 276409 276421 277395 277400) (-240 "DIFRING.spad" 276247 276255 276389 276404) (-239 "DIFFSPC.spad" 275826 275834 276237 276242) (-238 "DIFFSPC.spad" 275403 275413 275816 275821) (-237 "DIFFMOD.spad" 274892 274902 275371 275398) (-236 "DIFFDOM.spad" 274057 274068 274882 274887) (-235 "DIFFDOM.spad" 273220 273233 274047 274052) (-234 "DIFEXT.spad" 273039 273049 273200 273215) (-233 "DIAGG.spad" 272669 272679 273019 273034) (-232 "DIAGG.spad" 272307 272319 272659 272664) (-231 "DHMATRIX.spad" 270502 270512 271647 271674) (-230 "DFSFUN.spad" 264142 264150 270492 270497) (-229 "DFLOAT.spad" 260873 260881 264032 264137) (-228 "DFINTTLS.spad" 259104 259120 260863 260868) (-227 "DERHAM.spad" 257018 257050 259084 259099) (-226 "DEQUEUE.spad" 256225 256235 256508 256535) (-225 "DEGRED.spad" 255842 255856 256215 256220) (-224 "DEFINTRF.spad" 253379 253389 255832 255837) (-223 "DEFINTEF.spad" 251889 251905 253369 253374) (-222 "DEFAST.spad" 251257 251265 251879 251884) (-221 "DECIMAL.spad" 249266 249274 249627 249720) (-220 "DDFACT.spad" 247079 247096 249256 249261) (-219 "DBLRESP.spad" 246679 246703 247069 247074) (-218 "DBASIS.spad" 246305 246320 246669 246674) (-217 "DBASE.spad" 244969 244979 246295 246300) (-216 "DATAARY.spad" 244431 244444 244959 244964) (-215 "D03FAFA.spad" 244259 244267 244421 244426) (-214 "D03EEFA.spad" 244079 244087 244249 244254) (-213 "D03AGNT.spad" 243165 243173 244069 244074) (-212 "D02EJFA.spad" 242627 242635 243155 243160) (-211 "D02CJFA.spad" 242105 242113 242617 242622) (-210 "D02BHFA.spad" 241595 241603 242095 242100) (-209 "D02BBFA.spad" 241085 241093 241585 241590) (-208 "D02AGNT.spad" 235899 235907 241075 241080) (-207 "D01WGTS.spad" 234218 234226 235889 235894) (-206 "D01TRNS.spad" 234195 234203 234208 234213) (-205 "D01GBFA.spad" 233717 233725 234185 234190) (-204 "D01FCFA.spad" 233239 233247 233707 233712) (-203 "D01ASFA.spad" 232707 232715 233229 233234) (-202 "D01AQFA.spad" 232153 232161 232697 232702) (-201 "D01APFA.spad" 231577 231585 232143 232148) (-200 "D01ANFA.spad" 231071 231079 231567 231572) (-199 "D01AMFA.spad" 230581 230589 231061 231066) (-198 "D01ALFA.spad" 230121 230129 230571 230576) (-197 "D01AKFA.spad" 229647 229655 230111 230116) (-196 "D01AJFA.spad" 229170 229178 229637 229642) (-195 "D01AGNT.spad" 225237 225245 229160 229165) (-194 "CYCLOTOM.spad" 224743 224751 225227 225232) (-193 "CYCLES.spad" 221535 221543 224733 224738) (-192 "CVMP.spad" 220952 220962 221525 221530) (-191 "CTRIGMNP.spad" 219452 219468 220942 220947) (-190 "CTOR.spad" 219143 219151 219442 219447) (-189 "CTORKIND.spad" 218746 218754 219133 219138) (-188 "CTORCAT.spad" 217995 218003 218736 218741) (-187 "CTORCAT.spad" 217242 217252 217985 217990) (-186 "CTORCALL.spad" 216831 216841 217232 217237) (-185 "CSTTOOLS.spad" 216076 216089 216821 216826) (-184 "CRFP.spad" 209800 209813 216066 216071) (-183 "CRCEAST.spad" 209520 209528 209790 209795) (-182 "CRAPACK.spad" 208571 208581 209510 209515) (-181 "CPMATCH.spad" 208075 208090 208496 208501) (-180 "CPIMA.spad" 207780 207799 208065 208070) (-179 "COORDSYS.spad" 202789 202799 207770 207775) (-178 "CONTOUR.spad" 202200 202208 202779 202784) (-177 "CONTFRAC.spad" 197950 197960 202102 202195) (-176 "CONDUIT.spad" 197708 197716 197940 197945) (-175 "COMRING.spad" 197382 197390 197646 197703) (-174 "COMPPROP.spad" 196900 196908 197372 197377) (-173 "COMPLPAT.spad" 196667 196682 196890 196895) (-172 "COMPLEX.spad" 192044 192054 192288 192549) (-171 "COMPLEX2.spad" 191759 191771 192034 192039) (-170 "COMPILER.spad" 191308 191316 191749 191754) (-169 "COMPFACT.spad" 190910 190924 191298 191303) (-168 "COMPCAT.spad" 188982 188992 190644 190905) (-167 "COMPCAT.spad" 186782 186794 188446 188451) (-166 "COMMUPC.spad" 186530 186548 186772 186777) (-165 "COMMONOP.spad" 186063 186071 186520 186525) (-164 "COMM.spad" 185874 185882 186053 186058) (-163 "COMMAAST.spad" 185637 185645 185864 185869) (-162 "COMBOPC.spad" 184552 184560 185627 185632) (-161 "COMBINAT.spad" 183319 183329 184542 184547) (-160 "COMBF.spad" 180701 180717 183309 183314) (-159 "COLOR.spad" 179538 179546 180691 180696) (-158 "COLONAST.spad" 179204 179212 179528 179533) (-157 "CMPLXRT.spad" 178915 178932 179194 179199) (-156 "CLLCTAST.spad" 178577 178585 178905 178910) (-155 "CLIP.spad" 174685 174693 178567 178572) (-154 "CLIF.spad" 173340 173356 174641 174680) (-153 "CLAGG.spad" 169845 169855 173330 173335) (-152 "CLAGG.spad" 166221 166233 169708 169713) (-151 "CINTSLPE.spad" 165552 165565 166211 166216) (-150 "CHVAR.spad" 163690 163712 165542 165547) (-149 "CHARZ.spad" 163605 163613 163670 163685) (-148 "CHARPOL.spad" 163115 163125 163595 163600) (-147 "CHARNZ.spad" 162868 162876 163095 163110) (-146 "CHAR.spad" 160742 160750 162858 162863) (-145 "CFCAT.spad" 160070 160078 160732 160737) (-144 "CDEN.spad" 159266 159280 160060 160065) (-143 "CCLASS.spad" 157377 157385 158639 158678) (-142 "CATEGORY.spad" 156419 156427 157367 157372) (-141 "CATCTOR.spad" 156310 156318 156409 156414) (-140 "CATAST.spad" 155928 155936 156300 156305) (-139 "CASEAST.spad" 155642 155650 155918 155923) (-138 "CARTEN.spad" 151009 151033 155632 155637) (-137 "CARTEN2.spad" 150399 150426 150999 151004) (-136 "CARD.spad" 147694 147702 150373 150394) (-135 "CAPSLAST.spad" 147468 147476 147684 147689) (-134 "CACHSET.spad" 147092 147100 147458 147463) (-133 "CABMON.spad" 146647 146655 147082 147087) (-132 "BYTEORD.spad" 146322 146330 146637 146642) (-131 "BYTE.spad" 145749 145757 146312 146317) (-130 "BYTEBUF.spad" 143447 143455 144757 144784) (-129 "BTREE.spad" 142403 142413 142937 142964) (-128 "BTOURN.spad" 141291 141301 141893 141920) (-127 "BTCAT.spad" 140683 140693 141259 141286) (-126 "BTCAT.spad" 140095 140107 140673 140678) (-125 "BTAGG.spad" 139561 139569 140063 140090) (-124 "BTAGG.spad" 139047 139057 139551 139556) (-123 "BSTREE.spad" 137671 137681 138537 138564) (-122 "BRILL.spad" 135868 135879 137661 137666) (-121 "BRAGG.spad" 134808 134818 135858 135863) (-120 "BRAGG.spad" 133712 133724 134764 134769) (-119 "BPADICRT.spad" 131586 131598 131841 131934) (-118 "BPADIC.spad" 131250 131262 131512 131581) (-117 "BOUNDZRO.spad" 130906 130923 131240 131245) (-116 "BOP.spad" 126088 126096 130896 130901) (-115 "BOP1.spad" 123554 123564 126078 126083) (-114 "BOOLE.spad" 123204 123212 123544 123549) (-113 "BOOLE.spad" 122852 122862 123194 123199) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file
+((-3 NIL 2300671 2300676 2300681 2300686) (-2 NIL 2300651 2300656 2300661 2300666) (-1 NIL 2300631 2300636 2300641 2300646) (0 NIL 2300611 2300616 2300621 2300626) (-1327 "ZMOD.spad" 2300420 2300433 2300549 2300606) (-1326 "ZLINDEP.spad" 2299486 2299497 2300410 2300415) (-1325 "ZDSOLVE.spad" 2289430 2289452 2299476 2299481) (-1324 "YSTREAM.spad" 2288925 2288936 2289420 2289425) (-1323 "YDIAGRAM.spad" 2288559 2288568 2288915 2288920) (-1322 "XRPOLY.spad" 2287779 2287799 2288415 2288484) (-1321 "XPR.spad" 2285574 2285587 2287497 2287596) (-1320 "XPOLY.spad" 2285129 2285140 2285430 2285499) (-1319 "XPOLYC.spad" 2284448 2284464 2285055 2285124) (-1318 "XPBWPOLY.spad" 2282885 2282905 2284228 2284297) (-1317 "XF.spad" 2281348 2281363 2282787 2282880) (-1316 "XF.spad" 2279791 2279808 2281232 2281237) (-1315 "XFALG.spad" 2276839 2276855 2279717 2279786) (-1314 "XEXPPKG.spad" 2276090 2276116 2276829 2276834) (-1313 "XDPOLY.spad" 2275704 2275720 2275946 2276015) (-1312 "XALG.spad" 2275364 2275375 2275660 2275699) (-1311 "WUTSET.spad" 2271167 2271184 2274974 2275001) (-1310 "WP.spad" 2270366 2270410 2271025 2271092) (-1309 "WHILEAST.spad" 2270164 2270173 2270356 2270361) (-1308 "WHEREAST.spad" 2269835 2269844 2270154 2270159) (-1307 "WFFINTBS.spad" 2267498 2267520 2269825 2269830) (-1306 "WEIER.spad" 2265720 2265731 2267488 2267493) (-1305 "VSPACE.spad" 2265393 2265404 2265688 2265715) (-1304 "VSPACE.spad" 2265086 2265099 2265383 2265388) (-1303 "VOID.spad" 2264763 2264772 2265076 2265081) (-1302 "VIEW.spad" 2262443 2262452 2264753 2264758) (-1301 "VIEWDEF.spad" 2257644 2257653 2262433 2262438) (-1300 "VIEW3D.spad" 2241605 2241614 2257634 2257639) (-1299 "VIEW2D.spad" 2229496 2229505 2241595 2241600) (-1298 "VECTOR.spad" 2228017 2228028 2228268 2228295) (-1297 "VECTOR2.spad" 2226656 2226669 2228007 2228012) (-1296 "VECTCAT.spad" 2224560 2224571 2226624 2226651) (-1295 "VECTCAT.spad" 2222271 2222284 2224337 2224342) (-1294 "VARIABLE.spad" 2222051 2222066 2222261 2222266) (-1293 "UTYPE.spad" 2221695 2221704 2222041 2222046) (-1292 "UTSODETL.spad" 2220990 2221014 2221651 2221656) (-1291 "UTSODE.spad" 2219206 2219226 2220980 2220985) (-1290 "UTS.spad" 2214153 2214181 2217673 2217770) (-1289 "UTSCAT.spad" 2211632 2211648 2214051 2214148) (-1288 "UTSCAT.spad" 2208755 2208773 2211176 2211181) (-1287 "UTS2.spad" 2208350 2208385 2208745 2208750) (-1286 "URAGG.spad" 2203023 2203034 2208340 2208345) (-1285 "URAGG.spad" 2197660 2197673 2202979 2202984) (-1284 "UPXSSING.spad" 2195305 2195331 2196741 2196874) (-1283 "UPXS.spad" 2192601 2192629 2193437 2193586) (-1282 "UPXSCONS.spad" 2190360 2190380 2190733 2190882) (-1281 "UPXSCCA.spad" 2188931 2188951 2190206 2190355) (-1280 "UPXSCCA.spad" 2187644 2187666 2188921 2188926) (-1279 "UPXSCAT.spad" 2186233 2186249 2187490 2187639) (-1278 "UPXS2.spad" 2185776 2185829 2186223 2186228) (-1277 "UPSQFREE.spad" 2184190 2184204 2185766 2185771) (-1276 "UPSCAT.spad" 2181977 2182001 2184088 2184185) (-1275 "UPSCAT.spad" 2179470 2179496 2181583 2181588) (-1274 "UPOLYC.spad" 2174510 2174521 2179312 2179465) (-1273 "UPOLYC.spad" 2169442 2169455 2174246 2174251) (-1272 "UPOLYC2.spad" 2168913 2168932 2169432 2169437) (-1271 "UP.spad" 2166019 2166034 2166406 2166559) (-1270 "UPMP.spad" 2164919 2164932 2166009 2166014) (-1269 "UPDIVP.spad" 2164484 2164498 2164909 2164914) (-1268 "UPDECOMP.spad" 2162729 2162743 2164474 2164479) (-1267 "UPCDEN.spad" 2161938 2161954 2162719 2162724) (-1266 "UP2.spad" 2161302 2161323 2161928 2161933) (-1265 "UNISEG.spad" 2160655 2160666 2161221 2161226) (-1264 "UNISEG2.spad" 2160152 2160165 2160611 2160616) (-1263 "UNIFACT.spad" 2159255 2159267 2160142 2160147) (-1262 "ULS.spad" 2149039 2149067 2149984 2150413) (-1261 "ULSCONS.spad" 2140173 2140193 2140543 2140692) (-1260 "ULSCCAT.spad" 2137910 2137930 2140019 2140168) (-1259 "ULSCCAT.spad" 2135755 2135777 2137866 2137871) (-1258 "ULSCAT.spad" 2133987 2134003 2135601 2135750) (-1257 "ULS2.spad" 2133501 2133554 2133977 2133982) (-1256 "UINT8.spad" 2133378 2133387 2133491 2133496) (-1255 "UINT64.spad" 2133254 2133263 2133368 2133373) (-1254 "UINT32.spad" 2133130 2133139 2133244 2133249) (-1253 "UINT16.spad" 2133006 2133015 2133120 2133125) (-1252 "UFD.spad" 2132071 2132080 2132932 2133001) (-1251 "UFD.spad" 2131198 2131209 2132061 2132066) (-1250 "UDVO.spad" 2130079 2130088 2131188 2131193) (-1249 "UDPO.spad" 2127572 2127583 2130035 2130040) (-1248 "TYPE.spad" 2127504 2127513 2127562 2127567) (-1247 "TYPEAST.spad" 2127423 2127432 2127494 2127499) (-1246 "TWOFACT.spad" 2126075 2126090 2127413 2127418) (-1245 "TUPLE.spad" 2125561 2125572 2125974 2125979) (-1244 "TUBETOOL.spad" 2122428 2122437 2125551 2125556) (-1243 "TUBE.spad" 2121075 2121092 2122418 2122423) (-1242 "TS.spad" 2119674 2119690 2120640 2120737) (-1241 "TSETCAT.spad" 2106801 2106818 2119642 2119669) (-1240 "TSETCAT.spad" 2093914 2093933 2106757 2106762) (-1239 "TRMANIP.spad" 2088280 2088297 2093620 2093625) (-1238 "TRIMAT.spad" 2087243 2087268 2088270 2088275) (-1237 "TRIGMNIP.spad" 2085770 2085787 2087233 2087238) (-1236 "TRIGCAT.spad" 2085282 2085291 2085760 2085765) (-1235 "TRIGCAT.spad" 2084792 2084803 2085272 2085277) (-1234 "TREE.spad" 2083250 2083261 2084282 2084309) (-1233 "TRANFUN.spad" 2083089 2083098 2083240 2083245) (-1232 "TRANFUN.spad" 2082926 2082937 2083079 2083084) (-1231 "TOPSP.spad" 2082600 2082609 2082916 2082921) (-1230 "TOOLSIGN.spad" 2082263 2082274 2082590 2082595) (-1229 "TEXTFILE.spad" 2080824 2080833 2082253 2082258) (-1228 "TEX.spad" 2077970 2077979 2080814 2080819) (-1227 "TEX1.spad" 2077526 2077537 2077960 2077965) (-1226 "TEMUTL.spad" 2077081 2077090 2077516 2077521) (-1225 "TBCMPPK.spad" 2075174 2075197 2077071 2077076) (-1224 "TBAGG.spad" 2074224 2074247 2075154 2075169) (-1223 "TBAGG.spad" 2073282 2073307 2074214 2074219) (-1222 "TANEXP.spad" 2072690 2072701 2073272 2073277) (-1221 "TALGOP.spad" 2072414 2072425 2072680 2072685) (-1220 "TABLE.spad" 2070383 2070406 2070653 2070680) (-1219 "TABLEAU.spad" 2069864 2069875 2070373 2070378) (-1218 "TABLBUMP.spad" 2066667 2066678 2069854 2069859) (-1217 "SYSTEM.spad" 2065895 2065904 2066657 2066662) (-1216 "SYSSOLP.spad" 2063378 2063389 2065885 2065890) (-1215 "SYSPTR.spad" 2063277 2063286 2063368 2063373) (-1214 "SYSNNI.spad" 2062468 2062479 2063267 2063272) (-1213 "SYSINT.spad" 2061872 2061883 2062458 2062463) (-1212 "SYNTAX.spad" 2058078 2058087 2061862 2061867) (-1211 "SYMTAB.spad" 2056146 2056155 2058068 2058073) (-1210 "SYMS.spad" 2052169 2052178 2056136 2056141) (-1209 "SYMPOLY.spad" 2051175 2051186 2051257 2051384) (-1208 "SYMFUNC.spad" 2050676 2050687 2051165 2051170) (-1207 "SYMBOL.spad" 2048179 2048188 2050666 2050671) (-1206 "SWITCH.spad" 2044950 2044959 2048169 2048174) (-1205 "SUTS.spad" 2041998 2042026 2043417 2043514) (-1204 "SUPXS.spad" 2039281 2039309 2040130 2040279) (-1203 "SUP.spad" 2036001 2036012 2036774 2036927) (-1202 "SUPFRACF.spad" 2035106 2035124 2035991 2035996) (-1201 "SUP2.spad" 2034498 2034511 2035096 2035101) (-1200 "SUMRF.spad" 2033472 2033483 2034488 2034493) (-1199 "SUMFS.spad" 2033109 2033126 2033462 2033467) (-1198 "SULS.spad" 2022880 2022908 2023838 2024267) (-1197 "SUCHTAST.spad" 2022649 2022658 2022870 2022875) (-1196 "SUCH.spad" 2022331 2022346 2022639 2022644) (-1195 "SUBSPACE.spad" 2014446 2014461 2022321 2022326) (-1194 "SUBRESP.spad" 2013616 2013630 2014402 2014407) (-1193 "STTF.spad" 2009715 2009731 2013606 2013611) (-1192 "STTFNC.spad" 2006183 2006199 2009705 2009710) (-1191 "STTAYLOR.spad" 1998818 1998829 2006064 2006069) (-1190 "STRTBL.spad" 1996869 1996886 1997018 1997045) (-1189 "STRING.spad" 1995656 1995665 1995877 1995904) (-1188 "STREAM.spad" 1992457 1992468 1995064 1995079) (-1187 "STREAM3.spad" 1992030 1992045 1992447 1992452) (-1186 "STREAM2.spad" 1991158 1991171 1992020 1992025) (-1185 "STREAM1.spad" 1990864 1990875 1991148 1991153) (-1184 "STINPROD.spad" 1989800 1989816 1990854 1990859) (-1183 "STEP.spad" 1989001 1989010 1989790 1989795) (-1182 "STEPAST.spad" 1988235 1988244 1988991 1988996) (-1181 "STBL.spad" 1986319 1986347 1986486 1986501) (-1180 "STAGG.spad" 1985394 1985405 1986309 1986314) (-1179 "STAGG.spad" 1984467 1984480 1985384 1985389) (-1178 "STACK.spad" 1983707 1983718 1983957 1983984) (-1177 "SREGSET.spad" 1981375 1981392 1983317 1983344) (-1176 "SRDCMPK.spad" 1979936 1979956 1981365 1981370) (-1175 "SRAGG.spad" 1975079 1975088 1979904 1979931) (-1174 "SRAGG.spad" 1970242 1970253 1975069 1975074) (-1173 "SQMATRIX.spad" 1967785 1967803 1968701 1968788) (-1172 "SPLTREE.spad" 1962181 1962194 1967065 1967092) (-1171 "SPLNODE.spad" 1958769 1958782 1962171 1962176) (-1170 "SPFCAT.spad" 1957578 1957587 1958759 1958764) (-1169 "SPECOUT.spad" 1956130 1956139 1957568 1957573) (-1168 "SPADXPT.spad" 1947725 1947734 1956120 1956125) (-1167 "spad-parser.spad" 1947190 1947199 1947715 1947720) (-1166 "SPADAST.spad" 1946891 1946900 1947180 1947185) (-1165 "SPACEC.spad" 1931090 1931101 1946881 1946886) (-1164 "SPACE3.spad" 1930866 1930877 1931080 1931085) (-1163 "SORTPAK.spad" 1930415 1930428 1930822 1930827) (-1162 "SOLVETRA.spad" 1928178 1928189 1930405 1930410) (-1161 "SOLVESER.spad" 1926706 1926717 1928168 1928173) (-1160 "SOLVERAD.spad" 1922732 1922743 1926696 1926701) (-1159 "SOLVEFOR.spad" 1921194 1921212 1922722 1922727) (-1158 "SNTSCAT.spad" 1920794 1920811 1921162 1921189) (-1157 "SMTS.spad" 1919066 1919092 1920359 1920456) (-1156 "SMP.spad" 1916541 1916561 1916931 1917058) (-1155 "SMITH.spad" 1915386 1915411 1916531 1916536) (-1154 "SMATCAT.spad" 1913496 1913526 1915330 1915381) (-1153 "SMATCAT.spad" 1911538 1911570 1913374 1913379) (-1152 "SKAGG.spad" 1910501 1910512 1911506 1911533) (-1151 "SINT.spad" 1909441 1909450 1910367 1910496) (-1150 "SIMPAN.spad" 1909169 1909178 1909431 1909436) (-1149 "SIG.spad" 1908499 1908508 1909159 1909164) (-1148 "SIGNRF.spad" 1907617 1907628 1908489 1908494) (-1147 "SIGNEF.spad" 1906896 1906913 1907607 1907612) (-1146 "SIGAST.spad" 1906281 1906290 1906886 1906891) (-1145 "SHP.spad" 1904209 1904224 1906237 1906242) (-1144 "SHDP.spad" 1891887 1891914 1892396 1892495) (-1143 "SGROUP.spad" 1891495 1891504 1891877 1891882) (-1142 "SGROUP.spad" 1891101 1891112 1891485 1891490) (-1141 "SGCF.spad" 1884240 1884249 1891091 1891096) (-1140 "SFRTCAT.spad" 1883170 1883187 1884208 1884235) (-1139 "SFRGCD.spad" 1882233 1882253 1883160 1883165) (-1138 "SFQCMPK.spad" 1876870 1876890 1882223 1882228) (-1137 "SFORT.spad" 1876309 1876323 1876860 1876865) (-1136 "SEXOF.spad" 1876152 1876192 1876299 1876304) (-1135 "SEX.spad" 1876044 1876053 1876142 1876147) (-1134 "SEXCAT.spad" 1873816 1873856 1876034 1876039) (-1133 "SET.spad" 1872104 1872115 1873201 1873240) (-1132 "SETMN.spad" 1870554 1870571 1872094 1872099) (-1131 "SETCAT.spad" 1870039 1870048 1870544 1870549) (-1130 "SETCAT.spad" 1869522 1869533 1870029 1870034) (-1129 "SETAGG.spad" 1866071 1866082 1869502 1869517) (-1128 "SETAGG.spad" 1862628 1862641 1866061 1866066) (-1127 "SEQAST.spad" 1862331 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122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 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"ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index aa7805eb..b69dce5b 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,15 +1,15 @@
-(205732 . 3497194941)
-(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) #0#) |has| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (-321 (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)))))
-((((-578)) . T) (($) -2230 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (((-421 (-578))) -2230 (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T))
+(205732 . 3498909343)
+(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) #0#) |has| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)))))
+((((-578)) . T) (($) -2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T))
(((|#2| |#2|) . T))
((((-578)) . T))
-((($ $) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2| |#2|) . T) ((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))))
+((($ $) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2| |#2|) . T) ((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))))
((($) . T))
(((|#1|) . T))
((($) . T) (((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#2|) . T))
-((($) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))))
(|has| |#1| (-938))
((((-886)) . T))
((((-886)) . T))
@@ -23,23 +23,23 @@
((((-550)) . T) (((-1189)) . T) (((-229)) . T) (((-392)) . T) (((-917 (-392))) . T))
(((|#1|) . T))
((((-229)) . T) (((-886)) . T))
-(-2230 (|has| |#2| (-815)) (|has| |#2| (-871)))
-(-2230 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871))))
+(-2225 (|has| |#2| (-815)) (|has| |#2| (-871)))
+(-2225 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871))))
(((|#1|) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-870)))
-((($ $) . T) ((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1| |#1|) . T))
-(-2230 (|has| |#1| (-842)) (|has| |#1| (-871)))
+(-2225 (|has| |#1| (-21)) (|has| |#1| (-870)))
+((($ $) . T) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1| |#1|) . T))
+(-2225 (|has| |#1| (-842)) (|has| |#1| (-871)))
((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T))
((((-886)) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-570)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-570)))
(|has| |#1| (-870))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((((-328 |#1|)) . T) (((-578)) . T) (($) . T))
(((|#1| |#2| |#3|) . T))
((((-578)) . T) (((-894 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
-((($) . T) (((-421 (-578))) -2230 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
+((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
((((-421 (-578))) . T) (((-721)) . T) (($) . T))
((((-886)) . T))
((((-1212)) . T))
@@ -52,14 +52,14 @@
(((|#1|) . T) ((|#2|) . T))
((((-1212)) . T))
(((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))))
-(-2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
-(-2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
-(((|#2| (-496 (-3225 |#1|) (-793))) . T))
-((((-1207)) -2230 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207)))))
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+(-2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+(((|#2| (-496 (-4415 |#1|) (-793))) . T))
+((((-1207)) -2225 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207)))))
(((|#1| (-545 (-1207))) . T))
((((-1189)) . T) (((-987 (-131))) . T) (((-886)) . T))
((((-886)) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((#0=(-894 |#1|) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T))
(|has| |#4| (-381))
(|has| |#3| (-381))
@@ -75,14 +75,14 @@
(|has| |#1| (-147))
(|has| |#1| (-149))
(|has| |#1| (-570))
-((((-578)) . T) (((-421 (-578))) -2230 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))) ((|#2|) . T) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-888 |#1|)) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-570)))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-570)))
-((((-2 (|:| -2085 |#1|) (|:| -3761 |#2|))) . T))
+((((-578)) . T) (((-421 (-578))) -2225 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))) ((|#2|) . T) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-888 |#1|)) . T))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-570)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-570)))
+((((-2 (|:| -2480 |#1|) (|:| -3945 |#2|))) . T))
((($) . T))
((((-886)) |has| |#1| (-632 (-886))) ((|#1|) . T))
-((((-578)) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T) (($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((-1207)) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
+((((-578)) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) ((|#1|) . T) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) (((-1207)) . T))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
((((-550)) |has| |#1| (-633 (-550))))
((((-1207)) . T))
(((|#1|) . T))
@@ -103,12 +103,12 @@
((((-886)) . T))
(((|#1| |#2|) . T))
(((|#1|) . T))
-(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
(|has| |#1| (-1131))
(((|#1|) . T))
((((-118 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
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(((|#1|) . T) (((-421 (-578))) . T) (($) . T))
((((-118 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) . T) (($) . T))
@@ -116,14 +116,14 @@
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(((|#2|) . T) (((-578)) . T) ((|#6|) . T))
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((($) . T))
((($) . T))
(((|#2|) . T))
(((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (((-578)) . T) (($) . T))
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((($ $) . T))
((($) . T))
((((-578)) . T) (($) . T) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
@@ -132,30 +132,30 @@
(|has| |#1| (-381))
(((|#1|) . T))
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(((|#1|) . T))
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+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
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(((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (($) . T))
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((((-578)) . T))
((((-886)) . T))
(((|#1| |#2|) . T))
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(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(|has| |#1| (-570))
(((|#1|) . T) (((-578)) . T) (($) . T))
((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-870)))
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((($ $) . T) ((#0=(-421 (-578)) #0#) . T))
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(|has| |#1| (-1131))
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(|has| |#1| (-870))
(((|#1| |#1|) . T))
((($) . T) (((-421 (-578))) . T))
@@ -170,12 +170,12 @@
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(|has| |#3| (-815))
(((|#1| |#2|) . T))
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((((-1212)) . T))
(((|#1| |#2|) . T))
(((|#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) (((-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))))
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-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
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((((-578)) . T) (((-421 (-578))) . T))
(((|#1| (-1207) (-1119 (-1207)) (-545 (-1119 (-1207)))) . T))
((((-578) |#1|) . T))
@@ -195,29 +195,29 @@
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((((-1265 (-578)) $) . T) (((-578) (-131)) . T))
(((|#1|) . T))
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(((|#3| (-793)) . T))
(|has| |#1| (-149))
(|has| |#1| (-147))
((($) . T) (((-421 (-578))) . T))
((($) . T))
((($) . T))
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((((-421 (-578))) . T) (($) . T))
((($) . T))
((($) . T))
(|has| |#1| (-1131))
((((-421 (-578))) . T) (((-578)) . T))
((((-578)) . T) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))))
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((((-1207) |#2|) |has| |#2| (-528 (-1207) |#2|)) ((|#2| |#2|) |has| |#2| (-321 |#2|)))
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(((|#1|) . T) (($) . T))
((((-578)) . T))
((((-578)) . T))
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((((-578)) . T))
((((-578)) . T))
((((-421 (-578))) . T) (($) . T))
@@ -228,7 +228,7 @@
(((|#1|) . T))
(|has| |#2| (-376))
((((-1265 (-578)) $) . T) (((-578) |#1|) . T))
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((($) . T) (((-578)) . T) (((-421 (-578))) . T))
(((|#1| |#2|) . T))
((((-886)) . T))
@@ -241,13 +241,13 @@
((((-886)) . T))
((((-886)) . T))
(((|#1| |#1|) . T))
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(((|#1|) . T))
(((|#1|) . T))
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((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
@@ -258,10 +258,10 @@
((((-172 (-229))) |has| |#1| (-1053)) (((-172 (-392))) |has| |#1| (-1053)) (((-550)) |has| |#1| (-633 (-550))) (((-1203 |#1|)) . T) (((-917 (-578))) |has| |#1| (-633 (-917 (-578)))) (((-917 (-392))) |has| |#1| (-633 (-917 (-392)))))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1|) . T))
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(|has| |#1| (-376))
((((-886)) . T))
((($) . T))
@@ -269,7 +269,7 @@
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(-12 (|has| |#4| (-240)) (|has| |#4| (-1080)))
(-12 (|has| |#3| (-240)) (|has| |#3| (-1080)))
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(|has| |#4| (-1080))
(|has| |#3| (-1080))
((((-886)) . T) (((-1212)) . T))
@@ -280,45 +280,45 @@
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((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T))
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-(((|#1|) . T) (((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
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+((((-2 (|:| -2480 |#1|) (|:| -3945 |#2|))) . T))
((((-886)) . T))
((((-886)) . T))
((((-550)) . T) (((-578)) . T) (((-917 (-578))) . T) (((-392)) . T) (((-229)) . T))
@@ -326,15 +326,15 @@
(((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))))
((($) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
((((-421 $) (-421 $)) |has| |#2| (-570)) (($ $) . T) ((|#2| |#2|) . T))
-((($ (-1207)) -2230 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))))
-((((-2 (|:| -3172 (-1189)) (|:| -2754 (-52)))) . T))
+((($ (-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))))
+((((-2 (|:| -2338 (-1189)) (|:| -2078 (-52)))) . T))
(((|#1|) . T))
(|has| |#2| (-938))
((((-1189) (-52)) . T))
((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T))
((((-550)) . T) (((-229)) . T) (((-392)) . T) (((-917 (-392))) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
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(((|#1|) |has| |#1| (-175)))
(((|#1| $) |has| |#1| (-298 |#1| |#1|)))
((((-886)) . T))
@@ -349,15 +349,15 @@
(|has| |#1| (-1131))
((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
(((|#1|) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
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((((-550)) |has| |#1| (-633 (-550))))
((((-886)) . T) (((-1212)) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
((((-1212)) . T))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
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(|has| |#1| (-240))
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+((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#1| (-545 (-840 (-1207)))) . T))
(((|#1| (-1002)) . T))
((((-578)) . T) ((|#2|) . T))
@@ -369,7 +369,7 @@
(((|#1|) . T))
(((|#2| |#2|) . T))
(|has| |#1| (-1183))
-((((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
+((((-2 (|:| -2338 (-1189)) (|:| -2078 |#1|))) . T))
(|has| (-1284 |#1| |#2| |#3| |#4|) (-147))
(|has| (-1284 |#1| |#2| |#3| |#4|) (-149))
(|has| |#1| (-147))
@@ -381,28 +381,28 @@
(((|#2|) . T))
(((|#1|) . T))
(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
-((((-1156 |#1| (-1207))) . T) (((-578)) . T) (((-840 (-1207))) . T) (($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . T))
+((((-1156 |#1| (-1207))) . T) (((-578)) . T) (((-840 (-1207))) . T) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-1207)) . T))
(|has| |#2| (-381))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((($) . T) ((|#1|) . T))
(((|#2|) |has| |#2| (-1080)))
((((-886)) . T))
(|has| |#1| (-870))
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+(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) #0#) |has| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)))))
(((|#1|) . T))
-((((-1298 (-352 (-2423) (-2423 (QUOTE X)) (-721)))) . T))
-(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((#0=(-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) #0#) |has| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (-321 (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)))))
+((((-1298 (-352 (-2876) (-2876 (QUOTE X)) (-721)))) . T))
+(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((#0=(-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) #0#) |has| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (-321 (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)))))
((((-886)) . T))
((((-578) |#1|) . T))
((((-550)) -12 (|has| |#1| (-633 (-550))) (|has| |#2| (-633 (-550)))) (((-917 (-392))) -12 (|has| |#1| (-633 (-917 (-392)))) (|has| |#2| (-633 (-917 (-392))))) (((-917 (-578))) -12 (|has| |#1| (-633 (-917 (-578)))) (|has| |#2| (-633 (-917 (-578))))))
((($) . T))
((((-886)) . T))
-((($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))))
+((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))))
((((-886)) . T))
((($) . T))
((($) . T))
((($) . T))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
((((-886)) . T))
((((-886)) . T))
(|has| (-1283 |#2| |#3| |#4|) (-149))
@@ -415,18 +415,18 @@
(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
+(-2225 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
(((|#1|) . T))
((($) . T))
((((-578) |#1|) . T))
(((|#2|) |has| |#2| (-175)))
(((|#1|) . T))
(((|#1|) |has| |#1| (-175)))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-870)))
+(-2225 (|has| |#1| (-21)) (|has| |#1| (-870)))
((((-886)) |has| |#1| (-1131)))
-((($) -2230 (|has| |#1| (-240)) (|has| |#1| (-239))))
-(-2230 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-362)))
+((($) -2225 (|has| |#1| (-240)) (|has| |#1| (-239))))
+(-2225 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-362)))
((((-939 |#1|)) . T))
((((-421 |#2|) |#3|) . T))
(|has| |#1| (-15 * (|#1| (-578) |#1|)))
@@ -437,7 +437,7 @@
((((-886)) . T))
((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)))
(|has| |#1| (-376))
-(-2230 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|))))
+(-2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-578) |#1|))))
(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-376))
(|has| |#1| (-15 * (|#1| (-793) |#1|)))
@@ -451,23 +451,23 @@
((((-1265 (-578)) $) . T) (((-578) |#1|) . T))
((((-886)) . T))
(((|#2|) . T))
-(-2230 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
+(-2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
((((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)))
((($) |has| |#1| (-570)) (((-578)) . T))
(|has| |#2| (-815))
(|has| |#2| (-815))
-((((-1290 |#1| |#2| |#3|)) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2230 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-578)) . T) ((|#1|) |has| |#1| (-175)))
-((((-1294 |#2|)) . T) (((-1290 |#1| |#2| |#3|)) . T) (((-1262 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-578)) . T) (($) -2230 (|has| |#1| (-376)) (|has| |#1| (-570))))
+((((-1290 |#1| |#2| |#3|)) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-578)) . T) ((|#1|) |has| |#1| (-175)))
+((((-1294 |#2|)) . T) (((-1290 |#1| |#2| |#3|)) . T) (((-1262 |#1| |#2| |#3|)) . T) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-578)) . T) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (((-578)) . T))
(((|#1|) . T))
((((-1207)) -12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))))
(((|#1|) . T))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(-12 (|has| |#1| (-376)) (|has| |#2| (-842)))
-(-2230 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570)))
-(((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))) ((|#1| |#1|) . T) (($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-570))))
+(-2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570)))
+(((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))) ((|#1| |#1|) . T) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))))
((($ $) |has| |#1| (-570)) ((|#1| |#1|) . T))
-((($ (-1207)) -2230 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207)))))
+((($ (-1207)) -2225 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207)))))
(((#0=(-721) (-1203 #0#)) . T))
((((-595 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
((((-421 (-578))) . T) (($) . T))
@@ -475,18 +475,18 @@
((((-886)) . T) (((-1298 |#3|)) . T))
((((-595 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
((($) . T) (((-421 (-578))) . T))
-((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-570))))
+((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))))
((($) |has| |#1| (-570)) ((|#1|) . T))
((((-886)) . T))
((($) . T) (((-578)) . T) (((-421 (-578))) . T))
((($) . T))
-((($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((#1=(-1290 |#1| |#2| |#3|) #1#) |has| |#1| (-376)) ((|#1| |#1|) . T))
-(((|#1| |#1|) . T) (($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . T))
-(((|#1|) . T) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
+((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((#1=(-1290 |#1| |#2| |#3|) #1#) |has| |#1| (-376)) ((|#1| |#1|) . T))
+(((|#1| |#1|) . T) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . T))
+(((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
(((|#3|) |has| |#3| (-1080)))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) |has| |#1| (-38 (-421 (-578)))))
(|has| (-1125 |#1|) (-1131))
(((|#2| (-841 |#1|)) . T))
((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T))
@@ -494,20 +494,20 @@
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
(((|#2|) . T) ((|#6|) . T))
(|has| |#1| (-376))
((((-578)) . T) ((|#2|) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (($) -2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (($) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
(((|#2|) . T) ((|#6|) . T))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((($) -2230 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
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@@ -717,8 +717,8 @@
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((((-421 (-578))) . T) (($) . T))
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@@ -729,13 +729,13 @@
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(|has| |#2| (-1080))
(|has| |#2| (-815))
(|has| |#2| (-815))
@@ -766,45 +766,45 @@
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((((-421 (-578))) . T) (((-578)) . T) (($) . T))
@@ -812,26 +812,26 @@
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(((#0=(-421 (-981 |#1|)) #0#) . T))
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((((-886)) . T) (((-1212)) . T))
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(((|#1| |#1|) |has| |#1| (-175)))
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(((|#1|) . T))
(((|#1|) . T) (((-578)) . T) (($) . T))
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((((-886)) . T))
((((-886)) . T))
((((-1284 |#1| |#2| |#3| |#4|)) . T))
@@ -840,8 +840,8 @@
(|has| |#3| (-1080))
(|has| |#3| (-815))
(|has| |#3| (-815))
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(((|#2|) . T))
((((-886)) . T))
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@@ -855,37 +855,37 @@
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(((|#2|) . T))
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((((-886)) . T))
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-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
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+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
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(|has| (-421 |#2|) (-147))
@@ -898,15 +898,15 @@
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(|has| |#1| (-38 (-421 (-578))))
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((((-886)) . T))
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(|has| |#1| (-38 (-421 (-578))))
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((((-886)) . T) (((-1212)) . T))
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@@ -924,7 +924,7 @@
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((((-578)) . T) (($) . T) (((-421 (-578))) . T))
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@@ -942,7 +942,7 @@
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((((-886)) . T))
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(((|#2|) |has| |#2| (-321 |#2|)))
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@@ -953,14 +953,14 @@
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@@ -968,8 +968,8 @@
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((((-886)) . T))
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@@ -981,7 +981,7 @@
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@@ -990,29 +990,29 @@
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((((-886)) . T))
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(((|#1|) . T))
(|has| |#1| (-1131))
((((-886)) . T))
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((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
@@ -1025,7 +1025,7 @@
((((-1212)) . T) (((-886)) . T))
((((-1212)) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
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(((|#1| (-1002)) . T))
(((|#1| |#1|) . T))
((($) . T))
@@ -1041,23 +1041,23 @@
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(-12 (|has| |#1| (-815)) (|has| |#2| (-815)))
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(((|#1| |#2|) . T))
(((|#1|) |has| |#1| (-175)) ((|#4|) . T) (((-578)) . T))
(((|#2|) |has| |#2| (-175)))
(((|#1|) |has| |#1| (-175)))
((((-886)) . T))
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(|has| |#1| (-362))
(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
((((-421 (-578))) . T) (($) . T))
(((|#2|) . T) (($) . T) (((-421 (-578))) . T))
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(|has| |#1| (-850))
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(((|#1| $) |has| |#1| (-298 |#1| |#1|)))
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((($) |has| |#1| (-570)))
@@ -1065,49 +1065,49 @@
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(((|#3|) |has| |#3| (-1131)))
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+((($) |has| |#1| (-570)) ((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-578)) . T))
((((-886)) . T))
(((|#1| |#2|) . T))
((((-886)) . T))
(|has| |#1| (-871))
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(((|#2|) . T))
(|has| |#2| (-376))
((((-421 (-578))) . T) (((-578)) . T))
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((($ (-888 |#1|)) . T))
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((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T))
(((|#1|) . T))
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(((|#2|) . T))
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(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
((((-146)) . T))
(((|#1|) . T))
(((|#1|) . T))
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((((-146)) . T))
((((-146)) . T))
((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#) ((|#2|) . T) (((-578)) . T))
(((|#1| |#2| |#3|) . T))
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(((|#1|) |has| |#1| (-175)))
(|has| $ (-149))
(|has| $ (-149))
((((-1212)) . T))
(((|#1|) |has| |#1| (-175)))
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((((-886)) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
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((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|)))
(((|#1| (-421 (-578))) . T))
(((|#1|) . T))
@@ -1116,8 +1116,8 @@
(((|#1|) . T))
((((-1207)) . T))
(|has| |#1| (-570))
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(|has| |#1| (-570))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
@@ -1129,7 +1129,7 @@
(|has| |#1| (-149))
(|has| |#1| (-147))
(|has| |#1| (-149))
-(((|#2| (-247 (-3225 |#1|) (-793)) (-888 |#1|)) . T))
+(((|#2| (-247 (-4415 |#1|) (-793)) (-888 |#1|)) . T))
(((|#1| (-545 |#3|) |#3|) . T))
(|has| |#1| (-147))
(((#0=(-421 (-578)) #0#) |has| |#2| (-376)) (($ $) . T))
@@ -1143,12 +1143,12 @@
(|has| |#1| (-147))
((((-421 (-578))) |has| |#2| (-376)) (($) . T))
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(|has| |#3| (-815))
((((-886)) . T))
@@ -1176,18 +1176,18 @@
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((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T))
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@@ -1211,10 +1211,10 @@
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@@ -1233,34 +1233,34 @@
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(((|#1| (-657 |#2|)) . T))
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@@ -1269,10 +1269,10 @@
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(((|#1| |#2|) . T))
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@@ -1280,46 +1280,46 @@
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((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
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((($) . T))
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((((-886)) . T))
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((((-886)) . T))
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((((-1212)) . T))
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@@ -1329,21 +1329,21 @@
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(((|#1| |#4|) . T))
(((|#1| |#3|) . T))
((($) . T))
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(((|#2|) . T) (((-886)) . T))
((((-886)) . T))
(((|#2|) . T))
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(((|#1| |#2|) . T))
((($) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
@@ -1352,7 +1352,7 @@
(((|#1|) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
(((|#1| |#1|) . T))
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(((|#1| |#2|) . T))
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@@ -1361,7 +1361,7 @@
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(|has| |#2| (-1080))
((($) . T) (((-578)) . T) ((|#2|) . T))
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+(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#2|) . T) (($) . T))
(|has| |#1| (-1233))
(((#0=(-578) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T))
@@ -1375,7 +1375,7 @@
(((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-578)) #0#) . T))
(|has| |#1| (-376))
((((-578)) . T) (((-421 (-578))) . T) (($) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
((((-886)) . T))
((((-886)) . T))
@@ -1383,39 +1383,39 @@
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
(((|#1|) . T))
((((-886)) . T))
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+((($ $) . T) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1| |#1|) . T))
((((-550)) |has| |#3| (-633 (-550))))
(((|#1| |#2|) . T))
(|has| |#1| (-870))
(|has| |#1| (-870))
((((-711 |#3|)) . T) (((-886)) . T))
-((($) . T) (((-421 (-578))) -2230 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
+((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
(((|#1|) . T))
-(-2230 (|has| |#1| (-175)) (|has| |#1| (-570)))
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((($) . T))
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((($) . T))
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((($) . T))
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((((-886)) . T))
(((|#2|) . T))
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+((($) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))))
((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T))
((($) . T) (((-578)) . T))
((((-578) (-146)) . T))
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+((((-578) (-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T) ((|#1| |#2|) . T))
((((-421 (-578))) . T) (($) . T))
(((|#1|) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((((-886)) . T))
((((-939 |#1|)) . T))
(|has| |#1| (-376))
@@ -1423,11 +1423,11 @@
(|has| |#1| (-376))
(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-870))
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+((($) -2225 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
(|has| |#1| (-376))
(((|#1|) . T) (($) . T))
(|has| |#1| (-870))
-((($) . T) (((-421 (-578))) -2230 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
+((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T))
((((-1207)) |has| |#1| (-927 (-1207))))
(|has| |#1| (-870))
((((-520)) . T))
@@ -1443,7 +1443,7 @@
((((-550)) . T))
((((-886)) . T))
((($) . T))
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(((|#1|) . T))
(((|#2|) . T) (($) . T))
(((|#1|) |has| |#1| (-175)))
@@ -1453,22 +1453,22 @@
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#3|) . T))
(((|#1|) |has| |#1| (-175)))
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(((|#1|) . T))
(((|#1|) . T))
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((((-886)) . T))
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((((-520)) . T))
((((-520)) . T))
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(|has| |#1| (-570))
(-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))
-(-2230 (|has| |#1| (-240)) (|has| |#1| (-239)))
+(-2225 (|has| |#1| (-240)) (|has| |#1| (-239)))
((((-894 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
(|has| |#1| (-381))
(|has| |#1| (-381))
@@ -1477,7 +1477,7 @@
((((-1189) |#1|) . T))
(|has| |#1| (-1183))
((((-987 |#1|)) . T))
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+(((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1| |#1|) . T))
((((-421 (-578))) |has| |#1| (-1069 (-578))) (((-578)) |has| |#1| (-1069 (-578))) (((-1207)) |has| |#1| (-1069 (-1207))) ((|#1|) . T))
((($) . T))
((($) . T))
@@ -1485,7 +1485,7 @@
((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T))
((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T))
((((-578)) |has| |#1| (-911 (-578))) (((-392)) |has| |#1| (-911 (-392))))
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+((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T) (($) . T) (((-578)) . T))
((((-666 |#4|)) . T) (((-886)) . T))
@@ -1493,37 +1493,37 @@
((((-550)) |has| |#4| (-633 (-550))))
((((-886)) . T) (((-666 |#4|)) . T))
((($) |has| |#1| (-870)))
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-((((-578)) -2230 (-12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1131)) (((-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))))
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(((|#1|) . T))
(((|#1|) . T))
((((-666 |#4|)) . T) (((-886)) . T))
((((-550)) |has| |#4| (-633 (-550))))
(((|#1|) . T))
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(((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (((-578)) . T) (($) . T))
((((-1207)) |has| (-421 |#2|) (-927 (-1207))))
(((|#2|) . T))
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((($) . T))
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((($) . T))
((($) . T))
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((($) . T))
((($) . T))
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+((((-886)) -2225 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-632 (-886))) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-381)) (|has| |#3| (-748)) (|has| |#3| (-815)) (|has| |#3| (-871)) (|has| |#3| (-1080)) (|has| |#3| (-1131))) (((-1298 |#3|)) . T))
(((|#2|) . T))
((((-578) |#2|) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1131)))
-(((|#2| |#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))))
+(-2225 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1131)))
+(((|#2| |#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))))
(((|#2|) . T) (((-578)) . T))
((((-886)) . T))
((((-886)) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T) ((|#2|) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T) ((|#2|) . T))
((((-886)) . T))
((((-886)) . T))
((((-1189) (-1207) (-578) (-229) (-886)) . T))
@@ -1559,9 +1559,9 @@
((((-421 (-578))) . T) (($) . T))
((((-886)) . T))
((((-550)) |has| |#1| (-633 (-550))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
((($) . T) (((-421 (-578))) . T))
-(((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))))
+(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))))
(|has| $ (-149))
((((-421 |#2|)) . T))
((((-421 (-578))) |has| #0=(-421 |#2|) (-1069 (-421 (-578)))) (((-578)) |has| #0# (-1069 (-578))) ((#0#) . T))
@@ -1570,11 +1570,11 @@
(|has| |#2| (-149))
(|has| |#1| (-149))
(|has| |#1| (-147))
-(-2230 (|has| |#1| (-147)) (|has| |#1| (-381)))
+(-2225 (|has| |#1| (-147)) (|has| |#1| (-381)))
(|has| |#1| (-149))
-(-2230 (|has| |#1| (-147)) (|has| |#1| (-381)))
+(-2225 (|has| |#1| (-147)) (|has| |#1| (-381)))
(|has| |#1| (-149))
-(-2230 (|has| |#1| (-147)) (|has| |#1| (-381)))
+(-2225 (|has| |#1| (-147)) (|has| |#1| (-381)))
(|has| |#1| (-149))
(((|#1|) . T))
(|has| |#2| (-240))
@@ -1611,9 +1611,9 @@
((((-886)) . T))
((((-886)) . T))
((((-1030 |#1|)) . T) ((|#1|) . T))
-((((-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . T))
+((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . T))
((((-886)) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((((-421 (-578))) . T) (((-421 |#1|)) . T) ((|#1|) . T) (($) . T))
(((|#1| (-1203 |#1|)) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
@@ -1622,8 +1622,8 @@
(((|#1|) . T) (((-578)) . T) (($) . T))
(((|#2|) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
-((((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-2 (|:| -2338 (-1189)) (|:| -2078 |#1|))) . T))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
((((-578) |#2|) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
((($) . T) (((-578)) . T) (((-421 (-578))) . T))
@@ -1634,9 +1634,9 @@
((((-886)) . T))
(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
(((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1131))))
-(-2230 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))
+(-2225 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))
(|has| |#1| (-38 (-421 (-578))))
-(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) #0#) |has| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (-321 (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)))))
+(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) #0#) |has| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)))))
(((|#2| |#2|) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#2| (-376))
@@ -1645,21 +1645,21 @@
(((|#2|) . T))
((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)))
(((|#1|) |has| |#1| (-175)))
-((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))))
-((($) -2230 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))))
+((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(|has| |#1| (-1131))
(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-38 (-421 (-578))))
((((-1189) (-52)) . T))
(((|#1|) . T))
-((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((($ (-1207)) -2230 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (($ (-1113)) . T))
+((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($ (-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (($ (-1113)) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
(((|#2|) |has| |#2| (-175)))
(((|#2|) . T))
-((((-578)) -2230 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) ((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080)))
+((((-578)) -2225 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) ((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080)))
(((|#1|) . T))
((((-578) |#3|) . T))
((((-578) (-146)) . T))
@@ -1675,7 +1675,7 @@
((((-578)) . T) (($) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1|) . T))
-((($ (-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))))
+((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))))
(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
((((-146)) . T))
((((-886)) . T))
@@ -1686,26 +1686,26 @@
(((|#1|) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1| |#2|) . T))
-(-2230 (|has| |#2| (-240)) (|has| |#2| (-239)))
+(-2225 (|has| |#2| (-240)) (|has| |#2| (-239)))
((((-578) (-146)) . T) (((-1265 (-578)) $) . T))
-(((#0=(-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) #0#) |has| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (-321 (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+(((#0=(-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) #0#) |has| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
+((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(|has| |#1| (-871))
(((|#2| (-793) (-1113)) . T))
(((|#1| |#2|) . T))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207)))))
(|has| |#1| (-813))
-(-2230 (|has| |#1| (-175)) (|has| |#1| (-570)))
-((((-1207)) -2230 (-12 (|has| (-1290 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1290 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
+(-2225 (|has| |#1| (-175)) (|has| |#1| (-570)))
+((((-1207)) -2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1290 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
(((|#1|) |has| |#1| (-175)))
(((|#4|) . T))
(((|#4|) . T))
(((|#1| |#2|) . T))
-(-2230 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149))))
+(-2225 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149))))
(((|#4|) . T))
-(-2230 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147))))
+(-2225 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147))))
((((-1189) |#1|) . T))
(|has| |#1| (-147))
(|has| |#1| (-149))
@@ -1719,24 +1719,24 @@
(((|#3|) . T))
((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)))
((($) . T) (((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T))
-((((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-578)) . T) (($) . T) ((|#1|) . T))
-(((|#1|) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-578)) . T) (($) . T))
+((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-578)) . T) (($) . T) ((|#1|) . T))
+(((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-578)) . T) (($) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1131)))
+(-2225 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1131)))
(((|#1|) . T))
(((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (((-578)) . T) (($) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))) (((-987 |#1|)) . T))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))) (((-987 |#1|)) . T))
(|has| |#1| (-870))
(|has| |#1| (-870))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((((-987 |#1|)) . T))
-(((|#4|) -2230 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748))))
-(((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748))))
+(((|#4|) -2225 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748))))
+(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748))))
(|has| |#2| (-376))
(((|#1|) |has| |#1| (-175)))
-(((|#4|) -2230 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080))))
-(((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))))
+(((|#4|) -2225 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080))))
+(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))))
(((|#2|) |has| |#2| (-1080)))
(((|#2|) |has| |#2| (-1080)))
((((-1189) |#1|) . T))
@@ -1748,8 +1748,8 @@
((((-402) (-1189)) . T))
((($ (-1207)) . T))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((((-886)) -2230 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-886))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1131))) (((-1298 |#2|)) . T))
-(((#0=(-52)) . T) (((-2 (|:| -3172 (-1189)) (|:| -2754 #0#))) . T))
+((((-886)) -2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-886))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1131))) (((-1298 |#2|)) . T))
+(((#0=(-52)) . T) (((-2 (|:| -2338 (-1189)) (|:| -2078 #0#))) . T))
(((|#1|) . T))
((((-886)) . T))
(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
@@ -1758,7 +1758,7 @@
((((-578)) . T))
(|has| |#2| (-149))
(|has| |#1| (-487))
-(-2230 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
+(-2225 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
(|has| |#1| (-376))
((((-886)) . T))
(|has| |#1| (-38 (-421 (-578))))
@@ -1769,8 +1769,8 @@
(|has| |#1| (-870))
((((-886)) . T))
(((|#2|) . T))
-((((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2230 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175)))
-(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2230 (|has| |#1| (-376)) (|has| |#1| (-570))))
+((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175)))
+(((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#2|) . T) (((-578)) . T) (((-841 |#1|)) . T))
(((|#1| |#2|) . T))
@@ -1779,8 +1779,8 @@
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
((((-886)) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
-(((|#2| (-496 (-3225 |#1|) (-793)) (-888 |#1|)) . T))
+(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131)))
+(((|#2| (-496 (-4415 |#1|) (-793)) (-888 |#1|)) . T))
((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#))
(((|#1| (-545 (-1207)) (-1207)) . T))
(((|#1|) . T))
@@ -1801,19 +1801,19 @@
(((|#2|) |has| |#2| (-175)))
(((|#1|) . T))
(((|#2|) . T))
-(((|#1|) . T) (((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+(((|#1|) . T) (((-2 (|:| -2338 (-1189)) (|:| -2078 |#1|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#2|) . T))
-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) . T))
+((((-2 (|:| -2338 (-1207)) (|:| -2078 (-52)))) . T))
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((((-1207) (-52)) . T))
((((-421 (-578)) |#1|) . T) (($ $) . T))
(((|#1| (-578)) . T))
((((-939 |#1|)) . T))
-(((|#1|) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))))
-((((-1207)) -2230 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080)))))
+(((|#1|) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))))
+((((-1207)) -2225 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080)))))
(((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))))
(|has| |#1| (-871))
(|has| |#1| (-871))
@@ -1834,15 +1834,15 @@
(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
(((|#1|) |has| |#1| (-175)))
(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
-(((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376))))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-(-2230 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-938)))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376))))
+((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+(-2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-938)))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
((($ |#2|) . T))
-((($ (-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T))
+((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T))
((($ $) . T) ((#0=(-421 (-578)) #0#) . T))
((((-578) |#2|) . T))
-(((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376))))
+(((|#2|) -2225 (|has| |#2| (-175)) (|has| |#2| (-376))))
(|has| |#1| (-362))
(((|#3| |#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1131))))
(((|#2|) . T) (((-578)) . T))
@@ -1851,7 +1851,7 @@
(|has| |#1| (-842))
(|has| |#1| (-842))
(((|#1|) . T))
-(-2230 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-362)))
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(|has| |#1| (-870))
(|has| |#1| (-870))
(|has| |#1| (-870))
@@ -1860,14 +1860,14 @@
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
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(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T))
(((|#1|) . T))
(|has| |#1| (-870))
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(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(|has| |#1| (-1131))
((((-886)) . T) (((-1212)) . T))
@@ -1891,14 +1891,14 @@
(((|#3|) . T))
(((|#1| (-793) (-1113)) . T))
((((-146)) . T))
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+((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) -2225 (|has| |#1| (-870)) (|has| |#1| (-1069 (-578)))) ((|#1|) . T))
(((|#1|) . T))
(((|#2|) . T))
((((-146)) . T))
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((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
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(((|#1|) . T))
(|has| |#1| (-147))
(|has| |#1| (-149))
@@ -1917,31 +1917,31 @@
((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)))
((($) |has| |#1| (-570)))
(((|#2|) . T))
-((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-570))))
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((($) |has| |#1| (-570)) ((|#1|) . T))
((($) |has| |#1| (-870)))
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
(|has| |#1| (-938))
((((-1207)) . T))
((((-886)) . T))
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+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-570))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((((-578) |#2|) . T))
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((($) |has| |#1| (-381)))
((($) |has| |#1| (-381)))
((($) |has| |#1| (-381)))
(((|#1| |#2|) . T))
-(-2230 (|has| |#2| (-466)) (|has| |#2| (-938)))
-(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((#0=(-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) #0#) |has| (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)) (-321 (-2 (|:| -3172 (-1189)) (|:| -2754 |#1|)))))
-(-2230 (|has| |#1| (-466)) (|has| |#1| (-938)))
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+(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((#0=(-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) #0#) |has| (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)) (-321 (-2 (|:| -2338 (-1189)) (|:| -2078 |#1|)))))
+(-2225 (|has| |#1| (-466)) (|has| |#1| (-938)))
(((|#1|) . T))
(((|#1|) . T) (($) . T))
(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
@@ -1950,23 +1950,23 @@
(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
-(((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376))))
+(((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376))))
(|has| |#1| (-871))
(|has| |#1| (-570))
((((-595 |#1|)) . T))
((($) . T))
(((|#2|) . T))
-(-2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-842))) (-12 (|has| |#1| (-376)) (|has| |#2| (-871))))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-570)))
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+(-2225 (|has| |#1| (-376)) (|has| |#1| (-570)))
((((-939 |#1|)) . T))
(((|#1| (-510 |#1| |#3|) (-510 |#1| |#2|)) . T))
(((|#1| |#4| |#5|) . T))
(((|#1| (-793)) . T))
((((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)))
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((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) . T))
+((((-2 (|:| -2338 (-1207)) (|:| -2078 (-52)))) . T))
((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T) (((-421 (-578))) . T) (($) . T))
((((-694 |#1|)) . T))
(((|#1| |#2| |#3| |#4|) . T))
@@ -1975,7 +1975,7 @@
((((-886)) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((((-886)) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
((((-1212)) . T))
((((-421 (-578))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-578)) . T))
(((|#3|) . T) (((-578)) . T) (((-631 $)) . T))
@@ -1983,12 +1983,12 @@
((((-886)) . T))
((((-886)) . T))
(((|#2|) . T))
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(|has| |#2| (-1080))
((((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T))
(|has| |#1| (-1233))
(|has| |#1| (-1233))
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(|has| |#1| (-1233))
(|has| |#1| (-1233))
((($) . T) (((-578)) . T) (((-421 (-578))) . T))
@@ -2007,16 +2007,16 @@
((((-1189) (-52)) . T))
(|has| |#1| (-1131))
(((|#1|) |has| |#1| (-175)) (($) . T))
-(-2230 (|has| |#2| (-842)) (|has| |#2| (-871)))
+(-2225 (|has| |#2| (-842)) (|has| |#2| (-871)))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
(((|#1|) . T) (((-421 (-578))) . T) (($) . T))
(((|#1|) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
((((-578)) . T) (($) . T))
((((-793)) . T))
-(-2230 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-362)))
-((((-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))))
-(-2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
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+(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
((((-886)) . T))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(|has| |#2| (-938))
@@ -2024,32 +2024,32 @@
(((|#2|) |has| |#2| (-1131)))
((($) . T) (((-578)) . T))
((($) . T))
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((((-550)) . T) (((-421 (-1203 (-578)))) . T) (((-229)) . T) (((-392)) . T))
((((-392)) . T) (((-229)) . T) (((-886)) . T))
(|has| |#1| (-938))
(|has| |#1| (-938))
-((($ (-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-840 (-1207))) . T))
+((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-840 (-1207))) . T))
((((-578)) . T) (((-421 (-578))) . T) (($) . T))
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(|has| |#1| (-938))
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((($) . T))
(((|#1|) . T))
((($) . T) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
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(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
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((((-886)) . T))
((((-886)) . T))
((($ $) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
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+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
+((($) -2225 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))))
((($) |has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))))
((((-1002)) . T))
((((-1002)) . T) (((-886)) . T))
@@ -2058,7 +2058,7 @@
((($) . T))
(((|#1|) . T))
((((-112)) . T))
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((((-578)) . T))
(((|#1| (-578)) . T))
((($) . T))
@@ -2081,7 +2081,7 @@
(((|#1| (-1262 |#1| |#2| |#3|)) . T))
((((-886)) . T))
(|has| |#1| (-1131))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#1| (-793)) . T))
((((-1189) |#1|) . T))
(((|#1|) . T))
@@ -2102,20 +2102,20 @@
((((-578)) . T))
((((-578)) . T))
((((-886)) . T))
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((((-886)) . T))
(|has| |#1| (-149))
(((|#3|) . T))
((((-886)) . T))
(|has| |#3| (-1080))
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((((-1283 |#2| |#3| |#4|)) . T) (((-1284 |#1| |#2| |#3| |#4|)) . T))
((((-886)) . T))
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(((|#1|) . T) (($) . T))
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(((|#1|) . T))
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(((|#1|) |has| |#1| (-321 |#1|)))
((((-1284 |#1| |#2| |#3| |#4|)) . T))
((((-578)) |has| |#1| (-911 (-578))) (((-392)) |has| |#1| (-911 (-392))))
@@ -2124,31 +2124,31 @@
(((|#1|) . T))
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(((|#1|) . T))
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((((-886)) . T))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
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(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
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((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
(((|#1|) |has| |#1| (-175)) (($) . T) (((-578)) . T))
(((|#1|) . T))
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(((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) (((-578)) . T) (($) . T))
(((|#3|) |has| |#3| (-1131)))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
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((((-888 |#1|)) . T))
((((-1283 |#2| |#3| |#4|)) . T))
((((-112)) . T))
@@ -2159,8 +2159,8 @@
(|has| |#1| (-870))
(|has| |#1| (-870))
(((|#1| (-578) (-1113)) . T))
-(-2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+(-2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#1| (-421 (-578)) (-1113)) . T))
(((|#1| (-793) (-1113)) . T))
(|has| |#1| (-871))
@@ -2174,41 +2174,41 @@
((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
(|has| |#1| (-1131))
((((-421 (-578))) |has| |#2| (-376)) (($) . T) (((-578)) . T))
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(((|#1|) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
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((((-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((|#2|) |has| |#1| (-376)))
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-((((-711 (-352 (-2423) (-2423 (QUOTE X) (QUOTE HESS)) (-721)))) . T))
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+((((-711 (-352 (-2876) (-2876 (QUOTE X) (QUOTE HESS)) (-721)))) . T))
(((|#2|) |has| |#2| (-175)))
(((|#1|) |has| |#1| (-175)))
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-((((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
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((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
((((-1283 |#2| |#3| |#4|) (-331 |#2| |#3| |#4|)) . T))
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(((|#1|) . T))
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(((|#1|) . T))
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(((|#1|) . T) (((-578)) . T))
(((|#2|) . T))
((((-578)) . T) ((|#3|) . T))
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(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
((((-886)) . T))
((((-886)) . T))
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((((-550)) . T) (((-578)) . T) (((-917 (-578))) . T) (((-392)) . T) (((-229)) . T))
((((-886)) . T))
((($) |has| |#1| (-240)))
@@ -2243,12 +2243,12 @@
(|has| |#1| (-147))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#1|) |has| |#1| (-175)))
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((((-578)) . T) ((|#1|) . T) (($) . T) (((-421 (-578))) . T) (((-1207)) |has| |#1| (-1069 (-1207))))
(((|#1| |#2|) . T))
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((((-146)) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
@@ -2259,13 +2259,13 @@
((((-886)) . T))
(((|#1|) . T) (((-421 (-578))) . T) (($) . T))
((($) . T) (((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
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(|has| |#1| (-376))
(|has| |#1| (-376))
((($ |#2|) . T))
(|has| (-421 |#2|) (-240))
((((-666 |#1|)) . T))
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+((($ (-1294 |#2|)) . T) (($ (-1207)) -2225 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-929 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
(|has| |#1| (-938))
@@ -2273,7 +2273,7 @@
(((|#2|) |has| |#2| (-1080)))
(|has| |#1| (-376))
((($) . T))
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(((|#1|) |has| |#1| (-175)))
((($ (-888 |#1|)) . T))
(((|#1| |#1|) . T))
@@ -2284,7 +2284,7 @@
(((|#1|) . T))
((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
((((-666 $)) . T) (((-1189)) . T) (((-1207)) . T) (((-578)) . T) (((-229)) . T) (((-886)) . T))
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((((-421 (-578))) . T) (((-578)) . T) (((-631 $)) . T))
(((|#1|) . T))
((((-886)) . T))
@@ -2300,7 +2300,7 @@
(((|#1| (-793) (-1113)) . T))
((((-886)) . T))
(((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-578)) #1#) . T) (($ $) . T))
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(((|#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) . T))
(((|#1|) |has| |#1| (-175)))
(((|#1|) . T))
@@ -2320,37 +2320,37 @@
((((-721)) . T))
((((-721)) . T))
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((((-578)) . T) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))))
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(((|#1|) . T) (($) . T))
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((($) . T) (((-578)) . T) (((-421 (-578))) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
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(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
((((-578)) . T) (($) . T) (((-421 (-578))) . T))
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((((-886)) . T))
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((((-392)) . T))
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(((|#1|) |has| |#1| (-175)))
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(((|#1|) . T))
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(((|#3|) |has| |#3| (-1080)))
@@ -2362,7 +2362,7 @@
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(|has| |#1| (-871))
((((-886)) . T))
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(|has| |#1| (-813))
((((-421 (-578))) . T) (($) . T))
(|has| |#1| (-487))
@@ -2370,8 +2370,8 @@
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((((-118 |#1|)) . T))
((((-118 |#1|)) . T))
(|has| |#1| (-362))
@@ -2382,7 +2382,7 @@
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(((|#2|) . T) (((-886)) . T))
(((|#2|) . T) (((-886)) . T))
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(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
@@ -2393,18 +2393,18 @@
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-871))
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(((|#1| |#2|) . T))
((($) . T) (((-578)) . T))
(|has| |#1| (-149))
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(((|#2|) . T))
(|has| |#1| (-15 * (|#1| (-578) |#1|)))
(((|#3|) . T))
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(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-871))
(((|#2|) . T) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-578)) |has| |#1| (-1069 (-578))) ((|#1|) . T))
@@ -2423,17 +2423,17 @@
(((|#1|) |has| |#1| (-376)))
(((|#1|) |has| |#1| (-376)))
((((-886)) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
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((($ $) . T) (((-631 $) $) . T))
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((($) . T) (((-1284 |#1| |#2| |#3| |#4|)) . T) (((-421 (-578))) . T))
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(|has| |#1| (-376))
(|has| |#1| (-376))
(|has| |#1| (-376))
((((-392)) . T) (((-578)) . T) (((-421 (-578))) . T))
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((((-666 (-802 |#1| (-888 |#2|)))) . T) (((-886)) . T))
((((-550)) |has| (-802 |#1| (-888 |#2|)) (-633 (-550))))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
@@ -2442,17 +2442,17 @@
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(((|#1|) |has| |#1| (-175)))
((((-886)) . T))
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(((|#1|) . T))
((($) . T))
((($) |has| |#1| (-570)) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
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(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))))
((((-793)) . T))
(|has| |#1| (-1131))
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((((-886)) . T))
((((-1189)) . T) (((-1207)) . T) (((-886)) . T))
((((-578)) -12 (|has| |#1| (-21)) (|has| |#2| (-21))))
@@ -2460,14 +2460,14 @@
(|has| |#1| (-147))
(|has| |#1| (-149))
((((-578)) . T))
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(((#0=(-1283 |#2| |#3| |#4|)) . T) (((-421 (-578))) |has| #0# (-38 (-421 (-578)))) (($) . T))
((((-578)) . T))
((($) . T))
(|has| |#1| (-376))
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(|has| |#1| (-376))
(|has| |#1| (-147))
(|has| |#1| (-149))
@@ -2488,29 +2488,29 @@
((((-421 (-578))) . #0=(|has| |#2| (-376))) (($) . #0#))
(|has| |#1| (-871))
((((-421 (-578))) |has| |#2| (-376)) (($) . T))
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(((|#1| |#2|) . T))
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+((((-578)) . T) ((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-1069 (-421 (-578))))))
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(((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
(((|#2|) . T) (($) . T) (((-578)) . T))
(((|#1|) . T) (($) . T) (((-578)) . T))
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((((-886)) . T))
((((-578)) . T))
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(((|#1| $) |has| |#1| (-298 |#1| |#1|)))
((((-421 (-578))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T))
((((-981 |#1|)) . T) (((-886)) . T))
(((|#3|) . T))
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+(((|#1| |#1|) . T) (($ $) -2225 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-578)) #0#) |has| |#1| (-376)))
((((-981 |#1|)) . T))
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((($) . T))
((((-578) |#1|) . T))
((((-1207)) |has| (-421 |#2|) (-927 (-1207))))
-(((|#1|) . T) (($) -2230 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-578))) |has| |#1| (-376)))
+(((|#1|) . T) (($) -2225 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-578))) |has| |#1| (-376)))
((((-550)) |has| |#2| (-633 (-550))))
((((-711 |#2|)) . T) (((-886)) . T))
(((|#1|) . T))
@@ -2518,24 +2518,24 @@
(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
((((-894 |#1|)) . T))
(((|#1|) |has| |#1| (-175)))
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-(-2230 (|has| |#3| (-815)) (|has| |#3| (-871)))
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(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
((((-886)) . T))
(((|#1|) . T))
((($) . T) (((-578)) . T) ((|#2|) . T))
((((-886)) . T))
(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
-(((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376))))
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(((|#2|) |has| |#2| (-1080)))
(((|#2|) |has| |#2| (-1080)))
(((|#3|) . T))
((($) . T))
(((|#1|) . T))
((((-421 |#2|)) . T))
-(((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748))))
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(((|#1|) . T))
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(((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1131))))
((((-1265 (-578)) $) . T) (((-578) |#1|) . T))
(((|#1|) . T))
@@ -2544,16 +2544,16 @@
((((-421 (-578))) . T) (($) . T))
((((-421 (-578))) . T) (($) . T))
((((-421 (-578))) . T) (($) . T))
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+(-2225 (|has| |#1| (-466)) (|has| |#1| (-1252)))
((($) . T))
((((-421 (-578))) |has| #0=(-421 |#2|) (-1069 (-421 (-578)))) (((-578)) |has| #0# (-1069 (-578))) ((#0#) . T))
(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
(((|#1| (-793)) . T))
(|has| |#1| (-871))
(((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
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@@ -2578,59 +2578,59 @@
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((($) |has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))))
(|has| |#1| (-147))
(|has| |#1| (-149))
@@ -2770,16 +2770,16 @@
(((|#2| |#3|) . T))
(((|#1| (-545 |#2|)) . T))
(((|#1| (-793)) . T))
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(((|#1| (-545 (-1119 (-1207)))) . T))
(((|#1|) |has| |#1| (-175)))
(((|#1|) . T))
(|has| |#2| (-938))
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((((-886)) . T))
-(((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748))))
-(((|#2|) -2230 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080))))
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((($ $) . T) ((#0=(-1283 |#2| |#3| |#4|) #0#) . T) ((#1=(-421 (-578)) #1#) |has| #0# (-38 (-421 (-578)))))
((((-939 |#1|)) . T))
(-12 (|has| |#1| (-376)) (|has| |#2| (-842)))
@@ -2787,14 +2787,14 @@
((((-886)) . T))
((($) . T) (((-578)) . T))
((($) . T))
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(|has| |#1| (-376))
(|has| |#1| (-376))
(((|#1| |#2|) . T))
((($) . T) ((#0=(-1283 |#2| |#3| |#4|)) . T) (((-421 (-578))) |has| #0# (-38 (-421 (-578)))))
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((((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T))
(((|#1| |#2|) . T))
((((-886)) . T))
@@ -2832,7 +2832,7 @@
((($) . T))
(((|#4|) . T))
((($) . T))
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((((-886)) . T))
(((|#1| (-545 (-1207))) . T))
((($ $) . T))
@@ -2842,29 +2842,29 @@
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(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
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(((|#2|) |has| |#2| (-175)))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)))
((((-886)) . T))
((((-886)) . T))
((((-550)) . T) (((-578)) . T) (((-917 (-578))) . T) (((-392)) . T) (((-229)) . T))
(((|#1| |#2|) . T))
((($) . T) (((-578)) . T))
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(((|#1|) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
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((((-886)) . T))
(((|#1| |#2|) . T))
((($) . T) (((-578)) . T))
(((|#1| (-421 (-578))) . T))
(((|#1|) . T))
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((((-146)) . T))
((((-578)) |has| #0=(-421 |#2|) (-660 (-578))) ((#0#) . T) (((-421 (-578))) . T) (($) . T))
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@@ -2880,7 +2880,7 @@
((((-886)) . T))
((((-886)) . T))
((((-190)) . T) (((-886)) . T))
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(((|#2| |#2|) . T) ((|#1| |#1|) . T))
((((-886)) . T))
((((-886)) . T))
@@ -2897,8 +2897,8 @@
(|has| |#1| (-871))
((((-886)) . T))
((((-550)) |has| |#1| (-633 (-550))))
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+((((-2 (|:| -2338 (-1189)) (|:| -2078 |#1|))) . T))
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((((-886)) . T))
(((|#2|) |has| |#2| (-376)))
((((-886)) . T))
@@ -2913,19 +2913,19 @@
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(|has| |#1| (-1131))
((((-1207) (-52)) . T))
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(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
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(|has| |#1| (-938))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
(|has| |#1| (-938))
(((|#1|) . T) (((-578)) . T) (((-421 (-578))) . T) (($) . T))
(((|#2|) . T))
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(((#0=(-421 (-578)) #0#) . T) (($ $) . T))
((((-578)) . T))
(((|#1|) . T))
@@ -2937,12 +2937,12 @@
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(|has| |#1| (-38 (-421 (-578))))
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(|has| |#1| (-842))
(((#0=(-939 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-578)) #1#) . T))
((((-421 |#2|)) . T))
(|has| |#1| (-870))
-((((-1234 |#1|)) . T) (((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-1234 |#1|)) . T) (((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
(((|#1| |#1|) . T) ((#0=(-421 (-578)) #0#) . T) ((#1=(-578) #1#) . T) (($ $) . T))
((((-939 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
(((|#2|) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))))
@@ -2961,36 +2961,36 @@
(((|#2|) |has| |#2| (-175)))
(((|#1|) . T))
(((|#2|) . T))
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-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) . T))
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((((-578) |#3|) . T))
(((|#1|) . T))
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(|has| |#1| (-362))
((((-578)) . T))
((((-886)) . T))
(((|#1|) . T))
(((#0=(-1284 |#1| |#2| |#3| |#4|) $) |has| #0# (-298 #0# #0#)))
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(((#0=(-1113) |#1|) . T) ((#0# $) . T) (($ $) . T))
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(((#0=(-421 (-578)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T))
((((-328 |#1|)) . T) (($) . T))
(((|#1|) . T) (((-421 (-578))) |has| |#1| (-376)))
((((-886)) . T))
(|has| |#1| (-1131))
(((|#1|) . T))
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(((|#2|) . T))
((((-421 (-578))) . T) (((-721)) . T) (($) . T))
((((-593)) . T))
(((|#3| |#3|) . T))
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(|has| |#1| (-871))
(|has| |#2| (-240))
((((-888 |#1|)) . T))
@@ -3011,10 +3011,10 @@
(|has| |#1| (-1131))
(((|#2|) . T))
(((|#1|) . T))
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+((($) -2225 (|has| |#1| (-240)) (|has| |#1| (-239))))
((((-578)) . T))
(((|#2|) . T) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) ((|#1|) . T) (($) . T) (((-578)) . T))
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(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
(((|#1| |#2|) . T))
((($) . T))
@@ -3057,7 +3057,7 @@
(|has| |#2| (-1053))
((($) . T))
(|has| |#1| (-938))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#4|) . T))
((($) . T))
(((|#2|) . T))
@@ -3067,32 +3067,32 @@
(|has| |#1| (-376))
((((-939 |#1|)) . T))
((($) . T) (((-578)) . T) ((|#1|) . T) (((-421 (-578))) . T))
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((($ $) . T) ((#0=(-421 (-578)) #0#) . T))
-(-2230 (|has| |#1| (-381)) (|has| |#1| (-871)))
+(-2225 (|has| |#1| (-381)) (|has| |#1| (-871)))
(((|#1|) . T))
((((-793)) . T))
((((-886)) . T))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((((-421 |#2|) |#3|) . T))
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((($) . T) (((-421 (-578))) . T))
((($) . T) (((-578)) . T) (((-421 (-578))) . T) (((-631 $)) . T))
((((-578)) . T) (($) . T))
((((-578)) . T) (($) . T))
((((-793) |#1|) . T))
-(((|#2| (-247 (-3225 |#1|) (-793))) . T))
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(((|#1| (-545 |#3|)) . T))
((((-421 (-578))) . T))
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+(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
((((-1189)) . T) (((-886)) . T))
-(((#0=(-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) #0#) |has| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (-321 (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))))))
+(((#0=(-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) #0#) |has| (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))) (-321 (-2 (|:| -2338 (-1207)) (|:| -2078 (-52))))))
((((-1189)) . T))
(|has| |#1| (-938))
(|has| |#2| (-376))
(((|#1|) . T) (($) . T) (((-578)) . T))
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((((-172 (-392))) . T) (((-229)) . T) (((-392)) . T))
((((-886)) . T))
(((|#1|) . T))
@@ -3109,11 +3109,11 @@
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
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(-12 (|has| |#1| (-559)) (|has| |#1| (-850)))
((((-886)) . T))
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(|has| |#1| (-376))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
(|has| |#1| (-376))
@@ -3126,13 +3126,13 @@
((((-578) |#1|) . T))
((((-1207)) |has| |#1| (-927 (-1207))))
(((|#1|) . T))
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(((|#2|) |has| |#1| (-376)))
(((|#2|) |has| |#1| (-376)))
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((((-578)) . T) (($) . T))
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+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#1|) . T))
(((|#1|) . T))
(((|#1|) |has| |#1| (-175)))
@@ -3171,32 +3171,32 @@
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(((|#1|) . T))
((($) . T) (((-578)) . T) ((|#2|) . T))
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(((|#3|) . T))
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(((|#1|) . T))
(|has| |#1| (-376))
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(|has| |#1| (-376))
(|has| |#1| (-570))
(((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
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(((|#2|) . T))
(((|#2|) . T))
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(((|#1| |#2|) . T))
(|has| |#1| (-38 (-421 (-578))))
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((($) . T))
(|has| |#1| (-149))
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((($) . T))
((((-595 |#1|)) . T))
@@ -3212,7 +3212,7 @@
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(((|#1|) . T))
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(|has| |#1| (-149))
((((-886)) . T))
((($) . T))
@@ -3232,15 +3232,15 @@
((((-421 |#2|)) . T))
((((-886)) . T))
(((|#1|) . T))
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-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
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(|has| |#1| (-813))
(|has| |#1| (-813))
((((-886)) . T))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
((((-886)) . T))
((((-550)) |has| |#1| (-633 (-550))))
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((((-116)) . T) ((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
@@ -3250,7 +3250,7 @@
(((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)) (((-421 (-578))) |has| |#1| (-570)))
((((-886)) . T))
((((-886)) . T))
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(((#0=(-939 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-578)) #1#) . T))
(((|#2|) . T))
(((|#1|) . T))
@@ -3262,10 +3262,10 @@
((((-886)) . T))
(((|#2|) . T))
((((-578)) . T))
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((((-886)) . T))
((((-578)) . T))
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((((-172 (-392))) . T) (((-229)) . T) (((-392)) . T))
((((-886)) . T))
((((-886)) . T))
@@ -3277,11 +3277,11 @@
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
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((((-886)) . T))
((((-578) $) . T) (((-666 (-578)) $) . T))
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((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
((($) . T))
@@ -3291,22 +3291,22 @@
(((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#)))
(((|#1|) |has| |#1| (-175)))
((((-328 |#1|)) . T) (((-578)) . T))
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(((|#1|) . T))
(((|#1| |#1|) . T))
((((-886)) . T))
(((|#1|) . T))
((((-116)) . T) ((|#1|) . T))
((((-886)) . T))
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(((|#1|) |has| |#1| (-321 |#1|)))
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(((|#1| |#2|) . T))
((((-1207) |#1|) . T))
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(((|#1|) . T))
((($ (-1207)) . T))
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((((-578)) . T) (((-421 (-578))) . T))
(((|#1|) . T))
(|has| |#1| (-570))
@@ -3315,15 +3315,15 @@
(((|#1|) . T))
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(|has| |#1| (-570))
((($) . T))
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(((|#1|) . T))
(((|#2| |#3|) . T))
(((|#1|) . T))
@@ -3332,17 +3332,17 @@
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(((|#1| (-545 (-1119 (-1207)))) . T))
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(((|#1|) . T))
(((|#1|) . T) (((-578)) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(|has| |#2| (-376))
((((-886)) . T))
((((-886)) . T))
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((((-886)) . T))
((((-1151)) . T) (((-886)) . T))
((((-550)) . T) (((-886)) . T))
@@ -3353,14 +3353,14 @@
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+((((-1156 |#1| |#2|)) . T) ((|#2|) . T) (($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))) (((-578)) . T))
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(((#0=(-595 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-578)) #1#) . T))
((($ $) . T) ((#0=(-421 (-578)) #0#) . T))
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(((|#1|) |has| |#1| (-175)))
(((|#1| (-1298 |#1|) (-1298 |#1|)) . T))
((((-595 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
@@ -3370,12 +3370,12 @@
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(((|#1|) . T))
((($) . T) (((-421 (-578))) . T))
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(((|#1|) . T))
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(((|#1|) . T))
((((-886)) . T))
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(((|#2| |#2|) . T) ((|#6| |#6|) . T))
((((-306 |#3|)) . T))
(((|#1|) . T))
@@ -3384,30 +3384,30 @@
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(((|#2|) . T))
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(((|#2|) . T) ((|#6|) . T))
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((((-886)) . T))
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((((-886)) . T))
(((|#1|) . T))
(((|#1|) . T))
-((((-2 (|:| -3172 (-1189)) (|:| -2754 |#1|))) . T))
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(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
(((|#1| |#1|) . T))
(((|#1|) . T))
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(((|#1|) . T))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
((((-1207)) . T) ((|#1|) . T))
@@ -3419,15 +3419,15 @@
(((#0=(-421 (-578)) #0#) . T))
((((-421 (-578))) . T))
(((|#1|) |has| |#1| (-175)))
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(((|#1|) . T))
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(((|#1|) . T))
((((-421 (-578))) . T) (((-578)) . T) (($) . T))
((((-550)) . T))
((((-886)) . T))
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(|has| |#1| (-871))
((((-886)) . T))
((((-578)) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)))
@@ -3443,21 +3443,21 @@
((($ $) . T) ((#0=(-421 (-578)) #0#) . T))
((((-1207)) |has| |#1| (-927 (-1207))))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
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+((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#1|) . T))
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((((-421 |#2|)) . T) (((-421 (-578))) . T) (($) . T))
((($) . T) (((-421 (-578))) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((|#2|) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))))
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(((|#1|) |has| |#1| (-376)))
((((-578)) . T))
((((-1207) #0=(-118 |#1|)) |has| #0# (-528 (-1207) #0#)) ((#0# #0#) |has| #0# (-321 #0#)))
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(|has| |#1| (-813))
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(((|#2|) . T) (((-578)) |has| |#2| (-1069 (-578))) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))))
((((-1113)) . T) ((|#2|) . T) (((-578)) |has| |#2| (-1069 (-578))) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))))
(((|#1|) . T))
@@ -3477,11 +3477,11 @@
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((($ (-1207)) |has| |#1| (-927 (-1207))))
(((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))))
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-(((|#1|) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) . T))
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+(((|#1|) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) . T))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
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(((|#1|) . T))
@@ -3496,7 +3496,7 @@
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(|has| |#1| (-376))
(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
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(((|#2|) . T))
(|has| |#1| (-376))
(((|#2|) . T))
@@ -3510,12 +3510,12 @@
(((|#2| (-793)) . T))
((((-1207)) . T))
((((-894 |#1|)) . T))
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((((-886)) . T))
(((|#1|) . T))
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((((-894 |#1|)) . T))
(((|#1|) . T))
(|has| |#1| (-381))
@@ -3533,7 +3533,7 @@
(((|#1|) . T))
((((-886)) . T))
((($) . T) ((|#2|) . T) (((-421 (-578))) . T) (((-578)) |has| |#2| (-660 (-578))))
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(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
@@ -3542,7 +3542,7 @@
(((|#1|) . T))
((((-886)) . T))
(|has| |#2| (-938))
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((((-550)) |has| |#2| (-633 (-550))) (((-917 (-392))) |has| |#2| (-633 (-917 (-392)))) (((-917 (-578))) |has| |#2| (-633 (-917 (-578)))))
((((-886)) . T))
((((-886)) . T))
@@ -3553,7 +3553,7 @@
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((((-886)) . T))
((((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))) (((-578)) |has| |#2| (-1069 (-578))) ((|#2|) . T) (((-888 |#1|)) . T))
-((((-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T))
+((((-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T))
((((-118 |#1|)) . T) (($) . T) (((-421 (-578))) . T))
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((((-886)) . T))
@@ -3573,10 +3573,10 @@
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((($) |has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))))
((($) . T) (((-578)) . T) (((-1284 |#1| |#2| |#3| |#4|)) . T) (((-421 (-578))) . T))
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((((-1212)) . T))
((((-578)) . T) (((-421 (-578))) . T))
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(((|#1|) . T))
((((-1212)) . T))
((((-1212)) . T))
@@ -3591,16 +3591,16 @@
((((-421 |#2|) |#3|) . T))
(((|#1|) . T))
((((-886)) . T))
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-(((|#2| (-496 (-3225 |#1|) (-793))) . T))
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+(((|#2| (-496 (-4415 |#1|) (-793))) . T))
((((-578) |#1|) . T))
((((-1189)) . T) (((-886)) . T))
(((|#2| |#2|) . T))
(((|#1| (-545 (-1207))) . T))
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((((-578)) . T))
(((|#2|) . T))
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(((|#2|) . T))
((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T))
(((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
@@ -3609,9 +3609,9 @@
((($) . T) (((-421 (-578))) . T))
((($) . T))
((($) . T))
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(((|#1|) . T))
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((((-886)) . T))
((((-146)) . T))
(((|#1|) . T) (((-421 (-578))) . T))
@@ -3620,7 +3620,7 @@
((((-886)) . T))
(((|#1|) . T))
(|has| |#1| (-1183))
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(((|#1|) . T))
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@@ -3645,44 +3645,44 @@
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(((|#1| (-545 |#3|)) . T))
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((((-550)) |has| |#1| (-633 (-550))))
(((|#1|) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
(((|#1|) . T) (((-421 (-578))) . T) (($) . T) (((-578)) . T))
@@ -3701,18 +3701,18 @@
(((|#3|) |has| |#3| (-1131)) (((-578)) -12 (|has| |#3| (-1069 (-578))) (|has| |#3| (-1131))) (((-421 (-578))) -12 (|has| |#3| (-1069 (-421 (-578)))) (|has| |#3| (-1131))))
(|has| |#2| (-376))
(((|#2|) |has| |#2| (-1080)) (((-578)) -12 (|has| |#2| (-660 (-578))) (|has| |#2| (-1080))))
-(-2230 (|has| |#1| (-381)) (|has| |#1| (-871)))
+(-2225 (|has| |#1| (-381)) (|has| |#1| (-871)))
(((|#1|) . T))
-(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
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+(((#0=(-421 (-578)) #0#) |has| |#2| (-38 (-421 (-578)))) ((|#2| |#2|) . T) (($ $) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
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(((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-578)) #0#) . T))
(((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-578)) #0#) . T))
(((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-578)) #0#) . T))
((((-1207)) |has| |#1| (-1080)))
(|has| |#2| (-376))
(((|#2| |#2|) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (($) -2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
-((($) -2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (($) -2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
(((|#1|) . T) (($) . T) (((-421 (-578))) . T))
@@ -3724,11 +3724,11 @@
(((|#1|) . T))
(|has| |#2| (-842))
(|has| |#2| (-842))
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(|has| |#1| (-376))
(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-376))
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+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(|has| |#1| (-376))
(((|#1|) |has| |#2| (-431 |#1|)))
(((|#1|) |has| |#2| (-431 |#1|)))
@@ -3737,7 +3737,7 @@
((((-886)) . T) (((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
-((((-666 |#1|)) . T) (((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
+((((-666 |#1|)) . T) (((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
((((-1212)) . T))
((((-1212)) . T))
((((-1212)) . T))
@@ -3752,19 +3752,19 @@
((((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
((((-1212)) . T))
-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) |has| (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))) (-321 (-2 (|:| -3172 (-1207)) (|:| -2754 (-52))))))
-(-2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
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+(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
((((-578) |#1|) . T))
((((-578) |#1|) . T))
((((-578) |#1|) . T))
-(-2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
((((-578) |#1|) . T))
(((|#1|) . T))
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-(-2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
-((($) -2230 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-578)) . T) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#1|) |has| |#1| (-175)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-578)) . T) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#1|) |has| |#1| (-175)))
((((-1207)) |has| |#1| (-927 (-1207))) (((-840 (-1207))) . T))
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((((-841 |#1|)) . T))
(((|#1| |#2|) . T))
((((-886)) . T))
@@ -3777,21 +3777,21 @@
(((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-570)) (((-421 (-578))) |has| |#1| (-570)))
(((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
(|has| |#1| (-376))
-(-2230 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))))
+(-2225 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))))
(|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|)))
(|has| |#1| (-376))
(((|#1|) . T))
-(((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1| |#1|) . T))
+(((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1| |#1|) . T))
((((-1265 (-578)) $) . T) (((-578) |#1|) . T))
((((-328 |#1|)) . T))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
(((#0=(-721) (-1203 #0#)) . T))
-((((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1|) . T))
+((((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((|#1|) . T))
(((|#1|) . T) (($) . T) (((-578)) . T) (((-421 (-578))) . T))
(((|#1| |#2| |#3| |#4|) . T))
(|has| |#1| (-870))
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+(((|#2|) . T) (((-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))) (((-578)) . T) ((|#1|) |has| |#1| (-175)))
+(((|#2|) . T) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) (((-578)) . T) (($) -2225 (|has| |#1| (-376)) (|has| |#1| (-570))))
((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T))
((((-1156 |#1| (-1207))) . T) (((-840 (-1207))) . T) ((|#1|) . T) (((-578)) |has| |#1| (-1069 (-578))) (((-421 (-578))) |has| |#1| (-1069 (-421 (-578)))) (((-1207)) . T))
((($) . T))
@@ -3810,12 +3810,12 @@
(((#0=(-1284 |#1| |#2| |#3| |#4|)) |has| #0# (-321 #0#)))
((($) . T))
(((|#1|) . T))
-((($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T))
-(((|#1| |#1|) . T) (($ $) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
+((($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#2| |#2|) |has| |#1| (-376)) ((|#1| |#1|) . T))
+(((|#1| |#1|) . T) (($ $) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) ((#0=(-421 (-578)) #0#) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
(|has| |#2| (-240))
(|has| $ (-149))
((((-886)) . T))
-((($) . T) (((-421 (-578))) -2230 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
+((($) . T) (((-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-362))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
((((-886)) . T))
(|has| |#1| (-870))
((((-131)) . T))
@@ -3823,7 +3823,7 @@
((((-421 (-578))) . T) (((-721)) . T) (($) . T) (((-578)) . T))
(((|#1|) . T))
((((-131)) . T))
-((($ (-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))))
+((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))))
((((-886)) . T))
(-12 (|has| |#1| (-319)) (|has| |#1| (-938)))
(((|#2| (-694 |#1|)) . T))
@@ -3832,24 +3832,24 @@
((((-886)) |has| |#1| (-1131)))
(((|#4|) . T))
(|has| |#1| (-570))
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-((((-1207)) -2230 (-12 (|has| (-1290 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
-(((|#1|) . T) (($) -2230 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2230 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
+((($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) ((|#1|) . T))
+((((-1207)) -2225 (-12 (|has| (-1290 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
+(((|#1|) . T) (($) -2225 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-570))) (((-421 (-578))) -2225 (|has| |#1| (-38 (-421 (-578)))) (|has| |#1| (-376))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((((-1265 (-578)) $) . T) (((-578) |#1|) . T))
-(-2230 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
+(-2225 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
(((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1131))))
(((|#1|) . T))
(((|#1| (-545 (-840 (-1207)))) . T))
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((((-578)) . T) ((|#2|) . T) (($) . T) (((-421 (-578))) . T) (((-1207)) |has| |#2| (-1069 (-1207))))
(((|#1|) . T))
-(-2230 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+(-2225 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
(((|#1|) . T))
-(-2230 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080)))
-(-2230 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815))))
+(-2225 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080)))
+(-2225 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815))))
((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)))
((($) . T) (((-894 |#1|)) . T) (((-421 (-578))) . T))
((((-1290 |#1| |#2| |#3|)) |has| |#1| (-376)))
@@ -3858,15 +3858,15 @@
(((|#1|) . T))
(((|#1|) . T))
((((-421 |#2|)) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-362)))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-362)))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
((((-550)) |has| |#1| (-633 (-550))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
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((((-550)) |has| |#1| (-633 (-550))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
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((((-550)) |has| |#1| (-633 (-550))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
(((|#1|) . T))
(((|#2| |#2|) . T) ((#0=(-421 (-578)) #0#) . T) (($ $) . T))
(((|#2|) . T) (((-421 (-578))) . T) (($) . T))
@@ -3886,7 +3886,7 @@
((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
-(-2230 (|has| |#1| (-240)) (|has| |#1| (-239)))
+(-2225 (|has| |#1| (-240)) (|has| |#1| (-239)))
(((|#1|) . T) (((-886)) . T) (((-1212)) . T))
((((-1212)) . T))
((((-886)) . T))
@@ -3895,21 +3895,21 @@
((((-657 |#2|)) . T))
(((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . T))
-((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
+((((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) |has| |#2| (-175)) (($) -2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))))
(((|#2|) . T) ((|#6|) . T))
((($) . T) (((-421 (-578))) |has| |#2| (-38 (-421 (-578)))) ((|#2|) . T) (((-578)) |has| |#2| (-660 (-578))))
((($) . T) (((-578)) . T))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
((((-1135)) . T))
((((-886)) . T))
((((-1212)) . T) (((-886)) . T))
((((-1212)) . T) (((-886)) . T))
((((-1212)) . T))
((((-1212)) . T))
-((($) -2230 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
((($) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
((($) . T) (((-578)) . T))
-((($) -2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
+((($) -2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938))) ((|#1|) |has| |#1| (-175)) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(|has| |#2| (-938))
(((|#1| |#2| (-247 |#1| |#2|) (-247 |#1| |#2|)) . T))
((((-886)) . T))
@@ -3925,9 +3925,9 @@
(((|#1| |#1|) |has| |#1| (-175)))
((((-721)) . T))
((((-721)) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
((((-1212)) . T))
-(-2230 (|has| |#2| (-815)) (|has| |#2| (-871)))
+(-2225 (|has| |#2| (-815)) (|has| |#2| (-871)))
(((|#1|) |has| |#1| (-175)))
((((-1212)) . T))
(((|#1| |#1|) . T))
@@ -3940,19 +3940,19 @@
(((|#1| (-578)) . T))
(((|#1|) . T))
((((-421 (-578))) . T) (((-578)) . T) (($) . T))
-((($ (-1207)) -2230 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T))
+((($ (-1207)) -2225 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T))
(((|#1|) |has| |#1| (-175)))
((((-1212)) . T))
((((-1212)) . T))
((((-1212)) . T))
((((-1212)) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-362)))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-362)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-362)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-362)))
((((-1212)) . T))
((((-1212)) . T))
(|has| |#1| (-376))
(|has| |#1| (-376))
-(-2230 (|has| |#1| (-175)) (|has| |#1| (-570)))
+(-2225 (|has| |#1| (-175)) (|has| |#1| (-570)))
(((|#1| (-578)) . T))
(((|#1| (-421 (-578))) . T))
(((|#1| (-793)) . T))
@@ -3960,24 +3960,24 @@
(((|#1| (-545 |#2|) |#2|) . T))
((((-578) |#1|) . T))
((((-578) |#1|) . T))
-(-2230 (|has| |#1| (-102)) (|has| |#1| (-1131)))
-(-2230 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))
+(-2225 (|has| |#1| (-102)) (|has| |#1| (-1131)))
+(-2225 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))
((((-578) |#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
((((-917 (-392))) . T) (((-917 (-578))) . T) (((-1207)) . T) (((-550)) . T))
-(-2230 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080)))
-(-2230 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815))))
+(-2225 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080)))
+(-2225 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-133)) (|has| |#2| (-133))) (-12 (|has| |#1| (-815)) (|has| |#2| (-815))))
((((-886)) . T))
((((-578)) . T))
((((-578)) . T))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#1| |#2|) . T))
(((|#1|) . T))
((((-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))))
(|has| |#2| (-1080))
-(-2230 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748))))
+(-2225 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748))))
(|has| |#1| (-147))
(|has| |#1| (-149))
(|has| |#1| (-376))
@@ -4010,7 +4010,7 @@
(((|#1| |#2|) . T))
((((-578)) . T) ((|#2|) |has| |#2| (-175)))
((((-116)) . T) ((|#1|) . T) (((-578)) . T))
-(-2230 (|has| |#1| (-362)) (|has| |#1| (-381)))
+(-2225 (|has| |#1| (-362)) (|has| |#1| (-381)))
(((|#1| |#2|) . T))
((((-229)) . T))
((((-421 (-578))) . T) (($) . T) (((-578)) . T))
@@ -4019,11 +4019,11 @@
((($) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))) ((|#1|) . T) (((-578)) |has| |#1| (-660 (-578))))
((($) . T) (((-578)) |has| |#1| (-660 (-578))) ((|#1|) . T) (((-421 (-578))) |has| |#1| (-38 (-421 (-578)))))
(((|#2|) |has| |#2| (-1131)) (((-578)) -12 (|has| |#2| (-1069 (-578))) (|has| |#2| (-1131))) (((-421 (-578))) -12 (|has| |#2| (-1069 (-421 (-578)))) (|has| |#2| (-1131))))
-(-2230 (|has| |#2| (-240)) (|has| |#2| (-239)))
+(-2225 (|has| |#2| (-240)) (|has| |#2| (-239)))
(((|#1|) . T))
(((|#1|) . T))
((((-550)) |has| |#1| (-633 (-550))))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-871)) (|has| |#1| (-1131))))
((((-578) $) . T) (((-666 (-578)) $) . T))
((($) . T) (((-421 (-578))) . T))
(|has| |#1| (-938))
@@ -4035,14 +4035,14 @@
(((|#1| |#1|) |has| |#1| (-175)))
(((|#1|) . T) (((-578)) . T))
((((-1212)) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-570)))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-870)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-570)))
+(-2225 (|has| |#1| (-21)) (|has| |#1| (-870)))
(((|#2|) . T))
-(-2230 (|has| |#1| (-21)) (|has| |#1| (-870)))
+(-2225 (|has| |#1| (-21)) (|has| |#1| (-870)))
(((|#1|) |has| |#1| (-175)))
(((|#1|) . T))
(((|#1|) . T))
-((((-886)) -2230 (-12 (|has| |#1| (-632 (-886))) (|has| |#2| (-632 (-886)))) (-12 (|has| |#1| (-1131)) (|has| |#2| (-1131)))))
+((((-886)) -2225 (-12 (|has| |#1| (-632 (-886))) (|has| |#2| (-632 (-886)))) (-12 (|has| |#1| (-1131)) (|has| |#2| (-1131)))))
((((-421 |#2|) |#3|) . T))
((((-421 (-578))) . T) (($) . T))
(|has| |#1| (-38 (-421 (-578))))
@@ -4051,7 +4051,7 @@
((($) . T) (((-578)) . T))
(|has| (-421 |#2|) (-149))
(|has| (-421 |#2|) (-147))
-(-2230 (|has| |#3| (-815)) (|has| |#3| (-871)))
+(-2225 (|has| |#3| (-815)) (|has| |#3| (-871)))
((($) . T))
((((-721)) . T))
(((|#1|) . T) (((-421 (-578))) . T) (((-578)) . T) (($) . T))
@@ -4067,7 +4067,7 @@
((((-1212)) . T))
((((-578)) . T))
(((|#2|) . T))
-((((-1207)) -2230 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
+((((-1207)) -2225 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-578)) |#1|))) (|has| |#1| (-927 (-1207)))))
((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207)))))
(((|#1| |#1|) . T) (($ $) . T))
@@ -4083,11 +4083,11 @@
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
((((-1171 |#1| |#2|)) . T))
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
-(((|#2|) . T) (((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) . T))
+(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
+((((-2 (|:| -2338 (-1207)) (|:| -2078 (-52)))) . T))
((($) . T))
(|has| |#1| (-1053))
-(((|#2|) . T) (((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
((($) . T))
((((-886)) . T))
((((-550)) |has| |#2| (-633 (-550))) (((-917 (-578))) |has| |#2| (-633 (-917 (-578)))) (((-917 (-392))) |has| |#2| (-633 (-917 (-392)))) (((-392)) . #0=(|has| |#2| (-1053))) (((-229)) . #0#))
@@ -4096,7 +4096,7 @@
(((|#1|) . T))
(|has| |#1| (-38 (-421 (-578))))
(|has| |#1| (-38 (-421 (-578))))
-((((-1207)) -2230 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))))
+((((-1207)) -2225 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))))
((((-886)) . T))
(((|#2|) . T))
((((-886)) . T))
@@ -4106,15 +4106,15 @@
((((-1205 |#1| |#2| |#3|)) . T))
((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T))
((((-886)) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
((((-578) |#1|) . T))
((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)))
(((|#1| |#2| |#3| |#4|) . T))
(((|#1|) . T))
(((|#2|) . T))
(|has| |#2| (-376))
-(((|#3|) . T) ((|#2|) . T) ((|#4|) -2230 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-578)) -12 (|has| |#4| (-660 (-578))) (|has| |#4| (-1080))))
-(((|#2|) . T) ((|#3|) -2230 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-578)) -12 (|has| |#3| (-660 (-578))) (|has| |#3| (-1080))))
+(((|#3|) . T) ((|#2|) . T) ((|#4|) -2225 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-578)) -12 (|has| |#4| (-660 (-578))) (|has| |#4| (-1080))))
+(((|#2|) . T) ((|#3|) -2225 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-578)) -12 (|has| |#3| (-660 (-578))) (|has| |#3| (-1080))))
(((|#1|) . T))
(((|#1|) . T))
((((-118 |#1|)) . T))
@@ -4128,7 +4128,7 @@
((((-190)) . T) (((-886)) . T))
((((-886)) . T))
(((|#1|) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
((((-578) |#1|) . T) (((-1265 (-578)) $) . T))
((((-886)) . T))
(((|#1|) . T))
@@ -4136,14 +4136,14 @@
(((|#1|) . T))
(((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-578) |#1|) . T))
((($ $) . T) (((-421 (-578)) |#1|) . T))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-938)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-938)))
((($ (-1207)) |has| |#1| (-1080)))
-(-2230 (|has| |#1| (-871)) (|has| |#1| (-1131)))
+(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131)))
((((-886)) . T))
((((-886)) . T))
((((-886)) . T))
(((|#1| (-545 |#2|)) . T))
-((((-2 (|:| -3172 (-1207)) (|:| -2754 (-52)))) . T))
+((((-2 (|:| -2338 (-1207)) (|:| -2078 (-52)))) . T))
((((-578) (-131)) . T))
(((|#1| (-578)) . T))
(((|#1| (-421 (-578))) . T))
@@ -4158,8 +4158,8 @@
((((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
-(-2230 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
-(-2230 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
+(-2225 (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938)))
+(-2225 (|has| |#1| (-466)) (|has| |#1| (-570)) (|has| |#1| (-938)))
((($) . T))
(((|#2| (-545 (-888 |#1|))) . T))
((((-1212)) . T))
@@ -4174,7 +4174,7 @@
((((-1212)) . T))
((((-886)) . T) (((-1212)) . T))
((((-1212)) . T))
-((((-886)) -2230 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
+((((-886)) -2225 (|has| |#1| (-632 (-886))) (|has| |#1| (-1131))))
(((|#1| |#2|) . T))
(((|#1|) . T))
((((-1189) |#1|) . T))
@@ -4182,7 +4182,7 @@
((((-421 |#2|)) . T))
(|has| |#1| (-570))
(|has| |#1| (-570))
-((((-2 (|:| -3172 |#1|) (|:| -2754 |#2|))) . T))
+((((-2 (|:| -2338 |#1|) (|:| -2078 |#2|))) . T))
(((|#2| (-793)) . T))
((($) . T) ((|#2|) . T))
((($) . T) (((-421 (-578))) . T))
@@ -4192,14 +4192,14 @@
((((-578)) . T) (($) . T))
(((|#2| $) |has| |#2| (-298 |#2| |#2|)))
(((|#1| (-666 |#1|)) |has| |#1| (-870)))
-(-2230 (|has| |#1| (-240)) (|has| |#1| (-362)))
-(-2230 (|has| |#1| (-376)) (|has| |#1| (-362)))
+(-2225 (|has| |#1| (-240)) (|has| |#1| (-362)))
+(-2225 (|has| |#1| (-376)) (|has| |#1| (-362)))
((((-1294 |#1|)) . T) (((-578)) . T) ((|#2|) . T) (((-421 (-578))) |has| |#2| (-1069 (-421 (-578)))))
(|has| |#1| (-1131))
(((|#1|) . T))
((((-421 (-578))) . T) (($) . T))
-((((-1294 |#1|)) . T) (((-578)) . T) (($) -2230 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-1113)) . T) ((|#2|) . T) (((-421 (-578))) -2230 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))))
-((((-1030 |#1|)) . T) ((|#1|) . T) (((-578)) -2230 (|has| (-1030 |#1|) (-1069 (-578))) (|has| |#1| (-1069 (-578)))) (((-421 (-578))) -2230 (|has| (-1030 |#1|) (-1069 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))))
+((((-1294 |#1|)) . T) (((-578)) . T) (($) -2225 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-570)) (|has| |#2| (-938))) (((-1113)) . T) ((|#2|) . T) (((-421 (-578))) -2225 (|has| |#2| (-38 (-421 (-578)))) (|has| |#2| (-1069 (-421 (-578))))))
+((((-1030 |#1|)) . T) ((|#1|) . T) (((-578)) -2225 (|has| (-1030 |#1|) (-1069 (-578))) (|has| |#1| (-1069 (-578)))) (((-421 (-578))) -2225 (|has| (-1030 |#1|) (-1069 (-421 (-578)))) (|has| |#1| (-1069 (-421 (-578))))))
((((-939 |#1|)) . T) (((-421 (-578))) . T) (($) . T))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
(((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))))
@@ -4216,11 +4216,11 @@
(((|#1| |#2| |#3| |#4|) . T))
(((#0=(-1171 |#1| |#2|) #0#) |has| (-1171 |#1| |#2|) (-321 (-1171 |#1| |#2|))))
(((|#1|) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) #0#) |has| (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)) (-321 (-2 (|:| -3172 |#1|) (|:| -2754 |#2|)))))
-(-2230 (|has| |#1| (-240)) (|has| |#1| (-239)))
+(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1131))) ((#0=(-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) #0#) |has| (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)) (-321 (-2 (|:| -2338 |#1|) (|:| -2078 |#2|)))))
+(-2225 (|has| |#1| (-240)) (|has| |#1| (-239)))
(((#0=(-118 |#1|)) |has| #0# (-321 #0#)))
((($ $) . T))
-(-2230 (|has| |#1| (-871)) (|has| |#1| (-1131)))
+(-2225 (|has| |#1| (-871)) (|has| |#1| (-1131)))
((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T))
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. -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1111 . -376) 189777) ((-40 . -425) 189754) ((-77 . -1248) T) ((-895 . -938) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-366 . -341) 189722) ((-366 . -376) T) ((-358 . -341) 189706) ((-358 . -376) T) ((-328 . -296) 189685) ((-108 . -376) T) ((-70 . -1248) T) ((-661 . -1131) T) ((-1262 . -351) 189637) ((-895 . -670) 189582) ((-1262 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1256 . -683) T) ((-1118 . -175) 189155) ((-987 . -386) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-804 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-981 . -748) T) ((-1311 . -321) 188723) ((-1290 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1283 . -927) 188405) ((-1282 . -1087) 188240) ((-1262 . -927) 188073) ((-495 . -748) T) ((-1261 . -1087) 187881) 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-302) T) ((-532 . -302) T) ((-1262 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1248) T) ((-734 . -662) 181995) ((-1262 . -1053) NIL) ((-1111 . -133) T) ((-896 . -817) 181974) ((-146 . -102) T) ((-40 . -1131) T) ((-896 . -814) 181953) ((-666 . -1041) 181937) ((-594 . -1089) T) ((-578 . -1089) T) ((-509 . -1089) T) ((-421 . -466) T) ((-372 . -133) T) ((-328 . -414) 181921) ((-325 . -414) 181882) ((-366 . -133) T) ((-358 . -133) T) ((-1212 . -1131) T) ((-1151 . -38) 181869) ((-1125 . -632) 181836) ((-108 . -133) T) ((-983 . -1131) T) ((-950 . -1131) T) ((-793 . -1131) T) ((-694 . -1131) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-378 . -1248) T) ((-368 . -1087) 181772) ((-365 . -1087) 181724) ((-357 . -1087) 181676) ((-260 . -1248) T) ((-259 . -1248) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1252) 181320) ((-561 . -866) T) ((-328 . -929) 181286) ((-368 . -111) 181224) ((-365 . -111) 181162) ((-357 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -425) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-934 . -874) 180693) ((-131 . -683) T) ((-837 . -660) 180599) ((-839 . -570) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-939 . -1087) 180181) ((-734 . -102) T) ((-721 . -1089) T) ((-611 . -635) 180162) ((-599 . -635) 180143) ((-550 . -637) 180046) ((-356 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-88 . -632) 180028) ((-939 . -111) 179984) ((-40 . -739) 179929) ((-894 . -1131) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-365 . -635) 179761) ((-357 . -635) 179698) ((-561 . -1131) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-189 . -1248) T) ((-1261 . -814) 179062) 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177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-939 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1204 . -949) 177432) ((-1198 . -949) 177411) ((-1198 . -842) NIL) ((-1030 . -1082) 177307) ((-996 . -1248) T) ((-939 . -250) T) ((-839 . -376) 177286) ((-218 . -1131) T) ((-398 . -23) T) ((-129 . -1131) 177264) ((-123 . -1131) 177242) ((-939 . -240) T) ((-130 . -34) T) ((-392 . -670) 177207) ((-1030 . -662) 177155) ((-894 . -739) 177142) ((-1327 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1248) T) ((-886 . -1248) T) ((-40 . -175) T) ((-716 . -425) 177061) ((-734 . -321) 177048) ((-858 . -670) 177008) ((-849 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-680 . -298) 176961) ((-594 . -1131) T) ((-578 . -1131) T) ((-509 . -1131) T) ((-1203 . -1248) T) ((-252 . -300) 176938) ((-1156 . -1248) T) ((-878 . -1248) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1253 . -874) T) ((-1203 . -911) NIL) ((-55 . -1131) T) ((-1156 . -911) 176719) ((-131 . -871) T) ((-1203 . -1069) 176599) ((-1156 . -1069) 176482) ((-186 . -632) 176464) ((-878 . -1069) 176360) ((-804 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1030 . -102) T) ((-839 . -23) T) ((-734 . -1183) 176085) ((-716 . -1089) T) ((-616 . -386) 176069) ((-364 . -466) T) ((-356 . -302) T) ((-1299 . -1131) T) ((-256 . -1131) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1131) T) ((-721 . -1131) T) ((-374 . -487) T) ((-1242 . -632) 176051) ((-1203 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -425) 175981) ((-143 . -233) 175963) ((-392 . -816) T) ((-392 . -813) T) ((-894 . -175) T) ((-392 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1298 . -1296) 175758) ((-364 . -416) T) ((-1298 . -1131) 175708) ((-1221 . -1131) T) ((-594 . -739) 175695) ((-578 . -739) 175682) ((-509 . -739) 175647) ((-1284 . -668) 175537) ((-328 . -648) 175516) ((-858 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1252) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1252) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -570) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-328 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-366 . -25) T) ((-366 . -21) T) ((-221 . -570) T) ((-358 . -25) T) ((-358 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1089) T) ((-594 . -175) T) ((-578 . -175) T) ((-509 . -175) T) ((-1093 . -1248) T) ((-981 . -1248) T) ((-735 . -1248) T) ((-661 . -298) 173868) ((-680 . -632) 173850) ((-495 . -1248) T) ((-759 . -758) 173834) ((-349 . -632) 173816) ((-68 . -396) T) ((-68 . -409) T) ((-1133 . -107) 173800) ((-1093 . -911) 173782) ((-981 . -911) 173707) ((-675 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1125 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-981 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-675 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-804 . -633) NIL) ((-804 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-821 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -938) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1317) 172342) ((-365 . -1317) 172326) ((-357 . -1317) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-525 . -814) T) ((-525 . -817) T) ((-524 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1131) T) ((-896 . -670) 171980) ((-65 . -397) T) ((-286 . -632) 171962) ((-65 . -409) T) ((-981 . -390) 171946) ((-894 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) 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169722) ((-358 . -236) 169695) ((-177 . -466) T) ((-86 . -455) T) ((-226 . -321) 169633) ((-86 . -409) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1322 . -1315) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-578 . -302) T) ((-509 . -302) T) ((-1271 . -1248) T) ((-138 . -484) 169520) ((-879 . -1248) T) ((-676 . -668) 169479) ((-48 . -1131) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1248) T) ((-1271 . -911) NIL) ((-914 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1131) T) ((-172 . -390) 169413) ((-172 . -351) 169397) ((-1271 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1030 . -929) 169096) ((-684 . -814) 169075) ((-675 . -133) T) ((-684 . -817) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-306 . -1305) 168914) ((-1198 . -874) NIL) ((-890 . -102) T) ((-992 . -570) 168893) ((-1242 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-933 . -1131) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1178 . -1248) T) ((-1242 . -111) 168343) ((-488 . -670) 168240) ((-367 . -739) 168185) ((-172 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1327 . -1089) T) ((-1271 . -390) 168084) ((-432 . -1252) 168062) ((-1149 . -632) 168044) ((-325 . -870) NIL) ((-432 . -570) T) ((-229 . -319) T) ((-1261 . -813) 167997) ((-1261 . -816) 167950) ((-1282 . -748) T) ((-1261 . -748) T) ((-48 . -739) 167915) ((-229 . -1053) T) ((-1284 . -425) 167881) ((-1271 . -927) 167824) ((-364 . -1305) 167801) ((-1242 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-112 . -632) 167517) ((-112 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1321 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1321 . -662) 167115) ((-642 . -302) T) ((-600 . -1087) 167090) 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-1248) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1321 . -102) T) ((-1229 . -1248) T) ((-1228 . -635) 166423) ((-1119 . -1248) T) ((-1118 . -1087) 166266) ((-1107 . -1248) T) ((-275 . -938) 166245) ((-255 . -938) 166224) ((-804 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1248) T) ((-1195 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1248) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-804 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-365 . -670) 165041) ((-357 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1189 . -871) T) ((-1119 . -1069) 164755) ((-1107 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-992 . -1143) T) ((-987 . -1248) T) ((-128 . -1041) 164488) ((-872 . -1248) T) ((-895 . -1053) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-680 . -635) 164406) 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-1131) 146013) ((-1255 . -866) T) ((-331 . -1004) 145975) ((-105 . -102) T) ((-48 . -1087) 145940) ((-895 . -874) NIL) ((-1322 . -102) T) ((-394 . -102) T) ((-1284 . -632) 145922) ((-1164 . -1165) 145906) ((-1035 . -660) 145888) ((-900 . -1248) T) ((-48 . -111) 145844) ((-703 . -1248) T) ((-698 . -1248) T) ((-684 . -1248) T) ((-837 . -921) 145711) ((-492 . -1248) T) ((-252 . -1248) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1305) 145695) ((-140 . -1248) T) ((-139 . -1248) T) ((-135 . -1248) T) ((-1247 . -102) T) ((-1055 . -635) 145632) ((-839 . -239) T) ((-1203 . -1252) 145611) ((-218 . -381) T) ((-367 . -635) 145541) ((-1156 . -1252) 145520) ((-247 . -25) 145353) ((-247 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1203 . -570) 145127) ((-1156 . -570) 145058) ((-1255 . -1131) T) ((-560 . -874) T) ((-1066 . -298) 145033) ((-1197 . -1114) T) ((-1025 . -1114) T) ((-838 . -133) T) ((-119 . -817) NIL) ((-119 . -814) NIL) ((-368 . -319) T) 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. -133) T) ((-1135 . -1131) T) ((-1034 . -1131) T) ((-62 . -632) 142043) ((-1111 . -921) 141912) ((-1055 . -814) T) ((-1055 . -817) T) ((-1290 . -25) T) ((-1290 . -21) T) ((-1283 . -21) T) ((-1283 . -25) T) ((-894 . -670) 141899) ((-1262 . -21) T) ((-1262 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -949) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-186 . -1248) T) ((-950 . -816) T) ((-950 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1131) T) ((-516 . -1131) T) ((-793 . -748) T) ((-229 . -376) T) ((-1320 . -1082) 141537) ((-1318 . -1082) 141521) ((-1320 . -662) 141491) ((-1188 . -1131) 141469) ((-895 . -1252) T) ((-1318 . -662) 141439) ((-1119 . -874) T) ((-676 . -632) 141421) ((-895 . -570) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1327 . -635) 141387) ((-1321 . -1131) T) ((-692 . -102) T) ((-372 . -1305) 141371) ((-366 . -1305) 141355) ((-44 . -662) 141339) ((-358 . -1305) 141323) ((-562 . -102) T) ((-1242 . -1248) T) ((-534 . -871) 141302) ((-733 . -1248) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1131) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1214 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1213 . -874) T) ((-1111 . -746) 140934) ((-1327 . -1080) T) ((-838 . -660) 140882) ((-306 . -1089) 140824) ((-172 . -1252) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1198 . -1023) 140681) ((-1284 . -1087) 140586) ((-865 . -1131) T) ((-130 . -874) T) ((-1157 . -762) 140565) ((-1282 . -949) 140544) ((-1261 . -949) 140523) ((-894 . -748) T) ((-172 . -570) 140434) ((-594 . -670) 140421) ((-578 . -670) 140393) ((-421 . -1131) T) ((-272 . -1131) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1261 . -842) 140278) ((-1320 . -102) T) ((-505 . -1248) T) ((-367 . -1317) 140255) ((-1318 . -102) T) ((-1284 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-247 . -871) 139770) ((-600 . -1248) T) ((-1271 . -1252) 139749) ((-103 . -503) 139733) ((-1321 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-981 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1271 . -570) 139575) ((-804 . -47) 139552) ((-802 . -47) 139524) ((-1228 . -1248) T) ((-1203 . -133) T) ((-367 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-981 . -23) T) ((-585 . -570) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1248) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-578 . -816) T) ((-172 . -376) 137289) ((-578 . -813) T) ((-578 . -748) T) ((-509 . -748) T) ((-804 . -1248) T) ((-802 . -1248) T) ((-1177 . -503) 137273) ((-475 . -1248) T) ((-468 . -1248) T) ((-1320 . -1319) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -938) NIL) ((-1318 . -1319) 137228) ((-671 . -1248) T) ((-804 . -911) NIL) ((-802 . -911) 137087) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137065) ((-1137 . -409) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-804 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1248) T) ((-328 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1248) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1248) T) ((-532 . -1248) T) ((-226 . -503) 135750) ((-1298 . -34) T) ((-640 . -668) 135709) ((-301 . -1082) 135696) ((-138 . -635) 135680) ((-301 . -662) 135667) ((-654 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-85 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-804 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1248) T) ((-336 . -133) T) ((-328 . -1080) 135332) ((-325 . -1080) T) ((-172 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1023) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-328 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-306 . -1131) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-172 . -23) T) ((-821 . -149) 134957) ((-821 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1188 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1131) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-804 . -927) 134280) ((-802 . -927) 134264) ((-1320 . -38) 134234) ((-1318 . -38) 134204) ((-1271 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1131) T) ((-1271 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-524 . -874) T) ((-368 . -949) T) ((-365 . -949) T) ((-301 . -102) T) ((-357 . -949) T) ((-1001 . -1114) T) ((-981 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -938) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-432 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1248) T) ((-657 . -1131) T) ((-654 . -783) T) ((-620 . -783) T) ((-1262 . -871) NIL) ((-1111 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-364 . -1131) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-939 . -949) T) ((-1111 . -662) 133600) ((-496 . -1305) 133570) ((-1151 . -1080) T) ((-733 . -319) T) ((-723 . -1089) T) ((-372 . -1082) 133522) ((-366 . -1082) 133474) ((-358 . -1082) 133426) ((-372 . -662) 133378) ((-227 . -1069) 133355) ((-366 . -662) 133307) ((-108 . -1082) 133257) ((-358 . -662) 133209) ((-306 . -739) 133151) ((-661 . -1248) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1151 . -240) T) ((-307 . -153) 132963) ((-1030 . -633) 132924) ((-1030 . -632) 132906) ((-1020 . -632) 132888) ((-118 . -1089) T) ((-676 . -1087) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1085 . -1305) 132801) ((-676 . -111) 132780) ((-692 . -929) 132703) ((-1173 . -503) 132687) ((-1322 . -668) 132646) ((-394 . -668) 132615) ((-63 . -455) T) ((-63 . -409) T) ((-1190 . -102) T) ((-895 . -133) T) ((-498 . -102) 132565) ((-1149 . -1248) T) ((-1254 . -874) T) ((-1327 . -381) T) ((-1111 . -102) T) ((-1092 . -102) T) ((-364 . -739) 132510) ((-896 . -874) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1189 . -102) T) ((-1271 . -133) T) ((-1261 . -874) 131065) ((-1203 . -25) T) ((-1203 . -21) T) ((-1190 . -321) 130860) ((-356 . -1248) T) ((-1156 . -25) T) ((-879 . -133) T) ((-408 . -1248) T) ((-1156 . -21) T) ((-878 . -25) T) ((-878 . -21) T) ((-804 . -319) 130839) ((-1188 . -503) 130823) ((-1181 . -153) 130773) ((-1177 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1177 . -633) 130646) ((-585 . -133) T) ((-640 . -870) 130625) ((-1055 . -813) T) ((-1055 . -816) T) ((-1055 . -748) T) ((-837 . -929) 130494) ((-734 . -1087) 130317) ((-616 . -874) 130296) ((-498 . -321) 130234) ((-467 . -431) 130204) ((-364 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-356 . -1069) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . 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. -47) 98886) ((-372 . -175) T) ((-366 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-364 . -1317) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-358 . -175) T) ((-177 . -250) T) ((-1261 . -871) 98637) ((-108 . -175) T) ((-896 . -1023) 98621) ((-680 . -1143) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-328 . -319) 98564) ((-325 . -319) T) ((-616 . -871) 98543) ((-1144 . -739) 98485) ((-623 . -1248) T) ((-534 . -294) 98469) ((-680 . -23) T) ((-432 . -234) 98453) ((-432 . -274) 98437) ((-325 . -1053) NIL) ((-349 . -23) T) ((-103 . -1041) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-631 . -1131) T) ((-364 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-247 . -321) 98338) ((-1118 . -1143) T) ((-1321 . -670) 98312) ((-804 . -1143) T) ((-802 . -1143) T) ((-1209 . -425) 98296) ((-468 . -1143) T) ((-1093 . -466) T) ((-1182 . -1131) T) ((-981 . -466) 98247) ((-1146 . -1114) T) ((-110 . -1131) T) ((-1118 . -23) T) ((-1190 . -528) 98030) 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. -921) 60880) ((-987 . -321) 60818) ((-858 . -102) T) ((-441 . -739) 60802) ((-229 . -850) T) ((-849 . -102) T) ((-847 . -102) T) ((-1320 . -670) 60776) ((-1282 . -1281) 60755) ((-493 . -153) 60705) ((-1282 . -1276) 60675) ((-1151 . -1252) T) ((-352 . -1069) 60642) ((-1282 . -1279) 60626) ((-1271 . -929) 60533) ((-1261 . -1260) 60512) ((-80 . -632) 60494) ((-934 . -632) 60476) ((-1261 . -1276) 60453) ((-1151 . -570) T) ((-950 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-392 . -296) T) ((-1261 . -1258) 60308) ((-1284 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-578 . -236) 60125) ((-530 . -153) 60109) ((-59 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1317) 60048) ((-366 . -1317) 60032) ((-358 . -1317) 60016) ((-328 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1318 . -670) 59929) ((-130 . -321) NIL) ((-1284 . -23) T) 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. -871) T) ((-1034 . -949) T) ((-1209 . -635) 56019) ((-154 . -748) T) ((-1144 . -381) 55998) ((-659 . -102) T) ((-1055 . -25) T) ((-1035 . -528) NIL) ((-260 . -425) 55967) ((-259 . -425) 55936) ((-1055 . -21) T) ((-896 . -1082) 55888) ((-610 . -739) 55861) ((-609 . -739) 55758) ((-821 . -298) 55716) ((-128 . -102) 55666) ((-855 . -1069) 55562) ((-172 . -850) 55541) ((-331 . -670) 55438) ((-837 . -34) T) ((-736 . -102) T) ((-1151 . -1143) T) ((-1057 . -1248) T) ((-896 . -662) 55390) ((-392 . -38) 55355) ((-367 . -25) T) ((-367 . -21) T) ((-190 . -102) T) ((-164 . -102) T) ((-257 . -102) T) ((-159 . -102) T) ((-368 . -1305) 55339) ((-365 . -1305) 55323) ((-357 . -1305) 55307) ((-172 . -362) 55286) ((-578 . -871) T) ((-1118 . -239) 55237) ((-1151 . -23) T) ((-87 . -632) 55219) ((-804 . -239) T) ((-723 . -319) T) ((-858 . -38) 55189) ((-849 . -38) 55159) ((-1310 . -635) 55101) ((-1284 . -133) T) ((-1181 . -300) 55080) ((-993 . -748) 54979) ((-993 . -815) 54932) ((-993 . -816) 54885) 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. -949) T) ((-723 . -842) T) ((-441 . -632) 39859) ((-1151 . -21) T) ((-1151 . -25) T) ((-692 . -390) 39843) ((-118 . -949) T) ((-896 . -274) 39827) ((-896 . -234) 39811) ((-44 . -1248) T) ((-78 . -1248) T) ((-128 . -127) 39795) ((-1085 . -34) T) ((-1320 . -1069) 39769) ((-1318 . -1069) 39726) ((-1271 . -1089) T) ((-879 . -1089) T) ((-368 . -1183) 39705) ((-365 . -1183) 39684) ((-357 . -1183) 39663) ((-496 . -816) 39642) ((-496 . -815) 39621) ((-231 . -34) T) ((-496 . -748) 39599) ((-821 . -635) 39445) ((-684 . -1082) 39429) ((-60 . -503) 39413) ((-585 . -1089) T) ((-1203 . -175) 39304) ((-684 . -662) 39288) ((-488 . -929) 39194) ((-154 . -1248) T) ((-1156 . -175) 39105) ((-1093 . -1131) T) ((-1118 . -978) 39050) ((-981 . -1131) T) ((-839 . -670) 39001) ((-804 . -978) 38970) ((-735 . -1131) T) ((-802 . -978) 38937) ((-530 . -294) 38921) ((-692 . -927) 38880) ((-495 . -1131) T) ((-468 . -978) 38847) ((-79 . -1248) T) ((-368 . -38) 38812) ((-365 . -38) 38777) ((-357 . -38) 38742) ((-275 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. -1131) T) ((-981 . -175) 33211) ((-804 . -1274) 33195) ((-666 . -528) 33128) ((-77 . -632) 33110) ((-753 . -338) 33075) ((-1209 . -748) T) ((-585 . -1131) T) ((-495 . -175) 32986) ((-252 . -321) 32924) ((-1173 . -1143) T) ((-70 . -632) 32906) ((-1310 . -748) T) ((-1205 . -1080) T) ((-1204 . -1080) T) ((-1198 . -1080) T) ((-339 . -102) 32836) ((-1173 . -23) T) ((-2 . -1248) T) ((-1157 . -1080) T) ((-91 . -1152) 32820) ((-890 . -1143) T) ((-1205 . -240) 32779) ((-1204 . -250) 32758) ((-1204 . -240) 32710) ((-1198 . -240) 32597) ((-1198 . -250) 32576) ((-331 . -927) 32482) ((-890 . -23) T) ((-172 . -739) 32310) ((-421 . -1252) T) ((-1132 . -381) T) ((-1034 . -376) T) ((-894 . -466) T) ((-1055 . -149) T) ((-972 . -298) 32262) ((-325 . -871) NIL) ((-1282 . -668) 32144) ((-898 . -102) T) ((-1261 . -668) 31999) ((-734 . -25) T) ((-421 . -570) T) ((-734 . -21) T) ((-539 . -635) 31980) ((-367 . -149) 31962) ((-367 . -147) T) ((-1178 . -1131) 31940) ((-467 . -742) T) ((-75 . -632) 31922) 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. -632) 15850) ((-1311 . -1241) 15819) ((-495 . -632) 15801) ((-495 . -633) 15662) ((-275 . -425) 15646) ((-255 . -425) 15630) ((-325 . -239) NIL) ((-260 . -111) 15546) ((-259 . -111) 15462) ((-1255 . -683) T) ((-1205 . -670) 15387) ((-1204 . -670) 15284) ((-1198 . -670) 15136) ((-1157 . -670) 15061) ((-364 . -133) T) ((-82 . -455) T) ((-82 . -409) T) ((-1034 . -25) T) ((-1034 . -21) T) ((-897 . -1131) 15012) ((-40 . -1082) 14957) ((-896 . -739) 14909) ((-40 . -662) 14854) ((-392 . -302) T) ((-172 . -1033) 14805) ((-1118 . -929) 14704) ((-716 . -401) T) ((-1030 . -1028) 14688) ((-723 . -1143) T) ((-716 . -168) 14670) ((-804 . -929) 14577) ((-802 . -929) 14561) ((-1282 . -1131) T) ((-1261 . -1131) T) ((-1195 . -102) T) ((-328 . -1233) 14540) ((-328 . -1236) 14519) ((-468 . -929) 14496) ((-328 . -988) 14475) ((-136 . -1143) T) ((-118 . -1143) T) ((-1001 . -1248) T) ((-888 . -1248) T) ((-723 . -23) T) ((-675 . -1248) T) ((-616 . -1296) 14459) ((-616 . -1131) 14409) ((-545 . -874) T) 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. -949) T) ((-358 . -949) T) ((-229 . -111) 7873) ((-855 . -23) 7825) ((-441 . -748) T) ((-108 . -949) T) ((-40 . -38) 7770) ((-108 . -842) T) ((-595 . -362) T) ((-532 . -362) T) ((-680 . -668) 7729) ((-328 . -466) 7708) ((-325 . -466) T) ((-616 . -528) 7641) ((-421 . -236) 7586) ((-352 . -133) T) ((-177 . -133) T) ((-306 . -25) 7450) ((-306 . -21) 7333) ((-45 . -1224) 7312) ((-66 . -632) 7294) ((-55 . -102) T) ((-349 . -668) 7276) ((-1299 . -102) T) ((-1298 . -102) 7206) ((-1290 . -670) 7131) ((-1283 . -670) 7028) ((-45 . -107) 6978) ((-841 . -635) 6962) ((-1262 . -670) 6814) ((-1262 . -938) NIL) ((-1253 . -1248) T) ((-1229 . -632) 6796) ((-1221 . -102) T) ((-1133 . -439) 6780) ((-1133 . -381) 6759) ((-400 . -635) 6743) ((-336 . -635) 6727) ((-1127 . -93) T) ((-1118 . -668) 6637) ((-1094 . -1248) T) ((-1093 . -1087) 6624) ((-1093 . -111) 6609) ((-981 . -111) 6438) ((-981 . -1087) 6281) ((-804 . -668) 6191) ((-802 . -668) 6101) ((-686 . -739) 6085) ((-642 . -1082) 6072) ((-642 . -662) 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4610) ((-610 . -670) 4584) ((-609 . -670) 4509) ((-595 . -668) 4459) ((-229 . -1080) T) ((-532 . -668) 4389) ((-1093 . -635) 4361) ((-392 . -1033) T) ((-229 . -250) T) ((-229 . -240) T) ((-872 . -504) 4345) ((-1093 . -637) 4326) ((-987 . -633) 4287) ((-987 . -632) 4199) ((-981 . -635) 3988) ((-872 . -632) 3936) ((-894 . -38) 3923) ((-735 . -635) 3873) ((-1282 . -302) 3824) ((-1261 . -302) 3775) ((-495 . -635) 3560) ((-1151 . -466) T) ((-516 . -871) T) ((-328 . -1170) 3539) ((-1132 . -1248) T) ((-1030 . -149) 3518) ((-1030 . -147) 3497) ((-509 . -321) 3484) ((-1215 . -632) 3466) ((-307 . -1224) 3445) ((-1214 . -632) 3427) ((-1166 . -1248) T) ((-1213 . -632) 3409) ((-895 . -1087) 3354) ((-491 . -1143) T) ((-141 . -857) 3336) ((-116 . -857) 3317) ((-1234 . -503) 3301) ((-1093 . -1080) T) ((-642 . -102) T) ((-992 . -1248) T) ((-981 . -1080) T) ((-260 . -381) 3280) ((-259 . -381) 3259) ((-895 . -111) 3188) ((-307 . -107) 3138) ((-132 . -632) 3120) ((-130 . -633) NIL) ((-130 . -632) 3064) ((-119 . -102) T) ((-757 . -1248) T) ((-737 . -1248) T) ((-491 . -23) T) ((-467 . -1248) T) ((-495 . -1080) T) ((-1093 . -240) T) ((-981 . -338) 3033) ((-40 . -929) 2942) ((-495 . -338) 2899) ((-368 . -175) T) ((-365 . -175) T) ((-357 . -175) T) ((-275 . -175) 2810) ((-255 . -175) 2721) ((-992 . -1069) 2617) ((-531 . -504) 2598) ((-757 . -1069) 2569) ((-531 . -632) 2535) ((-432 . -1248) T) ((-1136 . -102) T) ((-1123 . -632) 2494) ((-1065 . -632) 2476) ((-716 . -1082) 2426) ((-1311 . -153) 2410) ((-1309 . -635) 2391) ((-1308 . -635) 2372) ((-1303 . -632) 2354) ((-1290 . -748) T) ((-716 . -662) 2304) ((-1283 . -748) T) ((-1262 . -813) NIL) ((-1262 . -816) NIL) ((-172 . -1087) 2214) ((-939 . -175) T) ((-895 . -635) 2144) ((-1262 . -748) T) ((-1034 . -355) 2118) ((-227 . -668) 2070) ((-1031 . -528) 2003) ((-865 . -871) 1982) ((-578 . -1183) T) ((-488 . -302) 1933) ((-610 . -748) T) ((-374 . -632) 1915) ((-334 . -632) 1897) ((-432 . -1069) 1793) ((-609 . -748) T) ((-421 . -871) 1744) ((-172 . -111) 1640) ((-855 . -133) 1592) ((-1298 . -321) 1530) ((-759 . -153) 1514) ((-993 . -874) 1413) ((-837 . -874) 1364) ((-501 . -319) T) ((-392 . -632) 1331) ((-534 . -1041) 1315) ((-392 . -633) 1229) ((-221 . -319) T) ((-143 . -153) 1211) ((-736 . -298) 1190) ((-501 . -1053) T) ((-594 . -38) 1177) ((-578 . -38) 1164) ((-509 . -38) 1129) ((-661 . -668) 1098) ((-221 . -1053) T) ((-895 . -1080) T) ((-858 . -632) 1080) ((-849 . -632) 1062) ((-847 . -632) 1044) ((-838 . -938) 1023) ((-1322 . -1143) T) ((-324 . -1248) T) ((-1271 . -1087) 846) ((-879 . -1087) 830) ((-895 . -250) T) ((-895 . -240) NIL) ((-711 . -1248) T) ((-1322 . -23) T) ((-838 . -670) 719) ((-564 . -1248) T) ((-432 . -351) 703) ((-585 . -1087) 690) ((-1271 . -111) 499) ((-723 . -660) 481) ((-879 . -111) 460) ((-394 . -23) T) ((-172 . -635) 238) ((-1220 . -528) 30) ((-900 . -1131) T) ((-703 . -1131) T) ((-698 . -1131) T) ((-684 . -1131) T)) \ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index c00d359c..6869a147 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3497194934)
-(4503 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3498909337)
+(4510 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -490,672 +490,677 @@
|XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram|
|ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
|IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |pmComplexintegrate| |yCoord| |extendedint| |e02adf|
- |dilog| |property| |imagE| |union| |aLinear| |complexForm| |nor|
- |flagFactor| |nextColeman| |min| |d02gbf| |newTypeLists|
- |fortranLogical| |sin| |superHeight| |setprevious!|
- |sturmVariationsOf| |primitiveElement| |inc| |step|
- |indicialEquations| |nonQsign| |color| |prefixRagits| |OMputSymbol|
- |cos| |leadingTerm| |tablePow| |resultantReduit| |say| |addPoint|
- |component| |primaryDecomp| |child?| |complexNormalize| |digamma|
- |tan| |extendedSubResultantGcd| |capacity| |normalizeIfCan| |mkcomm|
- |certainlySubVariety?| |contractSolve| |totalDifferential| |readable?|
- |cot| |cos2sec| |forLoop| |f04faf| |OMUnknownCD?| |cotIfCan|
- |associative?| |multMonom| |fortranCarriageReturn| |omError|
- |separateFactors| |sec| |appendPoint| |extendedEuclidean|
- |numericIfCan| |imaginary| |plus| |denomRicDE| |zero?| |meatAxe|
- |csubst| |f07aef| |csc| |thenBranch| |subCase?| |setOrder| |reset|
- |absolutelyIrreducible?| |option?| |iicsch| |edf2efi|
- |genericRightDiscriminant| |printStatement| |asin| |pointColorDefault|
- |iitanh| |zeroDimPrimary?| |univariatePolynomial| |c02aff| |light|
- |symmetricRemainder| |plenaryPower| |acos| |extractProperty|
- |gcdPrimitive| |acosIfCan| |stoseLastSubResultant| |write| |e01bff|
- |insertRoot!| |over| |baseRDEsys| |times| |seed| |fortranCharacter|
- |atan| |iisqrt2| |save| |leftRecip| |aspFilename| |OMgetEndError|
- |iiGamma| |randnum| |minPoints3D| |prime?| |swap!| |acot| |OMgetAtp|
- |compiledFunction| |acschIfCan| |iCompose| |argument| |pow| |imagk|
- |SturmHabicht| |sup| |asec| |newSubProgram| |tan2trig| |directory|
- |cAcosh| |fortranComplex| |rationalPower| |pade| |create| |acsc|
- |monicCompleteDecompose| |e01baf| |reciprocalPolynomial|
- |identityMatrix| |f01maf| |ratDenom| |escape| |getGoodPrime|
- |csch2sinh| |monom| |outputFixed| |sinh| |realEigenvalues| |f02fjf|
- |nullity| |getVariableOrder| |curve?| |sub| |modularFactor|
- |transpose| |assign| |minRowIndex| |leastAffineMultiple| |cosh| |mesh|
- |functionIsContinuousAtEndPoints| |write!| |lifting1| |idealiser|
- |generalLambert| |typeForm| |normal?| |restorePrecision| |getOrder|
- |chiSquare| |tanh| |socf2socdf| |leaves| |recur|
- |rightFactorCandidate| |palgint0| |sizeLess?| |expint|
- |stoseSquareFreePart| |common| |sumSquares| |addmod|
- |algebraicVariables| |OMgetInteger| |coth| |getZechTable| |neglist|
- |setPoly| |removeDuplicates| |cap| |linear?| |baseRDE| |ratDsolve|
- |irreducibleFactors| |zero| |deriv| |sech| |constant|
- |removeSuperfluousCases| |f04maf| |lowerBound| |constructor|
- |cot2trig| |more?| |linearDependenceOverZ| |kroneckerDelta|
- |primeFrobenius| |reverse| |mainCharacterization| |csch| |e01sff|
- |dihedralGroup| EQ |finite?| |bits| |totolex| |createZechTable| |And|
- |rur| |asinh| |monomial?| |PollardSmallFactor| |root| |iidprod|
- |subset?| |numberOfNormalPoly| |basisOfMiddleNucleus| |ParCond|
- |symmetricProduct| |Or| |mix| |binaryTree| |acosh| |tanQ| |compdegd|
- |lazyVariations| |lfextlimint| |Lazard2| |makeYoungTableau| |f02agf|
- |radix| |Not| |coefficient| |stoseInvertibleSet| |atanh| |removeZero|
- |OMconnectTCP| |partitions| |removeCosSq| |checkPrecision|
- |inputBinaryFile| |region| |iiatan| |untab| |sequence| |acoth|
- |solid?| |complexLimit| |ScanRoman| |innerSolve| |decimal| |palgint|
- |adaptive| |polygon?| |s21bbf| |algebraicSort| |asech| |subSet|
- |mainValue| |viewWriteDefault| |trailingCoefficient| |wronskianMatrix|
- |updatD| |OMread| |contract| |clearDenominator| |curveColorPalette|
- |normDeriv2| |nextPrimitivePoly| |generalizedInverse| |swapColumns!|
- |complete| |shrinkable| |Lazard| |blankSeparate| |viewDefaults|
- |represents| |multiple| |eyeDistance| |categories| |f07fdf|
- |infinityNorm| |expextendedint| |close| |binomThmExpt| |enqueue!|
- |writable?| |c05pbf| |applyQuote| |s21baf| |sncndn| |limitPlus|
- |range| |fill!| |cosh2sech| |expressIdealMember| |square?|
- |OMgetSymbol| |possiblyInfinite?| |compactFraction| |viewPosDefault|
- |symmetric?| |diag| |imagI| |basisOfRightNucloid| |display| |ipow|
- |interactiveEnv| |rightScalarTimes!| |content| |drawCurves|
- |mkIntegral| |toseSquareFreePart| |setnext!| |elaboration| |expt|
- |safetyMargin| |exponential1| |lazyResidueClass| |henselFact|
- |signatureAst| |eigenvectors| |genericRightTraceForm| |rootDirectory|
- |debug| |rootSimp| |e02daf| |asinIfCan| |mirror|
- |internalZeroSetSplit| |OMunhandledSymbol| |perfectSqrt| |weighted|
- |s17adf| D |uncouplingMatrices| |dfRange|
- |semiSubResultantGcdEuclidean2| |members| |isQuotient|
- |semicolonSeparate| |perfectNthRoot| |isList|
- |stoseInvertibleSetsqfreg| |OMUnknownSymbol?| |dec| |linearDependence|
- |subMatrix| |coerceImages| |birth| |expandPower| |elaborate|
- |initials| |iiexp| |squareFree| |readByte!| |input| |one?| |f02abf|
- |numerator| |semiIndiceSubResultantEuclidean| |currentCategoryFrame|
- |colorFunction| |limitedint| |findCycle| |delete| |infix| |setrest!|
- |library| |ran| |noValueMode| |nextSublist| |minimalPolynomial|
- |writeUInt8!| |randomR| |isOp| |cAsin| |normalise| |rootPoly|
- |iterationVar| |generalizedEigenvectors| |subresultantVector|
- |cothIfCan| |string?| |reduceByQuasiMonic| |ptree|
- |semiDiscriminantEuclidean| |dn| |c06frf| |showTheSymbolTable|
- |setProperty| |rename| |setColumn!| |df2fi| UP2UTS |height| |nlde|
- |lazyEvaluate| |froot| |createNormalPrimitivePoly|
- |selectOrPolynomials| |sin2csc| |doubleComplex?| |leftScalarTimes!|
- |univariatePolynomials| |linear| |writeInt8!| |coth2trigh|
- |outputAsTex| |OMgetString| |squareMatrix| |principalAncestors| |set|
- |att2Result| |linearlyDependentOverZ?| |separateDegrees| |unvectorise|
- |edf2df| |nextsousResultant2| |coord| |basisOfLeftNucleus| |bracket|
- |reducedDiscriminant| |hcrf| |d03eef| |hitherPlane| |polynomial|
- |discriminant| |yCoordinates| |hconcat| |changeVar| |copy!| |red|
- |f01qdf| |print| |ef2edf| |algSplitSimple| |getDatabase| |operation|
- |complex?| |OMputEndBVar| |moreAlgebraic?| |clipWithRanges|
- |invertibleElseSplit?| |ratpart| |resolve| |has?| |jvmVolatile|
- |changeNameToObjf| |extractPoint| |approxSqrt| |ldf2vmf| |bernoulliB|
- |fullDisplay| |rule| |showAllElements| |cons| |makeCos| |abelianGroup|
- |f04axf| |quasiMonicPolynomials| |exp1| |npcoef| |d01ajf|
- |printHeader| |OMreadFile| |cAtan| |particularSolution| |mappingAst|
- |bivariateSLPEBR| |e02dff| |revert| |disjunction| |solveLinearlyOverQ|
- |linGenPos| |chebyshevT| |curryLeft| |viewpoint| |extract!|
- |headRemainder| |critMTonD1| |completeEchelonBasis| |binaryTournament|
- |basicSet| |OMParseError?| |c06ecf| |OMgetEndBind| |drawComplex|
- |ode2| |semiResultantEuclideannaif| |purelyTranscendental?|
- |computeInt| |cCoth| |cCot| |setErrorBound| |cAsinh| |whileLoop|
- |infiniteProduct| |listBranches| |reducedForm| |log10|
- |OMconnInDevice| |quote| |nthRoot| |source| |radicalOfLeftTraceForm|
- |mainDefiningPolynomial| |numberOfComponents| |repeating|
- |expintegrate| |weights| |bernoulli| |hostByteOrder| |bitand| |s17aef|
- |symbolTable| |show| |cardinality| |leastPower| |lowerCase?| |f02aef|
- |roughEqualIdeals?| |normalDeriv| |integralBasis| |f02bbf| |bitior|
- |pseudoDivide| |factorList| |intChoose| |matrix| |powerAssociative?|
- |getGraph| |symmetricDifference| |rightExtendedGcd| |rank| |lprop|
- |cot2tan| |lighting| |pushFortranOutputStack| |trace| |f02aff|
- |monicDivide| |totalGroebner| |triangSolve| |factorSFBRlcUnit| |shift|
- |iteratedInitials| |cycle| |definingEquations| |distFact|
- |popFortranOutputStack| |target| |vark| |OMputError|
- |partialNumerators| |countRealRoots| |integerIfCan| |OMbindTCP|
- |btwFact| |transcendent?| |nthFactor| |outputAsFortran|
- |dualSignature| |exprToXXP| |rk4a| |readLineIfCan!| |ptFunc|
- |generalizedContinuumHypothesisAssumed| |s18aff| |postfix| |slex|
- |nullary?| |voidMode| |iitan| |selectfirst| |rightUnits| |eigenvector|
- |flexibleArray| |max| |leaf?| |s01eaf| |quotientByP| |back| |sPol|
- |distance| |tanhIfCan| |properties| |romberg| |SturmHabichtMultiple|
- |integralLastSubResultant| |stronglyReduce| |wordInGenerators|
- |options| |df2st| |cyclicEntries| F2FG |lastSubResultantEuclidean|
- |solve| |gbasis| |translate| |initializeGroupForWordProblem|
- |incrementKthElement| |ksec| |copies| |gcdcofact| |e02ddf|
- |monicDecomposeIfCan| |iExquo| |lists| |cyclePartition| |iomode|
- |blue| |isAbsolutelyIrreducible?| |sum| |fortranReal| |relationsIdeal|
- |clearTheFTable| |complexEigenvalues| |quotedOperators| |rootKerSimp|
- |jvmPrivate| |bindings| |deepestTail| |stFunc2| |string| |binding|
- |subResultantChain| |linearPart| |insert!| |cross| |s19abf|
- |lieAdmissible?| |d02bbf| |fi2df| |exactQuotient!| |terms| |e01bef|
- |addMatchRestricted| |clipSurface| |OMcloseConn| |extendedResultant|
- |row| |sparsityIF| |prod| |ode1| |palgextint| |indiceSubResultant|
- |toseLastSubResultant| |bat| |find| |innerint| |wrregime|
- |increasePrecision| |universe| |lexico| |qqq| |cosSinInfo| |eof?|
- |resetBadValues| |coshIfCan| |bothWays| |basisOfCentroid| |associator|
- |minPoly| |bitTruth| |jacobian| |solid| |showAll?| |parametersOf|
- |powerSum| |polar| |edf2ef| |convergents| |outputArgs|
- |generalizedContinuumHypothesisAssumed?| |e02baf| |OMputEndAttr|
- |zoom| |moduleSum| |vector| |recolor| |partition| |factorFraction|
- |scalarMatrix| |merge| |chainSubResultants| |functorData|
- |selectPDERoutines| |setStatus!| |differentiate| |mat| |fractionPart|
- |bfEntry| |getProperty| |rightRank| |generalPosition| |comp|
- |quickSort| |removeRoughlyRedundantFactorsInPols|
- |setAttributeButtonStep| |sort| |abs| |cycleLength| |stFuncN|
- |argumentList!| |super| |computeCycleEntry| |prinpolINFO| |iiperm|
- |OMencodingSGML| |lex| |digit?| |antiAssociative?| |genericLeftNorm|
- |mesh?| |multiEuclideanTree| |kmax| |unitNormal| |minrank| |random|
- |firstDenom| |LyndonWordsList| |quasiAlgebraicSet| |zeroDimPrime?|
- |lexGroebner| |df2mf| |symbol| |OMgetEndApp| |evaluate| |algebraicOf|
- |leadingCoefficientRicDE| |euler| |iicos| |wholeRagits|
- |rootNormalize| |expression| |replace| |OMlistCDs| |isPlus| |cyclic|
- |elliptic| |irCtor| |kovacic| |index| |e02zaf| |integer| |recip|
- |transform| |trivialIdeal?| |coth2tanh| |rightZero|
- |integralDerivationMatrix| |OMsupportsSymbol?| |bezoutResultant|
- |rightGcd| |ridHack1| |createRandomElement| |nonLinearPart| |exprex|
- |condition| |polynomialZeros| |OMclose| |OMwrite|
- |shanksDiscLogAlgorithm| |hexDigit?| |listOfMonoms| |determinant|
- |secIfCan| |bombieriNorm| |algintegrate| |gensym| |imports| |d01gaf|
- |pair| |regularRepresentation| |readInt8!| |genericPosition|
- |jvmFinal| |sayLength| |measure| |deref| |OMgetEndBVar| |sinIfCan|
- |monomialIntPoly| |pol| |mapSolve| |mdeg| |move| |jordanAdmissible?|
- |modularGcd| |dequeue!| |monicRightFactorIfCan| |duplicates?| |f04qaf|
- |c06fpf| |doubleDisc| |balancedBinaryTree| |OMgetAttr| |anticoord|
- |checkForZero| |intPatternMatch| |output|
- |rewriteSetByReducingWithParticularGenerators| |epilogue| |pToHdmp|
- |normal01| |innerSolve1| |cSinh| |divideIfCan!| |contains?| |rspace|
- |iisin| |upperBound| F |pack!| |curryRight| |useEisensteinCriterion|
- |fTable| |concat!| |realSolve| |bumptab| |LyndonCoordinates| |mpsode|
- |printCode| |rewriteIdealWithRemainder| BY |createPrimitiveNormalPoly|
- |primPartElseUnitCanonical| |primes| |setchildren!| |bipolar| |Ei|
- |d01akf| |initiallyReduce| |s20acf| |laplacian| |medialSet|
- |noncommutativeJordanAlgebra?| |s14baf| |changeThreshhold|
- |radicalSolve| |simplifyExp| |predicate| |newLine| |deepCopy|
- |integral| |selectFiniteRoutines| |monic?| |showSummary|
- |simpleBounds?| |expPot| |overlap| |randomLC| |rotatex| |externalList|
- |raisePolynomial| |polygon| |basisOfRightAnnihilator| |init|
- |GospersMethod| |mapGen| |rightOne| |bsolve| |removeZeroes|
- |arrayStack| |sincos| |setPrologue!| |box| |discreteLog| |Ci|
- |quatern| |internalInfRittWu?| |topPredicate| |dmp2rfi|
- |leftDiscriminant| |setMinPoints3D| |ratPoly| NOT |iiacsch|
- |divideExponents| |size| |discriminantEuclidean| |viewDeltaYDefault|
- |scale| |legendre| |symbolIfCan| |rubiksGroup| |taylorQuoByVar| OR
- |showAttributes| |OMgetEndAttr| |mindeg| |leadingBasisTerm|
- |minGbasis| |children| |sizeMultiplication| |call| |f04mbf|
- |rootPower| AND |whitePoint| |typeList| |genericRightTrace| |leftLcm|
- |cyclicParents| |An| |regime| |setProperties| |createNormalElement|
- |trim| |modTree| |e02aef| |currentEnv| |cCsch| |checkRur| |operators|
- |explimitedint| |open| |dmpToHdmp| |leftZero| |HermiteIntegrate|
- |degreeSubResultant| |mightHaveRoots| |function| |OMputApp|
- |generalTwoFactor| |increment| |ode| |endOfFile?| |f04adf|
- |resetVariableOrder| |triangular?| |create3Space| |parameters|
- |algebraic?| |e02dcf| |optpair| |cycles| |rationalApproximation|
- |OMputBVar| |lfextendedint| |conjugates| |packageCall| |laurentRep|
- |primlimintfrac| |cdr| |deepExpand| |factorByRecursion| |adaptive?|
- |primitivePart| |coerceListOfPairs| |localIntegralBasis|
- |numberOfFactors| |binary| |isConnected?| |null| |loadNativeModule|
- |semiLastSubResultantEuclidean| |useSingleFactorBound?| |inR?|
- |operations| |lSpaceBasis| |f07adf| |column| |leftMult| |tRange|
- |pToDmp| |not| |clip| |inrootof| |createThreeSpace| |leftTraceMatrix|
- |node| |bigEndian| |f02xef| |numberOfMonomials| |lazyPseudoDivide|
- |upperCase!| |and| |f01bsf| |varselect| |choosemon| |sinhIfCan|
- |clipBoolean| |ldf2lst| |prolateSpheroidal| |returnType!|
- |usingTable?| |roughBase?| |ruleset| |or| |OMgetError| |redPo|
- |wholePart| |eulerPhi| * |hue| |extensionDegree|
- |jvmIntegerConstantTag| |pushdown| |exprHasWeightCosWXorSinWX|
- |constDsolve| |xor| |rightMult| |divisors| |derivationCoordinates|
- |OMputBind| |category| |genericLeftTrace| |palgLODE|
- |rightExactQuotient| |nthr| |imagK| |case| |headReduced?| |e02bbf|
- |enterPointData| |pastel| |outerProduct| |domain| |nthCoef| |c06gcf|
- |updatF| |mapMatrixIfCan| |cPower| |suchThat| |Zero| |mapBivariate|
- |palgintegrate| |jvmProtected| |jokerMode| |package| |nthRootIfCan|
- |head| |leftUnits| |splitSquarefree| |roman| |One| |coefChoose|
- |merge!| |controlPanel| |FormatArabic| = |quadratic?|
- |sizePascalTriangle| |pdf2df| |OMconnOutDevice|
- |rootOfIrreduciblePoly| |lcm| |setRealSteps| |rootsOf|
- |definingInequation| |alphabetic?| |charpol| |inverseColeman|
- |iibinom| |laplace| |s21bdf| |c06fuf| |changeName| |weierstrass|
- |clearTheSymbolTable| < |toroidal| |overset?| |alternatingGroup|
- |exactQuotient| |insertBottom!| |append| |coerce| |subtractIfCan|
- |reducedSystem| |simplifyLog| |dAndcExp| > |OMgetApp| |tanIfCan|
- |singRicDE| |cyclicSubmodule| |polyred| |gcd| |construct|
- |linearElement| |yellow| |outlineRender| |createMultiplicationTable|
- |maximumExponent| <= |rules| |hasHi| |invertible?| |LiePolyIfCan|
- |nthFractionalTerm| |false| |elt| |algebraicCoefficients?|
- |constantOpIfCan| |c02agf| |KrullNumber| >= |exprToUPS|
- |quadraticForm| |trueEqual| |graphState| |factorAndSplit| |qinterval|
- |rightTrim| |s17dgf| |diagonals| |repeating?| |cubic|
- |internalAugment| |irVar| |mainVariable?| |readLine!| |makeViewport3D|
- |leftTrim| |zeroOf| |iipow| |OMputObject| |infieldint| |e04ycf|
- |removeConstantTerm| |rewriteIdealWithHeadRemainder| |s13acf|
- |outputBinaryFile| |tanintegrate| FG2F |nextsubResultant2| +
- |optional| |reverseLex| |points| |toScale| |elRow2!| |parents| |rk4qc|
- |showTheRoutinesTable| |basisOfRightNucleus| |resetAttributeButtons|
- |showArrayValues| |mr| - |copyInto!| |s14abf| |specialTrigs|
- |listOfLists| |approxNthRoot| |inGroundField?|
- |showFortranOutputStack| |sumOfDivisors| |unmakeSUP| /
- |firstSubsetGray| |diophantineSystem| |tensorProduct|
- |expandTrigProducts| |lift| |orbits| |pdf2ef| |OMencodingBinary|
- |groebner| |definingPolynomial| |constantToUnaryFunction| |comment|
- |localUnquote| |numberOfPrimitivePoly| |completeEval| |shufflein|
- |factorsOfDegree| |reduce| |OMopenFile| |powmod| |multiEuclidean|
- |green| |lintgcd| |numer| |explicitEntries?| |countRealRootsMultiple|
- |Vectorise| |binomial| |algDsolve| |setelt!| |pushuconst|
- |complexExpand| |multiset| |janko2| |denom| |irForm| |maxPoints3D|
- |variable?| |bitLength| |gcdcofactprim| |s17dcf|
- |balancedFactorisation| |implies| |roughSubIdeal?| |corrPoly| |dual|
- |drawStyle| |seriesSolve| |constantIfCan| |antiCommutative?|
- |euclideanNormalForm| |lquo| |prindINFO| |getStream| |quoted?| |pi|
- |tValues| |high| |rightCharacteristicPolynomial| |pole?| |errorKind|
- |categoryFrame| |componentUpperBound| |OMmakeConn| |OMputAttr|
- |infinity| |internalSubQuasiComponent?| |shellSort| |d02kef|
- |maxColIndex| |closed?| |overlabel| |directSum| |boundOfCauchy| |frst|
- |complexEigenvectors| |cycleRagits| |e01bhf| |tubeRadiusDefault|
- |tryFunctionalDecomposition| |crest| |shiftLeft| |expIfCan|
- |someBasis| |meshPar1Var| |atom?| |transcendentalDecompose|
- |moebiusMu| |supRittWu?| Y |qfactor| |matrixConcat3D| |dimension|
- |dequeue| |setelt| |totalfract| |completeHensel| |f07fef|
- |computeCycleLength| |kernel| |e02gaf| |split!| |divisorCascade|
- |lastSubResultant| |ideal| |s13adf| |indices| |getOperator| |sign|
- |cosIfCan| |list| |lfinfieldint| |rotatey| |Hausdorff|
- |numberOfComputedEntries| |univcase| |rowEchelonLocal| |s17akf|
- |moduloP| |brillhartTrials| |flexible?| |nsqfree| |draw| |f04asf|
- |permutationRepresentation| |taylorRep| |mainContent| |real?|
- |poisson| |iicot| |s18def| |factor1| |numberOfComposites| |floor|
- |getProperties| |nonSingularModel| |entries| |constantKernel|
- |infieldIntegrate| |removeSuperfluousQuasiComponents| |factorset|
- |before?| |setAdaptive3D| |minset| |mathieu24| |vectorise| |infinite?|
- |divideIfCan| |OMgetEndAtp| |groebner?| |rk4| |listConjugateBases|
- |bit?| |RittWuCompare| |monicModulo| |scripted?| |qPot|
- |perfectSquare?| |mathieu11| |indicialEquationAtInfinity| |OMputAtp|
- |result| |denominators| |lepol| |makeObject| |fullPartialFraction|
- |unknownEndian| |modifyPointData| |algint| |getBadValues| |cAcoth|
- |eq?| |oddintegers| |direction| |connect| |iFTable| |coef| |cartesian|
- |logpart| |s17dhf| |label| |stack| |leftFactorIfCan| |mapExpon|
- |readInt32!| |createLowComplexityTable| |primintfldpoly| |iicosh|
- |localReal?| |primitive?| |isobaric?| |mainVariable|
- |orthonormalBasis| |UP2ifCan| |makeFR| |basisOfCommutingElements|
- |algebraicDecompose| |internal?| |leftTrace| |characteristic|
- |palglimint0| |coHeight| |makeSUP| |findBinding| |OMputEndAtp|
- |startTableInvSet!| |completeHermite| |rewriteSetWithReduction|
- |setLabelValue| |jvmFloatConstantTag| |charthRoot| |slash| |prologue|
- |cyclotomicDecomposition| |csc2sin| |hdmpToP| |bfKeys| |sorted?|
- |iprint| |subTriSet?| |nodeOf?| |decompose| |build| GF2FG
- |dimensionsOf| |cAtanh| |solveRetract| |asimpson| |resultantEuclidean|
- |power| |imagj| |axesColorDefault| |closedCurve?| |parts|
- |extractClosed| |leftGcd| |bezoutMatrix| |factorSquareFreePolynomial|
- |selectAndPolynomials| |calcRanges| |remove| |maxrow| |e01sbf|
- |semiResultantReduitEuclidean| |Aleph| |fractionFreeGauss!|
- |evaluateInverse| |goodPoint| |cAcsch| |ramified?| |solveLinear|
- |univariate?| |getMatch| |permanent| |listLoops| |countable?| |maxint|
- |setFieldInfo| |nextPrimitiveNormalPoly| |entry| |UpTriBddDenomInv|
- |last| |option| |hasoln| |setMaxPoints3D| |atanIfCan| |biRank|
- |rename!| |hMonic| |subPolSet?| |cAcot| |assoc| |c05adf|
- |stopTableInvSet!| |pointColorPalette| |beauzamyBound| |returnTypeOf|
- |atanhIfCan| |readIfCan!| |d01gbf| |makingStats?| |every?|
- |oddlambert| |viewDeltaXDefault| |irreducibleRepresentation|
- |patternMatch| |alternative?| |pair?| |plot| |isTimes| |karatsuba|
- |d03edf| |cn| |leftRankPolynomial| |c06ekf| |drawToScale|
- |chineseRemainder| |qroot| |LowTriBddDenomInv| |octon| |f04arf|
- |unrankImproperPartitions0| |resultant| |factor| |factorSquareFree|
- |s19aaf| |viewPhiDefault| |fortranCompilerName| |nextPrime| |check|
- |datalist| |fortranDoubleComplex| |categoryMode| |sqrt| |lowerCase!|
- |currentSubProgram| |schema| |getMultiplicationTable| |OMgetBind|
- |bubbleSort!| |eisensteinIrreducible?| |cCsc| |retractIfCan|
- |monomRDEsys| |stoseInvertible?| |qualifier| |addPoint2| |real|
- |leader| |OMputEndBind| |log2| |reopen!| |gcdPolynomial| |cSec|
- |supersub| |const| RF2UTS |antisymmetric?| |imag| |collectUnder|
- |generateIrredPoly| |polyRicDE| |stFunc1|
- |removeRedundantFactorsInPols| |nullSpace| |directProduct| |laguerre|
- |sturmSequence| |lazyGintegrate| |degree| |generator| |zCoord|
- |pseudoRemainder| |genus| |rightDivide| |factorOfDegree|
- |setTopPredicate| |top| |intcompBasis| |exptMod| |HenselLift|
- |explicitlyEmpty?| |zeroVector| |maxRowIndex| |internalIntegrate|
- |isImplies| |noLinearFactor?| |s17ahf| |continue| |c06fqf|
- |deleteRoutine!| |traverse| |contours| |brace| |setClipValue| |s14aaf|
- |primitivePart!| |removeCoshSq| |OMputString| |hdmpToDmp| |fprindINFO|
- |putColorInfo| |inHallBasis?| |leadingExponent| |destruct| |logGamma|
- |mainPrimitivePart| |totalLex| |OMgetVariable| |surface| |invmod|
- |splitDenominator| |divide| |getCurve| |mapUnivariateIfCan| |linSolve|
- |RemainderList| |void| |tubePoints| |branchPoint?|
- |lazyPseudoQuotient| |e02bcf| |companionBlocks| |setIntersection|
- |s19acf| |wholeRadix| |palglimint| |selectPolynomials|
- |reduceBasisAtInfinity| |pattern| |signAround| |rootBound| |host|
- |close!| |f02axf| |byteBuffer| |karatsubaOnce| |showClipRegion|
- |jvmStrict| |zeroSetSplit| |f02wef| |FormatRoman| |c06gsf| |inverse|
- |complement| |remainder| |primeFactor| |lazyPseudoRemainder| |setref|
- |rangePascalTriangle| |monomial| |setImagSteps| |eigenvalues|
- |setright!| |multiple?| |radPoly| |unprotectedRemoveRedundantFactors|
- |subHeight| |diagonal| |multivariate| |rectangularMatrix|
- |selectMultiDimensionalRoutines| |shiftRoots| |leftDivide| |increase|
- |PDESolve| |rightNorm| |f02adf| |optimize| |integralRepresents|
- |genericRightNorm| |hspace| |redpps| |variables| |cylindrical|
- |message| |cExp| |iilog| |SturmHabichtSequence| |symmetricPower|
- |stoseInvertible?sqfreg| |delta| |select!| |e04naf| |ListOfTerms|
- |monomials| |stosePrepareSubResAlgo| |s20adf|
- |exprHasLogarithmicWeights| |sin?| |linearMatrix| |isNot| |f02bjf|
- |nextItem| |cAcsc| |laurentIfCan| |removeSinSq| |conical| |external?|
- |f01ref| |edf2fi| |solveLinearPolynomialEquation| |critpOrder|
- |positiveSolve| |read!| |ScanArabic| |getButtonValue| |bivariate?|
- |e01sef| |loopPoints| |rightRegularRepresentation| |pdct| |graeffe|
- |getCode| |integralAtInfinity?| |outputAsScript| |internalIntegrate0|
- |polarCoordinates| |jvmSuper| |e04gcf| |hermite| |resetNew| |symFunc|
- |tableForDiscreteLogarithm| |singleFactorBound| |palgextint0|
- |mainVariables| |ip4Address| |taylor| |eigenMatrix| |asinhIfCan|
- |combineFeatureCompatibility| |nthExpon| |s13aaf| |sech2cosh|
- |readUInt16!| |makeprod| |intermediateResultsIF| |formula|
- |finiteBasis| |headAst| |rightRecip| |laurent| |squareFreeFactors|
- |multinomial| |measure2Result| |initiallyReduced?| |plusInfinity|
- |besselI| |tube| |B1solve| |inconsistent?| |simplifyPower|
- |purelyAlgebraicLeadingMonomial?| |factorSquareFreeByRecursion|
- |rationalIfCan| |puiseux| |identification| |mantissa| |makeSketch|
- |iflist2Result| |normalDenom| |minusInfinity| |mainMonomials|
- |matrixDimensions| |low| |pomopo!| |lambda| |nthExponent| |integrate|
- |systemCommand| |fractRagits| |symmetricSquare| |dflist|
- |getSyntaxFormsFromFile| |returns| |difference| |coerceL| |prime|
- |pointLists| |pop!| |inv| |setfirst!| |graphStates| |getlo| |wreath|
- |OMputEndApp| |harmonic| |indiceSubResultantEuclidean| |root?|
- |viewport2D| |unravel| |nrows| |ground?| |refine| |cSech|
- |userOrdered?| |equality| |schwerpunkt| |zag| |selectsecond|
- |aQuadratic| |bandedJacobian| |complexNumericIfCan| |ground| |isExpt|
- |ncols| |setEpilogue!| |errorInfo| |normal| |tanNa| |hostPlatform|
- |insertTop!| |empty| |drawComplexVectorField| |sortConstraints|
- |interpretString| |OMserve| |oblateSpheroidal| |distribute| |repSq|
- |minIndex| |leadingMonomial| |push| |type| |maxIndex| |simpson|
- |selectODEIVPRoutines| |updateStatus!| |nativeModuleExtension|
- |standardBasisOfCyclicSubmodule| |getIdentifier| |jordanAlgebra?|
- |reduction| |leadingCoefficient| |sec2cos| |modularGcdPrimitive|
- |stiffnessAndStabilityOfODEIF| |lllp| |logical?| |leadingSupport|
- |initTable!| |numFunEvals| |decrease| |hasPredicate?| |geometric|
- |makeop| |primitiveMonomials| |inverseIntegralMatrix| |c06ebf|
- |solveid| |exQuo| |lambert| |connectTo| |curve| |basisOfNucleus|
- |splitConstant| |precision| |youngGroup| |leftAlternative?| |reductum|
- |nand| |mapdiv| |mainCoefficients| |integralCoordinates|
- |stopMusserTrials| |morphism| |tracePowMod| |nextNormalPoly|
- |tanh2coth| |iiacoth| |s17ajf| |numberOfCycles|
- |functionIsOscillatory| |oneDimensionalArray| |opeval| |atoms| |norm|
- |rem| |extension| |numberOfChildren| |s17acf| |stoseInvertible?reg|
- |mainSquareFreePart| |fixedDivisor| |e02ahf| |antiCommutator|
- |environment| |sylvesterSequence| |nextSubsetGray| |quo|
- |differentialVariables| |queue| |removeSquaresIfCan| |tab| |char|
- |dot| |key| |radicalEigenvalues| |selectIntegrationRoutines| |aCubic|
- |linears| |selectSumOfSquaresRoutines| |lagrange| |elColumn2!|
- |cfirst| |cscIfCan| |truncate| |sort!| |fixedPointExquo| |s18aef|
- |aQuartic| |rationalPoints| |imagi| |div| |principal?| |lazyPquo|
- |rightTrace| |processTemplate| |separant| |filename| |var2Steps|
- |insertMatch| |fmecg| |ramifiedAtInfinity?| |jvmNative| |exquo|
- |lookupFunction| |bumprow| |clearTheIFTable| |mathieu12| |block|
- |selectOptimizationRoutines| |iiasinh| |arity| |numberOfOperations|
- |halfExtendedSubResultantGcd2| ~= |fglmIfCan| |oddInfiniteProduct|
- |systemSizeIF| |scan| |hermiteH| |parse| |alphanumeric?| |central?|
- |positiveRemainder| |structuralConstants| |nextIrreduciblePoly|
- |jvmUTF8ConstantTag| |#| |basisOfLeftNucloid| |associatorDependence|
- |dictionary| |OMputInteger| |torsionIfCan| |c06gqf| |screenResolution|
- |changeWeightLevel| |lazyPremWithDefault| |subQuasiComponent?| ~
- |leftMinimalPolynomial| |fortranInteger| |limit| |expandLog|
- |diagonal?| |float| |keys| |element?| |comparison| |redmat| |eulerE|
- |generalInfiniteProduct| |complexRoots| |fortranLiteral| |top!|
- |figureUnits| |cAsec| |applyRules| |search| |conjugate| |delete!|
- |leftRemainder| |leftUnit| |physicalLength!| |rational?| UTS2UP
- |d01anf| |setlast!| |s17dlf| |attributeData| |in?| |unit?|
- |elseBranch| |strongGenerators| |twist| |e01bgf| |/\\| |iiatanh|
- |linearAssociatedLog| |leftFactor| |currentScope| |front|
- |sumOfKthPowerDivisors| |fortran| |f2df| |addPointLast| |makeSeries|
- |elements| |any| |\\/| |outputFloating| |testDim| |skewSFunction|
- |jvmInterfaceMethodConstantTag| |curveColor| |f01brf| |setCondition!|
- |reduced?| |pile| |subResultantGcd| |rombergo| |OMopenString| |po|
- |midpoints| |bottom!| |depth| |internalSubPolSet?| |getMeasure|
- |pseudoQuotient| |reducedQPowers| |Beta| |id| |routines| |mvar|
- |fortranLinkerArgs| |besselK| |getConstant| |matrixGcd| |rightPower|
- |relativeApprox| |heap| |zeroMatrix| |dom| |identity| |lo| |parent|
- |OMputVariable| |monomRDE| |gcdprim| |idealiserMatrix| |outputMeasure|
- |unitNormalize| |inRadical?| |commutator| |closed| |order|
- |paraboloidal| |mathieu23| |positive?| GE |bright| |rroot|
- |deepestInitial| |f02aaf| |squareFreePolynomial| |convert| |rotatez|
- |iiasech| |collectUpper| |stoseInvertibleSetreg| GT |viewZoomDefault|
- |graphCurves| |safeCeiling| |e04fdf| |iiacos| |collectQuasiMonic|
- |createNormalPoly| |normalizedAssociate| |character?| |perspective|
- |basisOfCenter| LE |e02def| |cCosh| |index?| |eval| |badNum|
- |multiplyExponents| |digit| |pascalTriangle| |listexp|
- |coercePreimagesImages| |solveLinearPolynomialEquationByRecursion| LT
- |mainExpression| |elaborateFile| |dihedral| |doubleFloatFormat|
- |finiteBound| |interpret| |title| |hyperelliptic| |numFunEvals3D|
- |rightRemainder| |qelt| |pmintegrate| |signature| |integral?|
- |setUnion| |redPol| |leadingIndex| |reindex| |createIrreduciblePoly|
- |upperCase?| |smith| |qsetelt| |rightQuotient| |d01fcf| |error|
- |identitySquareMatrix| |toseInvertible?| |OMreadStr| |unexpand|
- |factorGroebnerBasis| |mainMonomial| |integerBound| |sinhcosh|
- |gradient| |xRange| |unit| |OMgetObject| |car| |roughBasicSet|
- |tubePointsDefault| |e| |subscriptedVariables| |reseed| |tubeRadius|
- |lyndon| |genericLeftTraceForm| |yRange| |f02akf| |script| |irDef|
- |rationalFunction| |f04jgf| |less?| |createMultiplicationMatrix|
- |latex| |zRange| |airyBi| |trapezoidalo|
- |solveLinearPolynomialEquationByFractions| |wordInStrongGenerators|
- |tryFunctionalDecomposition?| |splitNodeOf!| |homogeneous?| |e02bdf|
- |isAnd| |tan2cot| |critMonD1| |map!| |s15adf| |patternVariable|
- |push!| |c06gbf| |cyclic?| |associatedSystem| |split| |bandedHessian|
- |youngDiagram| |qsetelt!| |padecf| |d01alf| |OMputFloat|
- |OMsupportsCD?| |tex| |mapExponents| |vconcat| |parametric?|
- |quotient| |ScanFloatIgnoreSpacesIfCan| |d02ejf| |shallowExpand|
- |size?| |singularitiesOf| |screenResolution3D| |lazyIntegrate|
- |pointPlot| |reverse!| |solveInField| |leftCharacteristicPolynomial|
- |plotPolar| |iicsc| |minimize| |groebnerIdeal| |coordinate|
- |exponentialOrder| |e04dgf| |factorials| |exponents|
- |numberOfIrreduciblePoly| |squareFreePrim| |showScalarValues|
- |constantCoefficientRicDE| |repeatUntilLoop| |limitedIntegrate|
- |adjoint| |startTable!| |useNagFunctions| |rk4f| |presub| |typeLists|
- |length| |d01aqf| |triangularSystems| |leviCivitaSymbol|
- |cRationalPower| |cup| |rightTraceMatrix| |ScanFloatIgnoreSpaces|
- |unaryFunction| |scripts| |d03faf| |acsch| |squareFreeLexTriangular|
- |eq| |iisec| |trigs| |halfExtendedResultant2| |coordinates|
- |setLegalFortranSourceExtensions| |radicalEigenvector| |orbit|
- |closedCurve| |leftRank| |cond| |conditionsForIdempotents| |retract|
- |iter| |f01rcf| |OMencodingXML| |setPredicates|
- |characteristicPolynomial| |addMatch| |semiResultantEuclidean1|
- |noKaratsuba| |asechIfCan| |twoFactor| |setButtonValue| |trapezoidal|
- |crushedSet| |generators| |headReduce| |denominator| |quoByVar|
- |chvar| |times!| |purelyAlgebraic?| |quasiComponent| |byte|
- |startTableGcd!| |scalarTypeOf| |completeSmith| |jvmSynchronized|
- |rst| |flatten| |complementaryBasis| |rightUnit| |iifact| |getRef|
- |removeDuplicates!| |parabolicCylindrical| |jvmFieldrefConstantTag|
- |resultantnaif| |isPower| |diagonalMatrix| |factorPolynomial|
- |setvalue!| |cAsech| |messagePrint| |components| |associatedEquations|
- |exists?| |unitVector| |substring?| |removeSinhSq| |BumInSepFFE|
- |e02agf| |viewWriteAvailable| |makeTerm| |rCoord| |cAcos| |substitute|
- |leftQuotient| |problemPoints| |expenseOfEvaluation|
- |variationOfParameters| |compose| |duplicates| |s21bcf|
- |genericLeftDiscriminant| |prepareSubResAlgo| |subst| |subscript|
- |gethi| |dimensionOfIrreducibleRepresentation| |computeBasis| |exp|
- |xn| |setEmpty!| |suffix?| |complexElementary| |composites|
- |halfExtendedResultant1| |normalForm| |myDegree| |addBadValue|
- |makeEq| |frobenius| |derivative| |hessian| |setRow!| |factors|
- |recoverAfterFail| |setLength!| |inf| |rightMinimalPolynomial|
- |primintegrate| |shade| |SFunction| |supDimElseRittWu?| |map|
- |setTex!| |writeBytes!| |vspace| |prefix?| |printingInfo?|
- |putProperties| |pquo| |inverseLaplace| |stripCommentsAndBlanks|
- |useSingleFactorBound| |padicFraction|
- |removeRedundantFactorsInContents| |int| |squareFreePart| |lyndon?|
- |setClosed| |createPrimitivePoly| |optAttributes| |sinh2csch|
- |elliptic?| |traceMatrix| |d02bhf| |vedf2vef| |evenInfiniteProduct|
- |minimumDegree| |rootOf| |objects| |closeComponent| |cyclicGroup|
- |makeFloatFunction| |negative?| |symbol?| |simplify| |outputGeneral|
- |exteriorDifferential| |leftNorm| |normalElement| |mappingMode| |base|
- |internalDecompose| |scopes| |createPrimitiveElement| |conjug|
- |s15aef| |lhs| |makeGraphImage| |critM| |swapRows!| |e01daf| |submod|
- |rischDE| |splitLinear| |mkPrim| |constantRight|
- |wordsForStrongGenerators| |rhs| |pointData| |double?| |hexDigit|
- |LazardQuotient2| |getMultiplicationMatrix| |insertionSort!|
- |jvmClassConstantTag| |polyRDE| |rangeIsFinite| |isOr| |setMaxPoints|
- |exprHasAlgebraicWeight| |acothIfCan| |minordet| |infix?|
- |ParCondList| |part?| |rationalPoint?| |mergeFactors| |rowEchLocal|
- |removeIrreducibleRedundantFactors| |debug3D| |width| |ricDsolve|
- |tubePlot| |padicallyExpand| |interReduce| |prem| |mask|
- |expintfldpoly| |lfintegrate| |explicitlyFinite?| |viewThetaDefault|
- |subResultantGcdEuclidean| |linearPolynomials| |infRittWu?| |concat|
- |se2rfi| |BasicMethod| |characteristicSet| |jvmInterface|
- |OMputEndObject| |sqfrFactor| |shiftRight| |ignore?| |lowerPolynomial|
- |cTan| |number?| |atrapezoidal| |OMsetEncoding| |iisinh| |empty?|
- |makeViewport2D| LODO2FUN |unitsColorDefault| |charClass| |Si|
- |modulus| |antisymmetricTensors| |binarySearchTree| |nil?|
- |conjunction| |symbolTableOf| |findConstructor| |pleskenSplit|
- |colorDef| |fortranDouble| |sequences| |lastSubResultantElseSplit|
- |table| |stop| |rightFactorIfCan| |acscIfCan| |extendIfCan|
- |factorsOfCyclicGroupSize| |f01qef| |obj| |integralMatrixAtInfinity|
- |quasiRegular| |solve1| |patternMatchTimes| |maxPoints| |new|
- |outputSpacing| |OMgetEndObject| |shallowCopy| |viewSizeDefault|
- |graphImage| |dim| |ravel| |cache| |Nul| |pushucoef|
- |jvmNameAndTypeConstantTag| |exponent| |product|
- |LagrangeInterpolation| |phiCoord| |autoReduced?| |permutations|
- |setScreenResolution3D| |reshape| |airyAi| |endSubProgram| |Is|
- |setStatus| |chebyshevU| |previous| |multisect| |getExplanations|
- |setVariableOrder| |palginfieldint| |semiResultantEuclidean2|
- |UnVectorise| |simpsono| |iroot| |composite| |seriesToOutputForm|
- |critBonD| |jacobi| |augment| |basisOfLeftAnnihilator|
- |showTheIFTable| |cyclotomicFactorization|
- |createLowComplexityNormalBasis| |maxrank| |euclideanGroebner|
- |s19adf| |rowEch| |toseInvertibleSet| |numberOfVariables| |tab1|
- |mulmod| |prevPrime| |degreePartition| |critB| |stopTable!| |equiv|
- |sample| |leastMonomial| |lineColorDefault| |commutativeEquality|
- |firstUncouplingMatrix| |OMgetBVar| |halfExtendedSubResultantGcd1|
- |rootRadius| |genericRightMinimalPolynomial| |knownInfBasis|
- |numberOfDivisors| |extend| |clearCache| |iiacosh| |basis| |s18acf|
- |rowEchelon| |bounds| |badValues| |c05nbf| |cyclotomic| |update|
- |makeUnit| |lazyPrem| |listYoungTableaus| |spherical| |style|
- |nthFlag| |interval| |idealSimplify| |setMinPoints|
- |rewriteIdealWithQuasiMonicGenerators| |vertConcat| |ddFact| |largest|
- |tail| |normalized?| |laguerreL| |doubleResultant| |round|
- |allRootsOf| |gderiv| |failed?| |lazyIrreducibleFactors| |failed|
- |highCommonTerms| |zeroDim?| |s17def| |magnitude| |digits| |left|
- |jvmStringConstantTag| |rootSplit| |subspace| |groebnerFactorize|
- |f01qcf| |divisor| |unknown| |writeLine!| |log| |squareTop|
- |outputForm| |iidsum| |right| |enterInCache| |rootProduct|
- |multiplyCoefficients| |showIntensityFunctions|
- |degreeSubResultantEuclidean| |nil| |denomLODE| |pointSizeDefault|
- |lowerCase| |coefficients| |OMputEndError| |roughUnitIdeal?|
- |distdfact| |callForm?| |alphanumeric| |fixedPoints| |leftPower|
- |trunc| |position| |hex| |printTypes| |prepareDecompose| |stirling2|
- |critT| |setleaves!| |acotIfCan| |mergeDifference| |integers| |cCos|
- |OMreceive| |s17aff| |isAtom| |meshPar2Var| |hasTopPredicate?| |tree|
- |resize| |inverseIntegralMatrixAtInfinity| |readInt16!| |e02bef|
- |s18dcf| |approximate| |SturmHabichtCoefficients| |decomposeFunc|
- |bringDown| |subNode?| |setScreenResolution| |linkToFortran|
- |bivariatePolynomials| |OMlistSymbols| |writeByte!| |htrigs| |second|
- |complex| |expr| |d02gaf| |removeRoughlyRedundantFactorsInContents|
- |makeMulti| |middle| |makeVariable| |permutation| |satisfy?|
- |torsion?| |primPartElseUnitCanonical!| |quartic| |third| SEGMENT
- |ceiling| |addiag| |elRow1!| |computePowers| |setFormula!| |units|
- |droot| |jacobiIdentity?| |extractTop!| |iiacsc| |li| |divergence|
- |singular?| |quasiRegular?| |notelem| |d01apf| |argscript|
- |extractIndex| |zeroSquareMatrix| |symmetricTensors| |fracPart|
- |stoseIntegralLastSubResultant| |rischNormalize| |OMencodingUnknown|
- |rightRankPolynomial| |rotate| |univariatePolynomialsGcds| |is?|
- |functionIsFracPolynomial?| |e04jaf| |doubleRank| |scaleRoots|
- |variable| |leftReducedSystem| |leftExactQuotient| |readBytes!|
- |principalIdeal| |constantOperator| |reducedContinuedFraction|
- |singularAtInfinity?| |clearFortranOutputStack| |bitCoef| |d01amf|
- |numeric| |copy| |iterators| |swap| |besselY| |df2ef| |sqfree|
- |parabolic| |radical| |changeBase| |lexTriangular| |mindegTerm|
- |zeroSetSplitIntoTriangularSystems| |dimensions| |bipolarCylindrical|
- |expenseOfEvaluationIF| |showTheFTable| |LyndonWordsList1| |code|
- |paren| |inspect| |setAdaptive| |removeRedundantFactors|
- |partialQuotients| |commutative?| |putProperty| |jvmStatic|
- |linearAssociatedOrder| |f01mcf| |dmpToP| |relerror|
- |encodingDirectory| |optional?| |normFactors| |integer?| |subNodeOf?|
- |delay| |mapUp!| |iiabs| |doublyTransitive?| |equation|
- |clipPointsDefault| |adaptive3D?| |startPolynomial| |upperCase|
- |hasSolution?| |setValue!| |extractSplittingLeaf| |bat1|
- |sumOfSquares| |realRoots| |pureLex| |ranges| |resultantEuclideannaif|
- |autoCoerce| |test| |primextendedint| |consnewpol| |quadraticNorm|
- |match?| |numericalOptimization| |scanOneDimSubspaces|
- |withPredicates| |invmultisect| |lazy?| |primextintfrac| |logIfCan|
- |radicalEigenvectors| |lp| |OMReadError?| |monicLeftDivide|
- |littleEndian| |rquo| |cschIfCan| |unparse| |d02raf| |rischDEsys|
- |incr| |reify| |LazardQuotient| |xCoord| |pushNewContour|
- |permutationGroup| |next| |mapUnivariate| |shape| |irreducibleFactor|
- |hi| |lieAlgebra?| |point?| |sts2stst| |ffactor| |jvmTransient|
- |minColIndex| |integralMatrix| |d01asf| |numberOfHues| |coerceP|
- |domainTemplate| |branchPointAtInfinity?| |subResultantsChain|
- |totalDegree| |jvmPublic| |upDateBranches| |nextNormalPrimitivePoly|
- |prefix| |sechIfCan| |radicalRoots| |arguments| |minus!| |thetaCoord|
- |isEquiv| |unitCanonical| |tanh2trigh| |coleman| |firstNumer| **
- |viewport3D| |double| |invertIfCan| |stronglyReduced?|
- |deleteProperty!| |extendedIntegrate| |var2StepsDefault|
- |complexIntegrate| |even?| |makeCrit| |position!| |trigs2explogs|
- |name| |setDifference| |belong?| |whatInfinity|
- |removeRoughlyRedundantFactorsInPol| |Gamma| |level| |pushup|
- |collect| |body| |status| |iiacot| |coerceS| |value|
- |numberOfFractionalTerms| |bytes| |argumentListOf|
- |jvmDoubleConstantTag| |nary?| |tanAn| |cLog| |lyndonIfCan| |presuper|
- |rdHack1| |clipParametric| |virtualDegree| |credPol| |outputList|
- |complexZeros| |zerosOf| |polCase| |c06eaf| |enumerate| |curry|
- |s18adf| |alternating| |iiasin| |groebgen| |prinshINFO| |aromberg|
- |extractIfCan| |ellipticCylindrical| |pushdterm| |nothing| |e02ajf|
- |mapCoef| |nextPartition| |elem?| |jvmLongConstantTag| |declare!|
- |generic| |cSin| |karatsubaDivide| |arbitrary| |fillPascalTriangle|
- |stopTableGcd!| |numberOfImproperPartitions| |sn| |palgLODE0|
- |mkAnswer| |predicates| |parseString| |generate| |rightAlternative?|
- |e04mbf| |compBound| |realEigenvectors| |quasiMonic?|
- |validExponential| |horizConcat| |symmetricGroup| |apply| |bag|
- |iisqrt3| |var1Steps| |generic?| |weakBiRank| |uniform01|
- |linearAssociatedExp| |port| |getPickedPoints| |incrementBy| |first|
- |exprToGenUPS| |nullary| |polygamma| |tanSum| |fibonacci| |reorder|
- |just| |univariateSolve| |rest| |expand| |constantLeft| |exponential|
- |leftRegularRepresentation| |buildSyntax| |perfectNthPower?|
- |numerators| |innerEigenvectors| |normalizedDivide| |compile| |t|
- |inputOutputBinaryFile| |filterWhile| |printInfo| |retractable?|
- |tableau| |entry?| |rotate!| |polyPart| |support|
- |generalizedEigenvector| |shuffle| |jvmMethodrefConstantTag|
- |filterUntil| |cycleElt| |cyclicCopy| |elementary| |setOfMinN| |lllip|
- |segment| |subresultantSequence| |selectNonFiniteRoutines| |child|
- |readUInt32!| |select| |groebSolve| |intersect| |iiasec| |chiSquare1|
- |clikeUniv| |nextLatticePermutation| |summation| |null?|
- |zeroDimensional?| |linearlyDependent?| |cycleTail| |mainKernel|
- |legendreP| |realElementary| |weight| |semiSubResultantGcdEuclidean1|
- |asecIfCan| |ReduceOrder| |startStats!| |readUInt8!| |diff|
- |euclideanSize| |jvmAbstract| |module| |assert| |quadratic|
- |safeFloor| |separate| |accuracyIF| |associates?| |OMgetFloat|
- |lifting| |probablyZeroDim?| |evenlambert| |f2st| |radicalSimplify|
- |palgRDE0| |e04ucf| |commaSeparate| |insert| |psolve| |ref| |iicoth|
- |f02awf| |transcendenceDegree| |lookup| |maxdeg| |f01rdf| |mapmult|
- |nilFactor| |reduceLODE| |overbar| |ODESolve|
- |stoseInternalLastSubResultant| |cycleSplit!| |diagonalProduct|
- |linearForm| |besselJ| |acoshIfCan| |makeRecord| |trace2PowMod|
- |f04atf| |space| |modifyPoint| |stirling1| |sylvesterMatrix|
- |indicialEquation| |fintegrate| |useEisensteinCriterion?| |true|
- |LyndonBasis| |node?| |LiePoly| |remove!| |fractRadix|
- |possiblyNewVariety?| |alphabetic| |ord| |binaryFunction| |hash|
- |unary?| |semiDegreeSubResultantEuclidean| |prinb| |isOpen?| |tower|
- |newReduc| |printInfo!| |integralBasisAtInfinity| |setsubMatrix!|
- |setleft!| |count| |fixedPoint| |commonDenominator|
- |genericLeftMinimalPolynomial| |gramschmidt| |uniform| |iisech|
- |stiffnessAndStabilityFactor| |float?| |ocf2ocdf| |irreducible?|
- |taylorIfCan| |explogs2trigs| |fixPredicate| |power!| |rarrow| |imagJ|
- |bumptab1| |localAbs| |hypergeometric0F1| |freeOf?| |isMult| |llprop|
- |partialFraction| |initial| |lflimitedint| |key?| |fortranTypeOf|
- |moebius| |brillhartIrreducible?| |preprocess| |showRegion|
- |constant?| |primlimitedint| |minPol| |meshFun2Var| |nodes|
- |makeResult| |goto| |generalSqFr| |d01bbf| |changeMeasure|
- |complexNumeric| |rational| |cyclicEqual?| |center|
- |topFortranOutputStack| |internalLastSubResultant| |areEquivalent?|
- |exportedOperators| |compound?| |conditionP| |infLex?|
- |monomialIntegrate| |realZeros| |leftExtendedGcd| |listRepresentation|
- |odd?| |saturate| |cycleEntry| |representationType| |powern| |kernels|
- |e01saf| |macroExpand| |numericalIntegration| |pointColor| |hclf|
- |cTanh| |bezoutDiscriminant| |member?| |rightLcm| |mainForm|
- |heapSort| |operator| |superscript| |musserTrials| |OMgetType|
- |decreasePrecision| |anfactor| |backOldPos| |printStats!|
- |clearTable!| |defineProperty| |factorial| |mathieu22| |kind| |sh|
- |minimumExponent| |f04mcf| |point| |pr2dmp| |list?| |monicRightDivide|
- |varList| |univariate| |graphs| |arg1| |approximants|
- |resultantReduitEuclidean| |rightDiscriminant| |op| |dark|
- |setPosition| |rdregime| |continuedFraction| |branchIfCan| |e02akf|
- |arg2| |f02ajf| |any?| |plus!| |unrankImproperPartitions1|
- |physicalLength| |getOperands| |normInvertible?| |intensity|
- |goodnessOfFit| |interpolate| |dioSolve| |leftOne| |midpoint|
- |sdf2lst| |leadingIdeal| |series| |dominantTerm| |mapDown!|
- |Frobenius| |erf| |s17agf| |conditions| |powers| |d02cjf| |putGraph|
- |testModulus| |partialDenominators| |axes| |complexSolve| |lfunc|
- |open?| |match| |characteristicSerie| |reflect| |triangulate| |OMsend|
- |var1StepsDefault| |declare| |extractBottom!| |fortranLiteralLine|
- |makeSin| |replaceKthElement| |createGenericMatrix| |invertibleSet|
- |normalizeAtInfinity| |normalize| |minPoints| |palgRDE| |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| |f01bsf| |f04maf| |convert| |OMputEndObject|
+ |denomLODE| |evaluateInverse| |cache| |generalizedEigenvectors|
+ |realZeros| |summation| |fortranLogical| |zeroDim?| |polyred|
+ |makeCrit| |round| |OMReadError?| |representationType| |cAsec|
+ |debug3D| |quotient| |mainVariables| |infinite?| |subResultantChain|
+ |decreasePrecision| |invmod| |makeCos| |startTableInvSet!|
+ |convergents| |badNum| |createIrreduciblePoly| |xCoord| |doubleRank|
+ |iisqrt2| |qPot| |f02bjf| |copy!| |float| |integrate|
+ |semiSubResultantGcdEuclidean2| |quasiMonic?| |aQuadratic|
+ |padicFraction| |trunc| |traceMatrix| |rightDiscriminant| |f04mbf|
+ |symmetricPower| |writeLine!| |binaryTournament| |SFunction|
+ |readBytes!| |normalized?| |removeDuplicates| |primlimintfrac| |droot|
+ |OMopenFile| |countRealRootsMultiple| |iiacos| |randomLC|
+ |alternating| |voidMode| |cyclic| |continuedFraction| |solid| |isOp|
+ |lifting| |rename| |factorsOfCyclicGroupSize| |f02bbf| |jvmPublic|
+ |perfectSquare?| |complexEigenvectors| |incrementKthElement|
+ |associatorDependence| |factorSquareFreePolynomial|
+ |getMultiplicationTable| |factor1| |numberOfFactors| |string?|
+ |prologue| |incr| |shift| |macroExpand| |squareTop| |infieldIntegrate|
+ |acotIfCan| |checkRur| |triangular?| |logpart| |OMgetObject|
+ |eigenvectors| |janko2| |ParCond| |hi| |trace2PowMod| |e04gcf| UP2UTS
+ |bright| |mainVariable?| |tan2trig| |e01bff| |points| |e02ajf|
+ |normalize| |functorData| |tanIfCan| |constDsolve| |isOpen?|
+ |ListOfTerms| |enumerate| |hexDigit| |iifact| |factorset|
+ |numberOfImproperPartitions| |curveColorPalette| |oblateSpheroidal|
+ |asechIfCan| |primes| |eval| |reducedDiscriminant|
+ |integralLastSubResultant| |createLowComplexityNormalBasis|
+ |jvmDoubleConstantTag| |f02abf| |fill!| GE |mapGen| |f02akf| |extend|
+ |byteBuffer| |contains?| |leftScalarTimes!| |head|
+ |mapUnivariateIfCan| |expr| |numer| |lift| GT |OMputError|
+ |univariatePolynomialsGcds| |prefixRagits| |iflist2Result|
+ |unrankImproperPartitions0| |mapBivariate| |clipWithRanges|
+ |functionIsContinuousAtEndPoints| |normFactors| |hasPredicate?| LE
+ |eq| |denom| |reduce| |OMputVariable| |getDatabase| |currentScope|
+ |cot2tan| |iisec| |setVariableOrder| |setFieldInfo| |clearTheFTable|
+ |e02daf| |tValues| |iter| |c06fqf| |push!| |complexElementary| LT
+ |internalSubQuasiComponent?| |jvmClassConstantTag| |isConnected?|
+ |tryFunctionalDecomposition| |negative?| |insertTop!|
+ |createMultiplicationMatrix| |pi| |call| |subscript| |problemPoints|
+ |leftUnit| |zeroOf| EQ |simpson| |associatedSystem| |fixedDivisor|
+ |hostByteOrder| |epilogue| |variable| |infinity| |testDim|
+ |explicitlyFinite?| |derivationCoordinates| |direction|
+ |generalizedContinuumHypothesisAssumed| |say| |pquo| |monomRDEsys|
+ |characteristicSet| |f02aaf| |intensity| |iterators| |sumOfSquares|
+ |printTypes| |pascalTriangle| |subresultantSequence| |schwerpunkt|
+ |insert| |numberOfComponents| |perfectSqrt| |quotientByP| |decompose|
+ |perspective| |e04mbf| |compound?| |checkForZero| |reflect|
+ |mathieu22| |numberOfFractionalTerms| |listConjugateBases| |s19aaf|
+ |mapCoef| |totalGroebner| |kernel| |OMwrite| |asinIfCan| |minPoly|
+ |ode2| |solve| |wordInStrongGenerators| |content| |changeWeightLevel|
+ |height| |outputFixed| |adaptive| |exp| |multinomial| |list|
+ |setErrorBound| |lastSubResultant| |leftMult| |squareFreePrim| |size|
+ |generate| |readLineIfCan!| |purelyAlgebraicLeadingMonomial?|
+ |mindegTerm| |branchPointAtInfinity?| |maxColIndex| |draw| |unit|
+ |getVariableOrder| |e02zaf| |mathieu23| |totalDifferential|
+ |currentEnv| |signature| |dominantTerm| |createGenericMatrix|
+ |complexNormalize| |completeEval| |minimize| |notelem| |blue| |gethi|
+ |meshPar2Var| |f04faf| |diagonals| |palgRDE0| |listYoungTableaus|
+ |subHeight| |removeRoughlyRedundantFactorsInPols| |retractable?|
+ |addPoint| |groebner| |separate| |reduction| |flagFactor|
+ |principalAncestors| |hdmpToP| |normal?| |stoseLastSubResultant|
+ |byte| |localAbs| |headReduced?| |topFortranOutputStack| |d02raf|
+ |generateIrredPoly| |OMputFloat| |pastel| |superscript|
+ |highCommonTerms| |sumOfDivisors| |makeObject| |setProperty|
+ |genericLeftMinimalPolynomial| |lfextendedint| |initiallyReduce|
+ |createMultiplicationTable| |irreducible?| |over| |hyperelliptic|
+ |numberOfCycles| |cTan| |hue| |coef| |powerSum| |parent| |elaborate|
+ |addMatchRestricted| |getOperator| |rootSplit| |specialTrigs|
+ |categoryFrame| |df2ef| |binary| |incrementBy| |e04jaf| |writeInt8!|
+ |monicCompleteDecompose| |nextIrreduciblePoly| |scalarTypeOf| |d01alf|
+ |quoByVar| |subtractIfCan| |putProperties| |lquo| |PollardSmallFactor|
+ |c02aff| |expand| |resultantReduitEuclidean| |polyRicDE|
+ |removeCoshSq| |c06fuf| |errorInfo| |viewport2D| |qqq| |biRank|
+ |elColumn2!| |coefficients| |makeViewport2D| |explicitEntries?|
+ |filterWhile| |integralCoordinates| |cdr| |sylvesterSequence| |trim|
+ |sturmVariationsOf| |viewWriteDefault| |dequeue|
+ |antisymmetricTensors| |dflist| |jvmFinal| |filterUntil|
+ |evenInfiniteProduct| |mapUnivariate| |reverseLex| |powmod|
+ |monicDecomposeIfCan| |kernels| |sech2cosh| |cartesian|
+ |collectQuasiMonic| |zeroSquareMatrix| |lfunc|
+ |combineFeatureCompatibility| |select| |int| |iidprod| |upperCase!|
+ |gcdPolynomial| |internalSubPolSet?| |operator| |rightQuotient|
+ |positiveSolve| |forLoop| |c06ecf| |s21bcf| |firstNumer|
+ |sortConstraints| |adjoint| |getProperty| |Lazard| |unknownEndian|
+ |d01ajf| |sncndn| |e02adf| |subResultantGcdEuclidean| |mainExpression|
+ |innerSolve1| |tube| |fortranDoubleComplex| |exponential| |leastPower|
+ |univariate| |cond| |transcendenceDegree| |augment| |primitivePart|
+ |ReduceOrder| |makingStats?| |center| |bipolarCylindrical| |critM|
+ |radix| |semiDiscriminantEuclidean| |tail| |SturmHabichtCoefficients|
+ |integralMatrix| |binaryTree| |alternative?| |bits| |vectorise|
+ |factorsOfDegree| |startTable!| |univcase|
+ |rewriteIdealWithHeadRemainder| |lyndonIfCan| |nextsousResultant2|
+ |createPrimitivePoly| |partialFraction| |algSplitSimple|
+ |removeSinhSq| |directSum| |true| |primitivePart!| |setAdaptive3D|
+ |createThreeSpace| |factor| |fintegrate| |capacity| |submod|
+ |roughEqualIdeals?| |makeRecord| |getCurve| |initial|
+ |inverseIntegralMatrix| |patternVariable| |surface| |atanhIfCan|
+ |jvmLongConstantTag| |sqrt| |signAround| |presub| |rquo| |setEmpty!|
+ |tree| |unitNormal| |decomposeFunc| |scopes| |even?| |ScanArabic|
+ |real| |size?| |fi2df| |modularGcd| |OMgetFloat| |reindex| |transpose|
+ |fixPredicate| |subTriSet?| |imag| |cyclotomic| |identitySquareMatrix|
+ |putColorInfo| |innerEigenvectors| |fmecg| |permutation|
+ |leadingBasisTerm| |directProduct| |characteristic| |lieAlgebra?|
+ |infieldint| |iroot| |quasiRegular| |associatedEquations|
+ |linearMatrix| |fortranCharacter| |hitherPlane| |discreteLog| |closed|
+ |c06gsf| |cyclicEntries| |indicialEquationAtInfinity|
+ |constantToUnaryFunction| |leadingSupport| |brace|
+ |selectMultiDimensionalRoutines| |commutative?| |f04mcf|
+ |fortranLiteralLine| |floor| |double?| |genericLeftTrace| |jvmStrict|
+ |linearlyDependent?| |destruct| |reducedQPowers| |cCot|
+ |argumentListOf| |stopTableGcd!| |minordet| |cAcosh| |cCsc| |lazyPrem|
+ |iomode| |exprToGenUPS| |nthFlag| |meshPar1Var| |unexpand| |colorDef|
+ |frst| |mesh| |resultantReduit| |logIfCan| |expint| |basis|
+ |cyclotomicFactorization| |gderiv| |safetyMargin| |makeprod| |cyclic?|
+ |fullDisplay| |failed| |bumptab1| |ran| |basisOfLeftNucleus| |lhs|
+ |monomial| |determinant| |finiteBound| |csc2sin| |identity|
+ |thenBranch| |options| |copyInto!| |jvmProtected| |rhs| |range|
+ |simplifyLog| |systemSizeIF| |multivariate| |ScanRoman| |mix|
+ |hessian| |resize| |removeSinSq| |safeFloor| |s21bdf|
+ |exponentialOrder| |variables| |rk4| |setClosed| |printInfo|
+ |exportedOperators| |identityMatrix| |nil| |width| |commonDenominator|
+ |iiacoth| |explogs2trigs| |listLoops| |littleEndian|
+ |screenResolution| |string| |unvectorise| |approxNthRoot| |connectTo|
+ |OMmakeConn| |setTex!| |insertBottom!| |lowerCase|
+ |numberOfOperations| |rewriteSetByReducingWithParticularGenerators|
+ |interReduce| |log| |nil?| |rangePascalTriangle| |unparse|
+ |endSubProgram| |d02bbf| |e01daf| |insertMatch| |cyclePartition| |po|
+ |approximate| |space| |associator| |OMencodingBinary| |delay|
+ |complexSolve| |leftFactor| |df2st| |imagJ| |complex| |OMclose|
+ |structuralConstants| |showClipRegion| |taylor| |makeFloatFunction|
+ |OMParseError?| |jvmFloatConstantTag| |d02kef| |numberOfHues|
+ |constructor| |removeConstantTerm| |linearForm| |heapSort| |expt|
+ |shallowExpand| |laurent| |inc| |rightTrim| |maxIndex| |removeCosSq|
+ |userOrdered?| |zoom| |variable?| |numberOfPrimitivePoly| |status|
+ |expandPower| |elem?| |li| |puiseux| |reset| |curryRight| |leftTrim|
+ |minimumExponent| |cos2sec| |coerceS| |pseudoQuotient|
+ |genericRightDiscriminant| |optional| |paraboloidal| |jacobiIdentity?|
+ |c05nbf| |keys| |noncommutativeJordanAlgebra?| |OMgetApp| |adaptive?|
+ |iFTable| |standardBasisOfCyclicSubmodule| |setPrologue!| |root|
+ |iicosh| |complexIntegrate| |leftTrace| |inv| |write| |stack|
+ |euclideanSize| |removeZeroes| |FormatRoman| |unitVector| |multMonom|
+ |uniform01| |compdegd| |lexGroebner| |d03eef| |save| |ground?|
+ |patternMatch| |factorSquareFree| |linearPart| |d01gbf| |curve|
+ |constant?| |bfEntry| |jvmStatic| |subNodeOf?| |ground| |empty?|
+ |monomial?| |unaryFunction| |mathieu24| |leftDiscriminant|
+ |pmintegrate| |mkIntegral| |f2df| |allRootsOf| |internalIntegrate0|
+ |leadingMonomial| |rangeIsFinite| |rk4f| |jordanAdmissible?|
+ |clearTheSymbolTable| |antiCommutative?| |increment| |cscIfCan|
+ |resetNew| |setEpilogue!| |e02agf| |leadingCoefficient| |subMatrix|
+ |dimension| |rowEchelon| |initiallyReduced?| |modulus|
+ |showArrayValues| |quasiRegular?| |carriageReturn| |leftQuotient|
+ |nodes| |primitiveMonomials| |reopen!| |times!| |asinhIfCan|
+ |makeYoungTableau| |left| |returnType!| |nand| |ipow| |dimensions|
+ |clikeUniv| |reductum| |iitanh| |radicalSimplify| |associates?| |norm|
+ |dAndcExp| |right| |rootOfIrreduciblePoly| |inrootof| |sin?| |e02def|
+ |stop| |solveid| |s21baf| |sumOfKthPowerDivisors| |numberOfComposites|
+ |f07fef| |mr| |factors| |createNormalElement| |shrinkable| |s18aef|
+ |outputList| |extendedint| |d01anf| |duplicates| |divideExponents|
+ |Nul| |useSingleFactorBound?| |indiceSubResultantEuclidean|
+ |startTableGcd!| |permanent| |partialQuotients| |nextPrimitivePoly|
+ |entry| |areEquivalent?| |scalarMatrix| |algintegrate| |comparison|
+ |before?| |attributeData| |baseRDE| |modularGcdPrimitive|
+ |jvmFieldrefConstantTag| |pointLists| |getPickedPoints|
+ |mainPrimitivePart| |primeFrobenius| |irCtor| |returnTypeOf|
+ |coordinate| |f02aef| |llprop| |nary?| |extractBottom!| |df2mf|
+ |f04adf| |raisePolynomial| |safeCeiling| |airyAi| |prefix| |cosIfCan|
+ |stoseInternalLastSubResultant| |lazyIrreducibleFactors| |low|
+ |setImagSteps| |leftGcd| |linears| |sinh2csch| |intChoose|
+ |euclideanNormalForm| |d01fcf| |Gamma| |trigs2explogs| |imagk|
+ |printingInfo?| |wordInGenerators| |logical?| |rightPower| |max|
+ |rightScalarTimes!| |OMputObject| |isAtom| |conjug| |csch2sinh| |bag|
+ |d02gbf| |rule| |constantLeft| |definingEquations| |normalise|
+ |d03edf| |basisOfCommutingElements| |yCoordinates| |idealiserMatrix|
+ |strongGenerators| BY |quadraticNorm| |qelt| |mesh?| |returns|
+ |e02bdf| |polygamma| |readInt32!| |An| |zeroMatrix| |simpsono|
+ |besselJ| |qsetelt| |fillPascalTriangle| |leadingIndex|
+ |sturmSequence| |pseudoDivide| |OMgetBVar| |absolutelyIrreducible?|
+ |nullSpace| |externalList| |viewThetaDefault| |symbol|
+ |triangularSystems| |xRange| |nor| |writeUInt8!| |gcdcofact|
+ |toseLastSubResultant| |algebraic?| |numerators| |symbolIfCan|
+ |squareMatrix| |HenselLift| F |expression| |sqfrFactor| |yRange|
+ |name| |realSolve| |npcoef| |OMreadStr| |testModulus| |primeFactor|
+ |setStatus!| |denominators| |c06frf| |integer| |zRange|
+ |normalizedAssociate| |body| |innerSolve| |minPoints|
+ |oddInfiniteProduct| |colorFunction| |rationalPower|
+ |LyndonCoordinates| |OMcloseConn| |map!| |leastMonomial|
+ |antiCommutator| |OMputApp| |invertIfCan| |cons| |datalist| |void|
+ |LyndonBasis| |diag| |shanksDiscLogAlgorithm| |readByte!| |qsetelt!|
+ |eigenMatrix| |ridHack1| |radicalSolve| |member?| NOT |cSin|
+ |denomRicDE| |ideal| |cCoth| |super| |UP2ifCan| |expenseOfEvaluation|
+ |quadratic| |hspace| OR |OMsupportsSymbol?| |tRange| |linefeed|
+ |powers| |eq?| |plotPolar| |noValueMode| |setelt!|
+ |rightCharacteristicPolynomial| AND |exprToXXP| |commutator|
+ |atanIfCan| |depth| |transcendentalDecompose| |radPoly| |delete!|
+ |mindeg| |fortranLiteral| |cAcsc| |indicialEquations| |rootsOf|
+ |integral| |swap| |inverseIntegralMatrixAtInfinity| |s14abf|
+ |OMputBind| |jvmIntegerConstantTag| |source| |iiabs| |mantissa|
+ |typeList| |supersub| |autoReduced?| |acsch| |s19acf| |getOperands|
+ |padicallyExpand| |terms| |parabolic| |fortranLinkerArgs| |roman|
+ |gramschmidt| |children| |ellipticCylindrical| |port| |overlabel|
+ |triangulate| |axesColorDefault| |calcRanges| |algint| |argumentList!|
+ |critMonD1| |torsion?| |LagrangeInterpolation| |positiveRemainder|
+ |semiResultantEuclideannaif| |stoseInvertibleSetsqfreg| |wreath|
+ |selectSumOfSquaresRoutines| |rCoord| |eulerE| UTS2UP |t| |tanh2trigh|
+ |reducedContinuedFraction| |sorted?| |monicRightFactorIfCan| |iicoth|
+ |separateFactors| |listBranches| |s17akf| |symbolTableOf| |bindings|
+ |encodingDirectory| |degreePartition| |rightRecip| |mathieu12|
+ |s17acf| |extendedEuclidean| |setLegalFortranSourceExtensions|
+ |sinhIfCan| |complementaryBasis| |sort!| |s17def| |myDegree|
+ |OMgetAtp| |enqueue!| |HermiteIntegrate| |c06fpf| |numberOfMonomials|
+ |LazardQuotient2| |common| |OMputEndAtp| |divideIfCan| |complete|
+ |deleteRoutine!| |nonSingularModel| * |iibinom| |radicalEigenvalues|
+ |differentialVariables| |semicolonSeparate| |ldf2vmf| |cycleEntry|
+ |Ei| |rischDEsys| |squareFreePart| |fprindINFO| |sechIfCan|
+ |idealSimplify| |mapmult| |key| |eigenvalues| |selectPolynomials|
+ |acscIfCan| |definingPolynomial| |rewriteIdealWithRemainder|
+ |primintegrate| |leftDivide| |hclf| |mergeDifference| |rootOf|
+ |exprHasAlgebraicWeight| |mainContent| |previous| |airyBi| =
+ |cotIfCan| |countRealRoots| |setClipValue| |clearTable!| |filename|
+ |numericalIntegration| |basisOfCentroid| |s13acf| |host| |hash|
+ |realEigenvalues| |sequences| |rightExactQuotient| |subset?| |euler|
+ |initials| |OMgetAttr| |interpolate| |count| < |category|
+ |eigenvector| |rotate!| |expandTrigProducts| |double| |medialSet|
+ |parse| |tableForDiscreteLogarithm| |mappingMode| |hMonic| > |domain|
+ |lazyResidueClass| |ode1| |minPol| |part?| |minimalPolynomial|
+ |showTheIFTable| |cyclicCopy| |characteristicPolynomial| <= |package|
+ |prinshINFO| |rk4qc| FG2F |LowTriBddDenomInv| |extractClosed|
+ |rightRank| |rightNorm| |outputMeasure| |OMencodingUnknown| >=
+ |hermiteH| |tubePointsDefault| |stirling1| |sinhcosh| |endOfFile?|
+ |leftRegularRepresentation| |matrixGcd| |fortranCarriageReturn|
+ |replace| |euclideanGroebner| |commutativeEquality| |curryLeft|
+ |distdfact| |integralBasisAtInfinity| |infRittWu?| |lex|
+ |splitSquarefree| |mvar| |exprToUPS| |generalLambert| |printHeader|
+ |leftTraceMatrix| |rational| |readUInt8!| + |fortranComplex| |stFuncN|
+ |headRemainder| |stoseInvertible?| |genericLeftNorm| |completeSmith|
+ |Hausdorff| |createZechTable| - |getlo| |fortranDouble| |infinityNorm|
+ |divergence| |declare!| |OMconnOutDevice| |irreducibleFactors| /
+ |sparsityIF| |currentCategoryFrame| |corrPoly| |pointColorDefault|
+ |knownInfBasis| |multiple?| |minus!| |aCubic| |symmetricRemainder|
+ |generic| |infiniteProduct| |dec| |edf2efi| |lSpaceBasis| |ptree|
+ |weight| |normalizeIfCan| |jvmNative| |changeThreshhold| |s19abf|
+ |leftZero| |axes| |integralAtInfinity?| |currentSubProgram|
+ |localReal?| |open| |redPo| |swapColumns!| |coHeight| |vertConcat|
+ |e04dgf| |dot| |index| |element?| |s17ajf| |bipolar| |viewSizeDefault|
+ |graphState| |cycle| |mainForm| |alphabetic| |unit?| |kind|
+ |linearAssociatedOrder| |palglimint| |cAcoth| |indiceSubResultant|
+ |genericRightTrace| |gcdprim| |s20adf| |integerBound| |rightUnits|
+ |generalizedContinuumHypothesisAssumed?| |mainKernel| |sample|
+ |rotatey| |op| |seriesToOutputForm| |monomialIntegrate| |OMUnknownCD?|
+ |randnum| |computeInt| |mainCharacterization| |segment|
+ |setButtonValue| |pair| |balancedBinaryTree| |push| |operations|
+ |btwFact| |makeTerm| |d02ejf| |maxrank| |bumptab| |fortranInteger|
+ |closedCurve| |isPower| |toseInvertible?| |nthExponent| |comment|
+ |padecf| |pile| |modifyPointData| |bezoutMatrix| |square?| |iiacot|
+ |unitCanonical| |copies| |prevPrime| |showAllElements| |complexForm|
+ |step| |prod| |graphStates| |reduceBasisAtInfinity| |lintgcd|
+ |interactiveEnv| |orthonormalBasis| |pr2dmp| |graphCurves| |trueEqual|
+ |digit?| |real?| |choosemon| |linearDependence|
+ |conditionsForIdempotents| |heap| |Aleph| |lfintegrate| |swap!|
+ |measure| |rewriteIdealWithQuasiMonicGenerators| |reverse!| |elRow2!|
+ |f04qaf| |vark| |setMaxPoints3D| |leftMinimalPolynomial| |curveColor|
+ |wronskianMatrix| |getConstant| |imagE| |bezoutDiscriminant|
+ |pointColor| |cAtanh| |c05pbf| |iicsch| |zero| |e02baf|
+ |fortranCompilerName| |disjunction| |rationalFunction|
+ |listRepresentation| |union| |symbolTable| |numberOfChildren|
+ |collectUpper| |inverseColeman| |laplacian| |newTypeLists|
+ |separateDegrees| |retract| |rightDivide| |dim| |saturate| |concat!|
+ |tubePlot| |rightFactorIfCan| |iisech| |rootSimp| |algDsolve|
+ |iteratedInitials| |select!| |And| |constantOperator| |index?|
+ |genericLeftTraceForm| |result| |physicalLength| |findBinding|
+ |pushFortranOutputStack| |setMaxPoints| |zeroVector|
+ |useSingleFactorBound| |internalIntegrate| |whitePoint| |tanintegrate|
+ |Or| |e01sbf| |popFortranOutputStack| |setvalue!| |d01amf| |root?|
+ |repSq| |antisymmetric?| |jordanAlgebra?| |rootProduct| |goto|
+ |entry?| |cCsch| |Not| |groebSolve| |imaginary| |makeMulti| |cubic|
+ |bitLength| |outputAsFortran| |degreeSubResultantEuclidean| |mapExpon|
+ |tensorProduct| |f02xef| |randomR| |midpoint| |pack!| |prime?|
+ |central?| |horizConcat| |squareFreeLexTriangular| |groebgen|
+ |nsqfree| |toseSquareFreePart| |nodeOf?|
+ |stoseIntegralLastSubResultant| |OMputEndAttr|
+ |semiResultantEuclidean2| |headAst| |resultantEuclidean| |cross|
+ |writeByte!| |scan| |stFunc1| |lineColorDefault| |froot| |backspace|
+ |product| |lazyEvaluate| |univariatePolynomial| |setPredicates|
+ |deleteProperty!| |roughBasicSet| |extract!| |OMgetEndError|
+ |getGraph| |any?| |e04fdf| |wrregime| |clipPointsDefault|
+ |linearlyDependentOverZ?| |rename!| |leader| |inRadical?| |curve?|
+ |isNot| |KrullNumber| |topPredicate| |jvmPrivate| |ratPoly| |sdf2lst|
+ |taylorQuoByVar| |taylorRep| |binomThmExpt| |search| |tubePoints|
+ |halfExtendedResultant1| |setRealSteps| |contours| |charClass|
+ |gensym| |binding| |createNormalPrimitivePoly| |iisin| |conjugate|
+ |composite| |f07fdf| |numberOfVariables| |addiag| |isQuotient|
+ |rational?| |upperBound| |iidsum| |qinterval| |recoverAfterFail|
+ |changeMeasure| |basisOfMiddleNucleus| |idealiser| |normalForm|
+ |acoshIfCan| |quoted?| |LazardQuotient| |solid?| |palgint0|
+ |invmultisect| |LiePoly| |RittWuCompare| |cap| |retractIfCan|
+ |eulerPhi| |fibonacci| |hdmpToDmp| |fractionFreeGauss!| |acosIfCan|
+ |updatF| |approxSqrt| |id| |multisect| |integerIfCan| |e02akf|
+ |clearDenominator| |morphism| |approximants| |optpair|
+ |solveLinearlyOverQ| |qroot| |subst| |quasiMonicPolynomials| |zerosOf|
+ |lo| |bat| |doubleResultant| |e02bcf| |readUInt32!| |df2fi| |eof?|
+ |character?| |hasSolution?| |revert| |error| |mainValue| |chiSquare|
+ |distance| |extractIfCan| |chainSubResultants| |cAcot|
+ |removeIrreducibleRedundantFactors| |rst| |normInvertible?|
+ |FormatArabic| |divisor| |second| |e01saf| |lp| |normalElement|
+ |bandedHessian| |indices| |realEigenvectors| |isPlus| |map| |irVar|
+ |nthFactor| |BasicMethod| |Si| |third| |clearTheIFTable|
+ |leadingCoefficientRicDE| |changeVar| |screenResolution3D|
+ |outlineRender| |pureLex| |cyclicParents| |c06eaf| |deepestInitial|
+ |genus| |objects| |formula| |LiePolyIfCan| |createRandomElement|
+ |refine| |PDESolve| |printInfo!| |factorial| |close| |tower|
+ |leftExactQuotient| |binomial| |iicsc| |e04naf| |f01qcf| |base|
+ |quadratic?| |drawToScale| |generalTwoFactor| |setFormula!|
+ |groebnerFactorize| |s18adf| |jvmSuper| |rdregime| |palgextint0|
+ |parametric?| |parents| |monicModulo| |exp1| |partition| |divisors|
+ |unitsColorDefault| |completeEchelonBasis| |display| |cycleElt|
+ |figureUnits| |vector| |critpOrder| |complexExpand| |companionBlocks|
+ |rightTraceMatrix| |minColIndex| |addmod| |seed| |totalDegree|
+ |iterationVar| |argscript| |differentiate| |decrease| |optional?|
+ |power| |nrows| |mainMonomials| |more?| |rationalIfCan| |signatureAst|
+ |column| |irreducibleFactor| |lexTriangular| |leftPower| |asecIfCan|
+ |rightOne| |ncols| |separant| |symFunc| |laurentIfCan| |pleskenSplit|
+ |nextNormalPrimitivePoly| |firstDenom| |showFortranOutputStack|
+ |solveLinearPolynomialEquationByRecursion| |ref| |next| |coerce|
+ |factorOfDegree| |maxdeg| |pointColorPalette| |c06gcf| |Beta|
+ |complexNumeric| |prinb| |selectsecond| |functionIsFracPolynomial?|
+ |less?| |invertible?| |categories| |construct| |represents| |bothWays|
+ |controlPanel| |sequence| |input| |edf2ef| |largest| |mkAnswer|
+ |bernoulliB| |aLinear| |opeval| |s17adf| |color| |library|
+ |contractSolve| |directory| |divideIfCan!| |mainSquareFreePart|
+ |jacobian| |resetVariableOrder| |youngDiagram| |s18def| |key?|
+ |shiftLeft| |cLog| |simplifyPower| |jvmMethodrefConstantTag| |ef2edf|
+ |genericPosition| |constantKernel| |mapMatrixIfCan| |expintegrate|
+ |subQuasiComponent?| |SturmHabichtSequence| |init| |insertionSort!|
+ |sn| |leadingIdeal| |s01eaf| |child?| |poisson| |matrix| |f01ref|
+ |crushedSet| |removeRoughlyRedundantFactorsInContents|
+ |semiResultantEuclidean1| |updateStatus!| |ratpart| |s17ahf|
+ |equality| |exprHasWeightCosWXorSinWX| |s17dgf| |midpoints|
+ |removeZero| |nthRootIfCan| |monicDivide| |isTimes| |divisorCascade|
+ |setScreenResolution| |roughUnitIdeal?| |quotedOperators|
+ |denominator| |set| |var1Steps| |cAtan| |primPartElseUnitCanonical|
+ |selectOrPolynomials| |nullity| |coleman| |fortranTypeOf| |delete|
+ |cyclicSubmodule| |elliptic?| |cothIfCan| |alphabetic?| |setleaves!|
+ |f02axf| |unprotectedRemoveRedundantFactors| |SturmHabichtMultiple|
+ |rootKerSimp| |iiasinh| |digit| |generalizedEigenvector| |s13aaf|
+ |maxint| |enterPointData| |quickSort| |iCompose| |f02ajf|
+ |regularRepresentation| |normalizeAtInfinity| |sts2stst| |escape|
+ |OMunhandledSymbol| |replaceKthElement| |primextintfrac| |lowerCase!|
+ |systemCommand| |OMgetEndBVar| |mapExponents| |complexNumericIfCan|
+ |rightRemainder| |leaves| |smith| |jacobi|
+ |jvmInterfaceMethodConstantTag| |bernoulli| |laurentRep| |coordinates|
+ |rewriteSetWithReduction| |splitLinear| |numberOfIrreduciblePoly|
+ |outputFloating| |jvmStringConstantTag|
+ |initializeGroupForWordProblem| |basisOfLeftNucloid|
+ |extendedSubResultantGcd| |ffactor| |linearDependenceOverZ| |d01aqf|
+ |OMgetType| |fullPartialFraction| |errorKind| |OMserve| |lazyPquo|
+ |assert| |besselY| |hostPlatform| |lazyIntegrate| |normal| |OMputAttr|
+ |lprop| |numericalOptimization| |viewDeltaYDefault| |relationsIdeal|
+ |solveLinearPolynomialEquationByFractions| |reciprocalPolynomial|
+ |tablePow| |ocf2ocdf| |shade| |leviCivitaSymbol| |iiperm| |sPol|
+ |cardinality| |primitive?| |moreAlgebraic?| |removeSuperfluousCases|
+ |solveLinear| |divide| |e01sef| |cup| |associative?| |constantRight|
+ |splitNodeOf!| |solveLinearPolynomialEquation| |iicos| |overlap|
+ |symmetricSquare| |OMgetEndApp| |xn| |getExplanations| |nthRoot|
+ |recolor| |rules| |checkPrecision| |integralBasis|
+ |localIntegralBasis| |indicialEquation| |show| |vedf2vef|
+ |domainTemplate| |f01mcf| |setrest!| |sumSquares| |anticoord|
+ |OMputBVar| |lexico| |basisOfNucleus| |scaleRoots|
+ |internalZeroSetSplit| |nonLinearPart| |universe| |setOfMinN| |has?|
+ |const| |rank| |drawComplex| |pushdterm| |trace| |makeViewport3D|
+ |realRoots| |rowEch| |pointPlot| |integralMatrixAtInfinity| |OMread|
+ |identification| |outputForm| |completeHensel| |characteristicSerie|
+ |setprevious!| |insertRoot!| |compBound| |Vectorise| |doubleComplex?|
+ |setPoly| |clipParametric| |pointData| |log10|
+ |lastSubResultantEuclidean| |unknown| |supDimElseRittWu?| |leaf?|
+ |LyndonWordsList1| |finite?| |bumprow| |lookup| |computePowers|
+ |complexEigenvalues| |bitand| |rectangularMatrix| |fortranReal|
+ |conditionP| |lowerPolynomial| |linearElement| |d01gaf|
+ |OMencodingSGML| |OMputEndError| |fortran| |invertibleElseSplit?|
+ |bitior| |write!| SEGMENT |primaryDecomp| |coth2trigh|
+ |repeatUntilLoop| |f07aef| |shuffle| |palginfieldint|
+ |inputBinaryFile| |subresultantVector| |quartic| |dihedral| |decimal|
+ |slex| |viewDefaults| |inHallBasis?| |s18aff| |firstSubsetGray|
+ |addMatch| |stoseInvertibleSet| |var2Steps| |partitions| |lyndon|
+ |inf| |fixedPoint| |henselFact| |lists| |implies| |OMputString|
+ |subPolSet?| |categoryMode| |trapezoidal| |factorPolynomial| |table|
+ |partialNumerators| |singularitiesOf| |coshIfCan| |listOfMonoms|
+ |linSolve| |c06gbf| |modTree| |numFunEvals| |mkPrim| |new|
+ |setTopPredicate| |nthCoef| |stopTableInvSet!| |dark| |minrank|
+ |changeName| |f02wef| |showSummary| |algebraicVariables| |ravel|
+ |getZechTable| |weighted| |var2StepsDefault| |readInt16!|
+ |doubleFloatFormat| |composites| |lowerBound| |lighting|
+ |rischNormalize| |reshape| |selectODEIVPRoutines|
+ |lazyPremWithDefault| |crest| |flexibleArray| |polar| |updatD|
+ |lyndon?| |loadNativeModule| |tanNa| |showAttributes| |cn|
+ |principal?| |singRicDE| |jvmInterface| |polygon?| |dihedralGroup|
+ |cSinh| |mirror| |weights| |position!| |split!| |laguerre| LODO2FUN
+ |unmakeSUP| |iiasin| |lazy?| |OMputEndBVar| |output|
+ |splitDenominator| |gbasis| |sum| |goodPoint| |reducedSystem| |back|
+ |elaboration| |erf| |leastAffineMultiple| |inconsistent?| |conjugates|
+ |green| |critBonD| |selectOptimizationRoutines|
+ |tryFunctionalDecomposition?| |factorSquareFreeByRecursion|
+ |fixedPointExquo| |sizeLess?| |complex?| |rotatex| |ramified?|
+ |float?| |palgintegrate| |update| |script| |s17dcf| |viewPhiDefault|
+ |curry| |linearAssociatedLog| |B1solve| |d02bhf| |internalAugment|
+ |bivariate?| |completeHermite| |seriesSolve| |symmetricTensors|
+ |headReduce| |dilog| |OMreadFile| |coefficient| |multiEuclidean|
+ |fixedPoints| |infix| |redPol| |merge!| |multiplyExponents|
+ |groebnerIdeal| |sin| |eisensteinIrreducible?| |monicLeftDivide|
+ |getMeasure| |connect| |plot| |binarySearchTree| |tex| |spherical|
+ |split| |subResultantsChain| |cos| |condition| |e02bbf| |pole?|
+ |neglist| |prime| |polyRDE| |iitan| |coerceListOfPairs|
+ |invertibleSet| |cot2trig| |tan| |factorByRecursion| |deriv| |ignore?|
+ |factorFraction| |trigs| |position| |repeating| |verticalTab|
+ |lflimitedint| |region| |cot| |c06gqf| |addPointLast|
+ |expenseOfEvaluationIF| |intPatternMatch| |e02bef| |nextItem|
+ |musserTrials| |Ci| |outputAsScript| |sec| |deepExpand|
+ |interpretString| |newline| |setLabelValue| |rdHack1| |varList|
+ |bytes| |pair?| |removeSuperfluousQuasiComponents| |cAsin| |csc|
+ |useNagFunctions| |makeSin| |measure2Result| |readInt8!| |units|
+ |tubeRadiusDefault| |f04atf| |totalfract| |hermite| |BumInSepFFE|
+ |asin| |matrixConcat3D| |zag| |f01rdf| |rarrow| |readUInt16!|
+ |iiacosh| |normalDeriv| |typeLists| |basisOfCenter| |acos| |component|
+ |expPot| |jokerMode| |reverse| |untab| |sh| |thetaCoord| |mapSolve|
+ |iiasec| |rightMult| |firstUncouplingMatrix| |atan| |f01brf|
+ |isAbsolutelyIrreducible?| |accuracyIF|
+ |dimensionOfIrreducibleRepresentation| |symmetricProduct| |prem|
+ |coord| |bivariateSLPEBR| |zeroSetSplitIntoTriangularSystems|
+ |getMatch| |acot| |simpleBounds?| |f2st| |acschIfCan| |front|
+ |constantIfCan| |totalLex| |middle| |substring?| |OMsupportsCD?|
+ |writeBytes!| |support| |nextPartition| |asec| |critT| |rur| |exists?|
+ |internalLastSubResultant| |prolateSpheroidal| |code|
+ |useEisensteinCriterion| |baseRDEsys| |nextPrimitiveNormalPoly|
+ |point?| F2FG |acsc| |diff| |shape| |nativeModuleExtension| |sin2csc|
+ |quote| |suffix?| |pdct| |OMgetEndBind| |numFunEvals3D|
+ |definingInequation| |roughBase?| |sinh| |minRowIndex| |resultant|
+ |zeroSetSplit| |clipSurface| |presuper| |mathieu11| |elliptic|
+ |findCycle| |changeNameToObjf| |genericRightNorm| |cosh| |iisinh|
+ |recur| |jvmUTF8ConstantTag| |pow| |mainDefiningPolynomial| |sign|
+ |prefix?| |components| |limitPlus| |subspace| |polygon| |deepestTail|
+ |tanh| |irreducibleRepresentation| |assign| |s18acf| |minset|
+ |bombieriNorm| |bivariatePolynomials| |polynomialZeros| |collect|
+ |taylorIfCan| |rightTrace| |removeRedundantFactorsInContents| |coth|
+ |swapRows!| |basicSet| |nextSubsetGray| |UnVectorise| |psolve|
+ |lagrange| |drawCurves| |optAttributes| |rischDE| |nullary| |compile|
+ |sech| |exactQuotient| |cosSinInfo| |iExquo| |vconcat| |palglimint0|
+ |plus| |mapDown!| |pdf2ef| |e01bhf| |latex| |csch| |log2| |qfactor|
+ |power!| |Lazard2| |primitiveElement| |style| |prinpolINFO|
+ |cschIfCan| |selectAndPolynomials| |asinh| |alternatingGroup|
+ |cyclicGroup| |GospersMethod| |exptMod| |mapUp!| |zeroDimPrime?|
+ |d01asf| |top| |karatsubaOnce| |create3Space| |acosh| |iiatanh|
+ |outputSpacing| |iiacsc| |OMputAtp| |vspace| |putProperty| |times|
+ |infix?| |nextColeman| |continue| |e04ycf| |fglmIfCan| |atanh| |cSec|
+ |normDeriv2| |OMgetString| |sort| |inGroundField?|
+ |resetAttributeButtons| |mask| |semiLastSubResultantEuclidean|
+ |ldf2lst| |open?| |badValues| |acoth| |remainder| |selectPDERoutines|
+ |localUnquote| |coerceL| |tubeRadius| |prindINFO| |setProperties|
+ |meatAxe| |nthExpon| |asech| |dn| |groebner?| |pointSizeDefault|
+ |arity| |random| |external?| |listOfLists| |formfeed| |e02ahf|
+ |viewport3D| |digits| RF2UTS |rowEchelonLocal| |getGoodPrime|
+ |rationalPoints| |null| |monom| |showRegion| |tanQ| |diagonalProduct|
+ |factorList| |complement| |ODESolve| |coerceP| |failed?|
+ |useEisensteinCriterion?| |not| |createNormalPoly| |substitute|
+ |simplify| |high| |value| |countable?|
+ |removeRoughlyRedundantFactorsInPol| |printStats!| |var1StepsDefault|
+ |lookupFunction| |and| |cfirst| |componentUpperBound| |tanh2coth|
+ |printCode| |chvar| |s17aff| |createPrimitiveElement| |lfextlimint|
+ |imagi| |or| |constantOpIfCan| |fractionPart| |lambert|
+ |extensionDegree| |node| |OMputEndBind| |boundOfCauchy| |satisfy?|
+ |newSubProgram| |shiftRoots| |xor| |leftAlternative?|
+ |getSyntaxFormsFromFile| |setref| |rootBound| |arg1|
+ |linearAssociatedExp| |function| |c06ebf| |legendre| |point|
+ |elseBranch| |nothing| |case| |cycleTail| |basisOfRightNucloid|
+ |UpTriBddDenomInv| |arg2| |birth| |scripted?| |goodnessOfFit|
+ |lowerCase?| |legendreP| |yCoord| |conjunction| |elements|
+ |consnewpol| |Zero| |leftCharacteristicPolynomial| |conical|
+ |quasiComponent| |karatsuba| |linear?| |arguments|
+ |removeRedundantFactors| |sec2cos| |s17agf| |blankSeparate| |One|
+ |diagonalMatrix| |basisOfLeftAnnihilator| |relerror|
+ |singularAtInfinity?| |OMconnInDevice| |conditions| |putGraph|
+ |parabolicCylindrical| |setAdaptive| |series| |hasTopPredicate?|
+ |move| |transcendent?| |inverseLaplace| |reseed| |order|
+ |rootNormalize| |match| |iipow| |isMult| |printStatement| |palgLODE|
+ |omError| |weakBiRank| |typeForm| |s17dlf| |rightGcd|
+ |setScreenResolution3D| |integralDerivationMatrix| |makeUnit| |makeFR|
+ |compose| |secIfCan| |flatten| |module| |commaSeparate|
+ |getProperties| |Is| |symmetric?| |newLine| |ParCondList|
+ |genericRightMinimalPolynomial| |setright!| |primintfldpoly| |lllp|
+ |restorePrecision| |exprHasLogarithmicWeights| |min| |discriminant|
+ |getCode| |readIfCan!| |deref| |elt| |realElementary| |setStatus|
+ |univariateSolve| |complexRoots| |OMreceive| |gcdPrimitive|
+ |primlimitedint| |squareFree| |graphImage| |messagePrint| |harmonic|
+ |exactQuotient!| |totolex| |constant| |redmat| |atom?| |chebyshevU|
+ |preprocess| |basisOfRightNucleus| |arbitrary| |light|
+ |rightAlternative?| |nextLatticePermutation| |recip| |modifyPoint|
+ |setOrder| |exprex| |bfKeys| |primextendedint| |sqfree|
+ |OMsetEncoding| |bat1| |lcm| |deepCopy| |truncate| |subSet| |ode|
+ |clip| |clearCache| |mightHaveRoots| |isList| |makeGraphImage|
+ |torsionIfCan| |minGbasis| |e01baf| |equation| |minIndex| |block|
+ |dequeue!| |whatInfinity| |overset?| |append| |makeEq| |members|
+ |symmetricGroup| |orbit| |reducedForm| |s14baf| |slash| |e01bgf|
+ |overbar| |gcd| |perfectNthPower?| |bracket| |setLength!| |pdf2df|
+ |limitedint| |drawStyle| |outerProduct| |internal?| |dom|
+ |setPosition| |imagK| |false| |phiCoord| |tan2cot| |rootRadius|
+ |antiAssociative?| |jvmAbstract| |pushup| |label| |linearPolynomials|
+ |stirling2| |prepareSubResAlgo| |exponential1| |dmpToP|
+ |stiffnessAndStabilityOfODEIF| |cycleSplit!| |moebius| |startStats!|
+ |closeComponent| |inverse| |shiftRight| |rotate| |logGamma| |bottom!|
+ |cAcos| |mappingAst| |setIntersection| |f04arf| |skewSFunction|
+ |drawComplexVectorField| |sup| |lazyVariations|
+ |semiResultantReduitEuclidean| |gcdcofactprim| |computeCycleEntry|
+ |lfinfieldint| |setCondition!| |radicalEigenvectors|
+ |rightMinimalPolynomial| |cycleLength| |setRow!| |intcompBasis| |odd?|
+ |generic?| |coefChoose| |coerceImages| |properties| |title| |palgint|
+ |create| |distFact| |d01akf| |makeSUP| |nextSublist|
+ |lazyPseudoRemainder| |purelyAlgebraic?| |hex| |univariate?|
+ |translate| |belong?| |inR?| |relativeApprox| |oddintegers|
+ |cylindrical| |bitCoef| |subscriptedVariables| |zeroDimPrimary?|
+ |extension| |paren| |OMgetEndAtp| |supRittWu?| |e01bef|
+ |variationOfParameters| |OMopenString| |equiv| |modularFactor|
+ |regime| |rightUnit| |permutations| |e| |monic?| |magnitude|
+ |environment| |isAnd| |pol| |bezoutResultant| |setlast!| |one?|
+ |uniform| |option| Y |rightFactorCandidate| |routines| |e02ddf|
+ |possiblyNewVariety?| |edf2df| |algebraicSort|
+ |algebraicCoefficients?| |zeroDimensional?| |imagI| |yellow|
+ |toroidal| |inputOutputBinaryFile| |viewPosDefault| |in?| |palgRDE|
+ |lifting1| |f02awf| |solveInField| |polyPart| |generalizedInverse|
+ |contract| |besselI| |permutationGroup| |extractProperty| |graeffe|
+ |OMsend| |nthFractionalTerm| |diophantineSystem| |youngGroup| |mat|
+ |cycleRagits| |getIdentifier| |f02agf| |maxPoints| |row| |backOldPos|
+ |leftRemainder| |cCosh| |unravel| |exQuo| |orbits|
+ |sizeMultiplication| |generalInfiniteProduct| |horizontalTab|
+ |bubbleSort!| |extendIfCan| |graphs| |aQuartic| |fTable| |isOr|
+ |reduced?| |pomopo!| |frobenius| |iiasech| |OMputInteger|
+ |integralRepresents| |difference| |partialDenominators|
+ |trailingCoefficient| |palgextint| |subResultantGcd| |schema|
+ |selectNonFiniteRoutines| |rightZero| |parametersOf| |cAcsch|
+ |maxPoints3D| |duplicates?| |apply| |test| |clipBoolean| |irDef|
+ |operation| |pToDmp| |halfExtendedSubResultantGcd2|
+ |showTheSymbolTable| |freeOf?| |reduceLODE| |extractTop!| |mdeg|
+ |charpol| |first| |intersect| |zero?| |karatsubaDivide|
+ |extendedResultant| |bounds| |chiSquare1| |viewDeltaXDefault|
+ |kovacic| |pushuconst| |rest| |rightLcm| |parts|
+ |balancedFactorisation| |wholeRadix| |hconcat| |degreeSubResultant|
+ |brillhartIrreducible?| |wholeRagits| |cCos| |bsolve| |reify|
+ |squareFreeFactors| |subCase?| |closedCurve?|
+ |selectIntegrationRoutines| |radicalRoots| |gradient|
+ |algebraicDecompose| |removeRedundantFactorsInPols| |scale|
+ |buildSyntax| |simplifyExp| |rombergo| |minPoints3D|
+ |doublyTransitive?| |createLowComplexityTable| |numberOfNormalPoly|
+ |nextsubResultant2| |kmax| |evenlambert| |selectfirst| |rootDirectory|
+ |makeResult| |chebyshevT| |s21bbf| |symbol?| |moebiusMu| |argument|
+ |pmComplexintegrate| |makeop| |iiexp| |callForm?| |viewWriteAvailable|
+ |exponent| |nextNormalPoly| |rubiksGroup| |limitedIntegrate| |merge|
+ |pattern| |leftFactorIfCan| |setfirst!| |leadingTerm| |cyclicEqual?|
+ |e02dcf| |isEquiv| |just| |OMlistSymbols| |twist| |mpsode| |remove|
+ |arrayStack| |flexible?| |numberOfComputedEntries|
+ |purelyTranscendental?| |halfExtendedSubResultantGcd1| |innerint|
+ |cAsech| |d03faf| |OMputEndApp| |getBadValues| |s18dcf| ** |whileLoop|
+ |atrapezoidal| |expressIdealMember| |hasoln| |writable?| |singular?|
+ |rk4a| |resultantnaif| |node?| |clearFortranOutputStack| |insert!|
+ |last| |bringDown| |normal01| |option?| |Frobenius| |stronglyReduced?|
+ |basisOfRightAnnihilator| |makeVariable| |resultantEuclideannaif|
+ |zCoord| |multiset| |stopTable!| |message| |assoc| |jvmTransient|
+ GF2FG |semiIndiceSubResultantEuclidean| |someBasis| |upperCase|
+ |powerAssociative?| |complexLimit| |alphanumeric?| |mulmod| |d02cjf|
+ |s15adf| |comp| |setsubMatrix!| |compactFraction| |dmpToHdmp| |iprint|
+ |child| |internalInfRittWu?| |OMgetError| |numericIfCan|
+ |viewZoomDefault| |univariatePolynomials| |SturmHabicht| |makeSketch|
+ |subNode?| |addPoint2| |compiledFunction| |f02fjf| |rootPoly|
+ |diagonal?| |finiteBasis| |e04ucf| |cTanh| |pop!| |maxRowIndex| |tab|
+ |getStream| |traverse| |close!| |normalDenom| |quasiAlgebraicSet|
+ |nonQsign| |dualSignature| |charthRoot| |rootPower| |mainCoefficients|
+ |physicalLength!| |check| |tanSum| |unrankImproperPartitions1|
+ |increase| |lazyGintegrate| |upperCase?| |parseString| |outputAsTex|
+ |abs| |packageCall| |reduceByQuasiMonic| |maxrow|
+ |radicalOfLeftTraceForm| |concat| |complexZeros| |quatern|
+ |shallowCopy| |discriminantEuclidean| |lazyPseudoDivide|
+ |brillhartTrials| |infLex?| |bigEndian| |acothIfCan| |degree|
+ |dmp2rfi| |findConstructor| |repeating?| |ricDsolve| |besselK|
+ |sizePascalTriangle| |setDifference| |rotatez| |precision|
+ |rowEchLocal| |leftRank| |jvmSynchronized| |leftOne| |applyRules|
+ |critB| |oneDimensionalArray| |distribute| |interpret|
+ |monomialIntPoly| |s15aef| |octon| |toScale| |removeSquaresIfCan|
+ |socf2socdf| |e02aef| |fracPart| |getMultiplicationMatrix|
+ |mainVariable| |showTheRoutinesTable| |lastSubResultantElseSplit|
+ |radicalEigenvector| |selectFiniteRoutines| |varselect|
+ |factorSFBRlcUnit| |f01qdf| |monicRightDivide| |unitNormalize| |iicot|
+ |appendPoint| |lazyPseudoQuotient| |collectUnder| |tanAn| |ptFunc|
+ |ceiling| |aspFilename| |internalDecompose| |OMlistCDs|
+ |perfectNthRoot| |roughSubIdeal?| |asimpson| |htrigs| |s14aaf| |imagj|
+ |leftReducedSystem| |s17dhf| |startPolynomial| |singleFactorBound|
+ |redpps| |sayLength| |virtualDegree| |c06ekf|
+ |genericLeftDiscriminant| |aromberg| |optimize| |setMinPoints|
+ |dimensionsOf| |OMgetBind| |addBadValue| |stripCommentsAndBlanks|
+ |d02gaf| |dfRange| |att2Result| |setMinPoints3D| |expextendedint|
+ |doubleDisc| |nthr| |sinIfCan| |delta| |mergeFactors| |monomRDE|
+ |generalPosition| |fractRadix| |top!| |nullary?| |exponents|
+ |withPredicates| |leftExtendedGcd| |noKaratsuba| |rationalPoint?|
+ |defineProperty| |setColumn!| |ratDsolve| |interval| |leftRecip|
+ |trapezoidalo| |iisqrt3| |edf2fi| |ksec| |extractPoint| |cPower|
+ |permutationRepresentation| |f07adf| |linear| |OMUnknownSymbol?|
+ |tableau| |c02agf| |coercePreimagesImages| |dioSolve| |find| |level|
+ |stFunc2| |iilog| |validExponential| |explicitlyEmpty?| |pade|
+ |explimitedint| |semiDegreeSubResultantEuclidean| |anfactor|
+ |constantCoefficientRicDE| |changeBase| |processTemplate| |lepol|
+ |outputArgs| |sincos| |extractSplittingLeaf| |polynomial|
+ |removeDuplicates!| |coth2tanh| |OMputSymbol| |outputBinaryFile|
+ |leadingExponent| |target| |twoFactor| |noLinearFactor?|
+ |principalIdeal| |nilFactor| |showIntensityFunctions| |dual|
+ |stosePrepareSubResAlgo| |f02adf| |mainMonomial| |f04axf|
+ |algebraicOf| |d01bbf| |branchIfCan| |ratDenom| |trivialIdeal?|
+ |polarCoordinates| |car| |rroot| |semiSubResultantGcdEuclidean1|
+ |leftLcm| |powern| |ramifiedAtInfinity?| |setchildren!| |s13adf|
+ |integers| |multiple| |any| |lambda| |patternMatchTimes|
+ |toseInvertibleSet| |chineseRemainder| |computeBasis| |debug|
+ |stoseInvertible?reg| |expintfldpoly| |getButtonValue| |lllip|
+ |critMTonD1| |OMbindTCP| |applyQuote| |prepareDecompose|
+ |RemainderList| |elementary| |f04jgf| |entries| D |read!|
+ |rationalApproximation| |ip4Address| |OMencodingXML| |unary?| |d01apf|
+ |genericRightTraceForm| |f01qef| |pseudoRemainder| |OMgetVariable|
+ |bandedJacobian| |usingTable?| |property| |hcrf| |shufflein|
+ |factorAndSplit| |readable?| |credPol| |polCase| |romberg|
+ |createPrimitiveNormalPoly| |functionIsOscillatory|
+ |computeCycleLength| |plusInfinity| |laguerreL| |nlde| |leftUnits|
+ |pushNewContour| |ruleset| |predicate| |stopMusserTrials| |ddFact|
+ |s20acf| |viewpoint| |pushdown| |isobaric?| |leftNorm| |minusInfinity|
+ |newReduc| |jvmVolatile| |moduloP| |integer?| |rightRankPolynomial|
+ |showTheFTable| |red| |lieAdmissible?| |setleft!| |bit?| |laplace|
+ |dictionary| |primPartElseUnitCanonical!| |kroneckerDelta| |empty|
+ |bitTruth| |splitConstant| |cosh2sech| |abelianGroup|
+ |stoseSquareFreePart| |linkToFortran| |rspace| |meshFun2Var|
+ |showAll?| |suchThat| |hypergeometric0F1| |operators| |palgLODE0|
+ |stoseInvertible?sqfreg| |iiatan| |leftRankPolynomial|
+ |rightExtendedGcd| |null?| |s17aef| |queue| |build| |oddlambert|
+ |iiacsch| |is?| |e02dff| |scanOneDimSubspaces| |sylvesterMatrix|
+ |plus!| |possiblyInfinite?| |setelt| |monomials| |csubst| |wholePart|
+ |weierstrass| |halfExtendedResultant2| |factorials| |e02gaf| |type|
+ |solveRetract| |hexDigit?| |qualifier| |rem| |multiEuclideanTree|
+ |digamma| |f02aff| |enterInCache| |cyclotomicDecomposition| |print|
+ |OMgetInteger| |intermediateResultsIF| |stoseInvertibleSetreg|
+ |quadraticForm| |stronglyReduce| |copy| |quo| |plenaryPower|
+ |minimumDegree| |shellSort| |listexp| |resolve| |upDateBranches|
+ |imports| |irForm| |cExp| |setAttributeButtonStep| |declare|
+ |readLine!| |atoms| |geometric| |se2rfi| |certainlySubVariety?|
+ |elRow1!| |extractIndex| |normalizedDivide| |numeric|
+ |ScanFloatIgnoreSpacesIfCan| |parameters| |div| |binaryFunction|
+ |eyeDistance| |beauzamyBound| |showScalarValues| |postfix|
+ |jvmNameAndTypeConstantTag| |tracePowMod| |reorder| |inspect| |mkcomm|
+ |radical| |superHeight| |exquo| |number?| |increasePrecision| |isExpt|
+ |positive?| |maximumExponent| |match?| |evaluate| |OMgetEndObject|
+ |generalSqFr| |numberOfDivisors| |pToHdmp| |diagonal| ~= |every?|
+ |cAsinh| |alphanumeric| |expIfCan| |fractRagits| |setUnion| |f04asf|
+ |cycles| |pushucoef| |autoCoerce| |#| |s19adf| |numerator|
+ |OMconnectTCP| |list?| |makeSeries| |rightRegularRepresentation|
+ |branchPoint?| |c05adf| |ord| |e01sff| ~ |matrixDimensions|
+ |squareFreePolynomial| |adaptive3D?| |tanhIfCan| |outputGeneral|
+ |moduleSum| |ranges| |resetBadValues| |predicates|
+ |multiplyCoefficients| |integral?| |ScanFloatIgnoreSpaces|
+ |triangSolve| |OMgetEndAttr| |initTable!| |length| |hasHi| |expandLog|
+ |exteriorDifferential| |sub| |setnext!| |setValue!|
+ |uncouplingMatrices| |char| |limit| |probablyZeroDim?| |closed?|
+ |homogeneous?| |scripts| |extendedIntegrate| |cRationalPower| |box|
+ |tab1| |transform| |f01maf| |/\\| |loopPoints| |solve1| |cSech|
+ |derivative| |nextPrime| |stiffnessAndStabilityFactor| |generator|
+ |wordsForStrongGenerators| |symmetricDifference| |particularSolution|
+ |f01rcf| |OMgetSymbol| |\\/| |getRef| |mapdiv| |factorGroebnerBasis|
+ |remove!| |getOrder| |obj| |linGenPos| |LyndonWordsList| |isImplies|
+ |iiGamma| |generators| |elaborateFile| |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
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 7dd047ca..55878981 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5471 +1,5471 @@
-(3471929 . 3497194955)
-((-2712 (((-112) (-1 (-112) |#2| |#2|) $) 86 T ELT) (((-112) $) NIL T ELT)) (-3183 (($ (-1 (-112) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-2589 ((|#2| $ (-578) |#2|) NIL T ELT) ((|#2| $ (-1265 (-578)) |#2|) 44 T ELT)) (-3467 (($ $) 80 T ELT)) (-2512 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3887 (((-578) (-1 (-112) |#2|) $) 27 T ELT) (((-578) |#2| $) NIL T ELT) (((-578) |#2| $ (-578)) 96 T ELT)) (-2728 (((-666 |#2|) $) 13 T ELT)) (-2026 (($ (-1 (-112) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-3439 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3610 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-4273 (($ |#2| $ (-578)) NIL T ELT) (($ $ $ (-578)) 67 T ELT)) (-1991 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29 T ELT)) (-2776 (((-112) (-1 (-112) |#2|) $) 23 T ELT)) (-2436 ((|#2| $ (-578) |#2|) NIL T ELT) ((|#2| $ (-578)) NIL T ELT) (($ $ (-1265 (-578))) 66 T ELT)) (-1707 (($ $ (-578)) 76 T ELT) (($ $ (-1265 (-578))) 75 T ELT)) (-4324 (((-793) (-1 (-112) |#2|) $) 34 T ELT) (((-793) |#2| $) NIL T ELT)) (-2485 (($ $ $ (-578)) 69 T ELT)) (-3979 (($ $) 68 T ELT)) (-2423 (($ (-666 |#2|)) 73 T ELT)) (-3703 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-666 $)) 85 T ELT)) (-2411 (((-886) $) 92 T ELT)) (-4434 (((-112) (-1 (-112) |#2|) $) 22 T ELT)) (-2384 (((-112) $ $) 95 T ELT)) (-2404 (((-112) $ $) 99 T ELT)))
-(((-18 |#1| |#2|) (-10 -8 (-15 -2384 ((-112) |#1| |#1|)) (-15 -2411 ((-886) |#1|)) (-15 -2404 ((-112) |#1| |#1|)) (-15 -3183 (|#1| |#1|)) (-15 -3183 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3467 (|#1| |#1|)) (-15 -2485 (|#1| |#1| |#1| (-578))) (-15 -2712 ((-112) |#1|)) (-15 -2026 (|#1| |#1| |#1|)) (-15 -3887 ((-578) |#2| |#1| (-578))) (-15 -3887 ((-578) |#2| |#1|)) (-15 -3887 ((-578) (-1 (-112) |#2|) |#1|)) (-15 -2712 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -2026 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -2589 (|#2| |#1| (-1265 (-578)) |#2|)) (-15 -4273 (|#1| |#1| |#1| (-578))) (-15 -4273 (|#1| |#2| |#1| (-578))) (-15 -1707 (|#1| |#1| (-1265 (-578)))) (-15 -1707 (|#1| |#1| (-578))) (-15 -3610 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3703 (|#1| (-666 |#1|))) (-15 -3703 (|#1| |#1| |#1|)) (-15 -3703 (|#1| |#2| |#1|)) (-15 -3703 (|#1| |#1| |#2|)) (-15 -2436 (|#1| |#1| (-1265 (-578)))) (-15 -2423 (|#1| (-666 |#2|))) (-15 -1991 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2512 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2512 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2512 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2436 (|#2| |#1| (-578))) (-15 -2436 (|#2| |#1| (-578) |#2|)) (-15 -2589 (|#2| |#1| (-578) |#2|)) (-15 -4324 ((-793) |#2| |#1|)) (-15 -2728 ((-666 |#2|) |#1|)) (-15 -4324 ((-793) (-1 (-112) |#2|) |#1|)) (-15 -2776 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -4434 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -3439 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3610 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3979 (|#1| |#1|))) (-19 |#2|) (-1248)) (T -18))
+(3472629 . 3498909354)
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NIL
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NIL
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NIL
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((* (($ (-950) $) 10 T ELT)))
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NIL
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(((-102) . T) ((-632 (-886)) . T) ((-1131) . T) ((-1248) . T))
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NIL
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-NIL
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+((-3998 (*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1131)) (-4 *4 (-1131)) (-5 *2 (-2 (|:| -2338 *3) (|:| -2078 *4))))))
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+NIL
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-((-4107 (*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-96)))))
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NIL
(((-98) (-142)) (T -98))
NIL
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-NIL
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+NIL
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(((-102) (-142)) (T -102))
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(((-1248) . T))
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NIL
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NIL
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(((-196) (-809)) (T -196))
NIL
(-809)
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(((-197) (-809)) (T -197))
NIL
(-809)
-((-3212 (((-112) $ $) NIL T ELT)) (-4389 (((-1066) (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 81 T ELT) (((-1066) (-2 (|:| |fn| (-328 (-229))) (|:| -1634 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-2121 (((-2 (|:| -2121 (-392)) (|:| |explanations| (-1189)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -2121 (-392)) (|:| |explanations| (-1189)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-328 (-229))) (|:| -1634 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3426 (((-1189) $) NIL T ELT)) (-4313 (((-1151) $) NIL T ELT)) (-2411 (((-886) $) NIL T ELT)) (-2636 (((-112) $ $) NIL T ELT)) (-2384 (((-112) $ $) NIL T ELT)))
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(((-198) (-809)) (T -198))
NIL
(-809)
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(((-199) (-809)) (T -199))
NIL
(-809)
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(((-200) (-809)) (T -200))
NIL
(-809)
-((-3212 (((-112) $ $) NIL T ELT)) (-4389 (((-1066) (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 93 T ELT) (((-1066) (-2 (|:| |fn| (-328 (-229))) (|:| -1634 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-2121 (((-2 (|:| -2121 (-392)) (|:| |explanations| (-1189)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -2121 (-392)) (|:| |explanations| (-1189)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-328 (-229))) (|:| -1634 (-666 (-1125 (-865 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3426 (((-1189) $) NIL T ELT)) (-4313 (((-1151) $) NIL T ELT)) (-2411 (((-886) $) NIL T ELT)) (-2636 (((-112) $ $) NIL T ELT)) (-2384 (((-112) $ $) NIL T ELT)))
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(((-201) (-809)) (T -201))
NIL
(-809)
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(((-202) (-809)) (T -202))
NIL
(-809)
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(((-203) (-809)) (T -203))
NIL
(-809)
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(((-204) (-809)) (T -204))
NIL
(-809)
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(((-205) (-809)) (T -205))
NIL
(-809)
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(((-206) (-809)) (T -206))
NIL
(-809)
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(((-209) (-822)) (T -209))
NIL
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(((-210) (-822)) (T -210))
NIL
(-822)
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NIL
(-822)
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NIL
(-822)
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NIL
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NIL
(-922)
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NIL
(-13 (-242 |t#1|))
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NIL
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(((-1248) . T))
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NIL
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NIL
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NIL
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NIL
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NIL
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NIL
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NIL
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(((-279) (-861)) (T -279))
NIL
(-861)
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(((-280) (-861)) (T -280))
NIL
(-861)
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(((-281) (-861)) (T -281))
NIL
(-861)
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(((-282) (-861)) (T -282))
NIL
(-861)
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(((-283) (-861)) (T -283))
NIL
(-861)
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(((-284) (-861)) (T -284))
NIL
(-861)
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(((-285) (-861)) (T -285))
NIL
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-NIL
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NIL
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(((-528 |#1| |#1|) . T))
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NIL
(-1131)
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(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-632 (-886)) . T) ((-668 (-578)) . T) ((-1131) . T) ((-1248) . T))
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-NIL
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+NIL
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(((-351 |#1|) (-142) (-1131)) (T -351))
-((-3610 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-351 *3)) (-4 *3 (-1131)))))
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 (-578)) . T) ((-635 |#1|) . T) ((-632 (-886)) . T) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 |#1|) . T) ((-670 $) . T) ((-662 |#1|) . T) ((-739 |#1|) . T) ((-748) . T) ((-1082 |#1|) . T) ((-1087 |#1|) . T) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1248) . T))
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-NIL
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(((-401) (-142)) (T -401))
NIL
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(((-402) (-403)) (T -402))
NIL
(-403)
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NIL
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NIL
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NIL
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NIL
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NIL
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(((-176) . T))
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NIL
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(((-570) (-142)) (T -570))
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 $) . T) ((-102) . T) ((-111 $ $) . T) ((-133) . T) ((-635 (-578)) . T) ((-635 $) . T) ((-632 (-886)) . T) ((-175) . T) ((-302) . T) ((-668 (-578)) . T) ((-668 $) . T) ((-670 $) . T) ((-662 $) . T) ((-739 $) . T) ((-748) . T) ((-1082 $) . T) ((-1087 $) . T) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1248) . T))
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|var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2754 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1634 (-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 (-573)))) (-2231 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1634 (-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 (-573)))) (-1970 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -3172 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2754 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1634 (-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 (-573)))) (-2159 (*1 *1 *2) (-12 (-5 *2 (-666 (-2 (|:| -3172 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2754 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1634 (-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 (-573)))) (-3243 (*1 *2 *1) (-12 (-5 *2 (-666 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-573)))) (-1958 (*1 *2) (-12 (-5 *2 (-1303)) 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(-229)) (|:| |relerr| (-229)))) (|:| -2078 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1188 (-229))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1868 (-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 (-573)))) (-3858 (*1 *1 *2) (-12 (-5 *2 (-666 (-2 (|:| -2338 (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229))) (|:| -1868 (-1125 (-865 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| 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NIL
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NIL
(-13 (-668 |t#1|) (-1082 |t#1|))
(((-102) . T) ((-632 (-886)) . T) ((-668 |#1|) . T) ((-1082 |#1|) . T) ((-1131) . T) ((-1248) . T))
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(((-1248) . T))
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-NIL
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NIL
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(((-753 |#1| |#2|) (-978 |#2| (-545 (-888 |#1|)) (-888 |#1|)) (-666 (-1207)) (-1080)) (T -753))
NIL
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NIL
(-277 |#1|)
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(((-842) (-142)) (T -842))
NIL
(-13 (-570) (-870))
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(((-868) (-142)) (T -868))
NIL
(-13 (-881) (-748))
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NIL
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(((-870) (-142)) (T -870))
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(((-871) (-142)) (T -871))
NIL
(-13 (-1131) (-874))
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NIL
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NIL
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(((-874) (-142)) (T -874))
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(((-102) . T) ((-1248) . T))
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NIL
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+NIL
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(((-1004 |#1| |#2| |#3|) (-142) (-1080) (-814) (-871)) (T -1004))
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(((-1005) (-142)) (T -1005))
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(((-632 (-886)) . T))
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NIL
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NIL
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NIL
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(((-637 |#1|) . T))
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NIL
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(((-637 |#1|) . T) ((-1124 |#1|) . T))
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-NIL
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+NIL
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(((-1129 |#1|) (-142) (-1131)) (T -1129))
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(((-34) . T) ((-102) . T) ((-632 (-886)) . T) ((-153 |#1|) . T) ((-633 (-550)) |has| |#1| (-633 (-550))) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((-503 |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1131))) ((-1131) . T) ((-1248) . T))
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NIL
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NIL
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NIL
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NIL
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T) ((-635 $) -2230 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2230 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-550)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-578))))) ((-236 $) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-239) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-578)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-578) (-1143)) ((-302) -2230 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-578)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-570) -2230 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-668 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-670 #3=(-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2230 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2230 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-817) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2230 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-578)))) ((-909 |#2|) |has| |#1| (-376)) ((-938) -12 (|has| |#1| (-376)) (|has| |#2| (-938))) ((-1004 |#1| #0# (-1113)) . T) ((-949) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-578)))) ((-1053) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-1069 (-421 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2230 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2230 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2230 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1233) |has| |#1| (-38 (-421 (-578)))) ((-1236) |has| |#1| (-38 (-421 (-578)))) ((-1248) . T) ((-1252) |has| |#1| (-376)) ((-1258 |#1|) . T) ((-1276 |#1| #0#) . T))
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+(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-578)) . T) ((-25) . T) ((-38 #1=(-421 (-578))) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-578)))) ((-95) |has| |#1| (-38 (-421 (-578)))) ((-102) . T) ((-111 #1# #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-635 (-578)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-632 (-886)) . T) ((-175) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-633 (-550)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-550)))) ((-633 (-917 (-392))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-392))))) ((-633 (-917 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-917 (-578))))) ((-236 $) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-239) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-578) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-578)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-578) (-1143)) ((-302) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-578)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-570) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-668 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-668 (-578)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-670 #3=(-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-578)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-817) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1207)) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-927 (-1207)) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-929 #4#) -2225 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))) (-12 (|has| |#1| (-15 * (|#1| (-578) |#1|))) (|has| |#1| (-927 (-1207))))) ((-911 (-392)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-392)))) ((-911 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-578)))) ((-909 |#2|) |has| |#1| (-376)) ((-938) -12 (|has| |#1| (-376)) (|has| |#2| (-938))) ((-1004 |#1| #0# (-1113)) . T) ((-949) |has| |#1| (-376)) ((-1023 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-578)))) ((-1053) -12 (|has| |#1| (-376)) (|has| |#2| (-1053))) ((-1069 (-421 (-578))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 (-578)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-578)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2225 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-578))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2225 (|has| |#1| (-570)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1089) . T) ((-1143) . T) ((-1131) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1233) |has| |#1| (-38 (-421 (-578)))) ((-1236) |has| |#1| (-38 (-421 (-578)))) ((-1248) . T) ((-1252) |has| |#1| (-376)) ((-1258 |#1|) . T) ((-1276 |#1| #0#) . T))
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+NIL
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NIL
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NIL
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(((-1327 |#1|) (-13 (-175) (-381) (-633 (-578)) (-1183)) (-950)) (T -1327))
NIL
(-13 (-175) (-381) (-633 (-578)) (-1183))
@@ -5481,4 +5481,4 @@ NIL
NIL
NIL
NIL
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T T) -9 NIL 3448221 NIL) (-1318 3442035 3444606 3444994 "XPBWPOLY" 3445747 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3437304 3440011 3440053 "XF" 3440674 NIL XF (NIL T) -9 NIL 3441074 NIL) (-1316 3436901 3437013 3437182 "XF-" 3437187 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1315 3431793 3433372 3433427 "XFALG" 3435599 NIL XFALG (NIL T T) -9 NIL 3436388 NIL) (-1314 3430908 3431030 3431235 "XEXPPKG" 3431685 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3428649 3430758 3430854 "XDPOLY" 3430859 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3427304 3428042 3428085 "XALG" 3428090 NIL XALG (NIL T) -9 NIL 3428201 NIL) (-1311 3420214 3425281 3425775 "WUTSET" 3426896 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3418316 3419266 3419589 "WP" 3420025 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3417864 3418138 3418208 "WHILEAST" 3418268 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3417276 3417581 3417675 "WHEREAST" 3417792 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416150 3416360 3416655 "WFFINTBS" 3417073 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414018 3414481 3414943 "WEIER" 3415722 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3412942 3413500 3413542 "VSPACE" 3413678 NIL VSPACE (NIL T) -9 NIL 3413752 NIL) (-1304 3412774 3412807 3412898 "VSPACE-" 3412903 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3412571 3412625 3412693 "VOID" 3412728 T VOID (NIL) -8 NIL NIL NIL) (-1302 3410671 3411066 3411472 "VIEW" 3412187 T VIEW (NIL) -7 NIL NIL NIL) (-1301 3406939 3407734 3408471 "VIEWDEF" 3409956 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1300 3395883 3398487 3400660 "VIEW3D" 3404788 T VIEW3D (NIL) -8 NIL NIL NIL) (-1299 3387900 3389794 3391373 "VIEW2D" 3394326 T VIEW2D (NIL) -8 NIL NIL NIL) (-1298 3382806 3387670 3387762 "VECTOR" 3387843 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3381359 3381642 3381960 "VECTOR2" 3382536 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1296 3374313 3379063 3379106 "VECTCAT" 3380101 NIL VECTCAT (NIL T) -9 NIL 3380688 NIL) (-1295 3373255 3373581 3373971 "VECTCAT-" 3373976 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3372661 3372906 3373026 "VARIABLE" 3373170 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3372594 3372599 3372629 "UTYPE" 3372634 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3371402 3371578 3371840 "UTSODETL" 3372420 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3368794 3369302 3369826 "UTSODE" 3370943 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3360104 3366555 3367035 "UTS" 3368372 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1289 3350111 3356037 3356080 "UTSCAT" 3357192 NIL UTSCAT (NIL T) -9 NIL 3357950 NIL) (-1288 3347237 3348181 3349170 "UTSCAT-" 3349175 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1287 3346858 3346907 3347040 "UTS2" 3347188 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1286 3340725 3343668 3343711 "URAGG" 3345781 NIL URAGG (NIL T) -9 NIL 3346504 NIL) (-1285 3337448 3338527 3339650 "URAGG-" 3339655 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3332817 3336083 3336548 "UPXSSING" 3337112 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3324295 3332199 3332463 "UPXS" 3332611 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1282 3316710 3324199 3324271 "UPXSCONS" 3324276 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1281 3305458 3312912 3312974 "UPXSCCA" 3313548 NIL UPXSCCA (NIL T T) -9 NIL 3313781 NIL) (-1280 3305078 3305181 3305355 "UPXSCCA-" 3305360 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1279 3293726 3300905 3300948 "UPXSCAT" 3301596 NIL UPXSCAT (NIL T) -9 NIL 3302205 NIL) (-1278 3293150 3293235 3293414 "UPXS2" 3293641 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1277 3291786 3292057 3292408 "UPSQFREE" 3292893 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3284614 3288052 3288107 "UPSCAT" 3289187 NIL UPSCAT (NIL T T) -9 NIL 3289953 NIL) (-1275 3283770 3284025 3284352 "UPSCAT-" 3284357 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3267904 3276897 3276940 "UPOLYC" 3279041 NIL UPOLYC (NIL T) -9 NIL 3280262 NIL) (-1273 3258752 3261658 3264805 "UPOLYC-" 3264810 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3258373 3258422 3258555 "UPOLYC2" 3258703 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1271 3248948 3258056 3258185 "UP" 3258292 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1270 3248269 3248394 3248558 "UPMP" 3248837 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1269 3247816 3247903 3248042 "UPDIVP" 3248182 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1268 3246354 3246633 3246949 "UPDECOMP" 3247565 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1267 3245567 3245697 3245883 "UPCDEN" 3246238 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1266 3245080 3245155 3245304 "UP2" 3245492 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1265 3243433 3244284 3244561 "UNISEG" 3244838 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3242638 3242775 3242980 "UNISEG2" 3243276 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1263 3241680 3241878 3242104 "UNIFACT" 3242454 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3223490 3240992 3241234 "ULS" 3241496 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3210200 3223394 3223466 "ULSCONS" 3223471 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3190000 3203280 3203342 "ULSCCAT" 3203980 NIL ULSCCAT (NIL T T) -9 NIL 3204269 NIL) (-1259 3188996 3189295 3189683 "ULSCCAT-" 3189688 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1258 3177441 3184542 3184585 "ULSCAT" 3185448 NIL ULSCAT (NIL T) -9 NIL 3186179 NIL) (-1257 3176865 3176950 3177129 "ULS2" 3177356 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3175780 3176480 3176594 "UINT8" 3176705 T UINT8 (NIL) -8 NIL NIL 3176797) (-1255 3174694 3175394 3175508 "UINT64" 3175619 T UINT64 (NIL) -8 NIL NIL 3175711) (-1254 3173608 3174308 3174422 "UINT32" 3174533 T UINT32 (NIL) -8 NIL NIL 3174625) (-1253 3172522 3173222 3173336 "UINT16" 3173447 T UINT16 (NIL) -8 NIL NIL 3173539) (-1252 3170601 3171768 3171798 "UFD" 3172010 T UFD (NIL) -9 NIL 3172124 NIL) (-1251 3170383 3170441 3170536 "UFD-" 3170541 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3169441 3169648 3169864 "UDVO" 3170189 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3167207 3167666 3168137 "UDPO" 3169005 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167140 3167145 3167175 "TYPE" 3167180 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3166852 3167095 3167126 "TYPEAST" 3167131 T TYPEAST (NIL) -8 NIL NIL NIL) (-1246 3165805 3166025 3166265 "TWOFACT" 3166646 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3164780 3165214 3165449 "TUPLE" 3165605 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3162417 3162990 3163529 "TUBETOOL" 3164263 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3161223 3161464 3161706 "TUBE" 3162210 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3155402 3160195 3160478 "TS" 3160975 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3143544 3148159 3148256 "TSETCAT" 3153525 NIL TSETCAT (NIL T T T T) -9 NIL 3155057 NIL) (-1240 3138012 3139876 3141767 "TSETCAT-" 3141772 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3132485 3133498 3134427 "TRMANIP" 3137148 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3131914 3131989 3132152 "TRIMAT" 3132417 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3129726 3130017 3130374 "TRIGMNIP" 3131663 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3129210 3129359 3129389 "TRIGCAT" 3129602 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3128855 3128958 3129099 "TRIGCAT-" 3129104 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3125469 3127713 3127994 "TREE" 3128609 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3124575 3125271 3125301 "TRANFUN" 3125336 T TRANFUN (NIL) -9 NIL 3125402 NIL) (-1232 3123794 3124045 3124325 "TRANFUN-" 3124330 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3123592 3123630 3123691 "TOPSP" 3123755 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3122922 3123055 3123209 "TOOLSIGN" 3123473 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3121436 3122099 3122338 "TEXTFILE" 3122705 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3119240 3119889 3120318 "TEX" 3121029 T TEX (NIL) -8 NIL NIL NIL) (-1227 3119015 3119052 3119124 "TEX1" 3119203 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3118651 3118726 3118816 "TEMUTL" 3118947 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3116745 3117085 3117410 "TBCMPPK" 3118374 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108072 3114831 3114887 "TBAGG" 3115287 NIL TBAGG (NIL T T) -9 NIL 3115498 NIL) (-1223 3102956 3104630 3106384 "TBAGG-" 3106389 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3102322 3102447 3102592 "TANEXP" 3102845 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3101773 3102097 3102187 "TALGOP" 3102267 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3094787 3101630 3101723 "TABLE" 3101728 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3094181 3094298 3094436 "TABLEAU" 3094684 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3088711 3090009 3091257 "TABLBUMP" 3092967 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3087921 3088080 3088261 "SYSTEM" 3088552 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3084326 3085079 3085862 "SYSSOLP" 3087172 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084088 3084281 3084312 "SYSPTR" 3084317 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3082923 3083615 3083741 "SYSNNI" 3083927 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084019) (-1213 3082126 3082681 3082760 "SYSINT" 3082820 NIL SYSINT (NIL NIL) -8 NIL NIL 3082865) (-1212 3078224 3079404 3080114 "SYNTAX" 3081438 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3075304 3075984 3076616 "SYMTAB" 3077614 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3070403 3071455 3072438 "SYMS" 3074343 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3067302 3069854 3070087 "SYMPOLY" 3070205 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3066807 3066894 3067017 "SYMFUNC" 3067214 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3062605 3064119 3064932 "SYMBOL" 3066016 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056078 3057833 3059553 "SWITCH" 3060907 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3048832 3055034 3055328 "SUTS" 3055842 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3040310 3048214 3048478 "SUPXS" 3048626 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3030833 3039928 3040054 "SUP" 3040219 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3029980 3030119 3030336 "SUPFRACF" 3030701 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3029595 3029660 3029773 "SUP2" 3029915 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3028019 3028317 3028673 "SUMRF" 3029294 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3027342 3027420 3027612 "SUMFS" 3027940 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3009187 3026654 3026896 "SULS" 3027158 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3008735 3009009 3009079 "SUCHTAST" 3009139 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3007976 3008260 3008400 "SUCH" 3008643 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3001615 3002882 3003841 "SUBSPACE" 3007064 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001035 3001135 3001299 "SUBRESP" 3001503 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2994229 2995700 2997011 "STTF" 2999771 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2988240 2989522 2990669 "STTFNC" 2993129 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2979357 2981422 2983216 "STTAYLOR" 2986481 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972111 2979221 2979304 "STRTBL" 2979309 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2966508 2971820 2971919 "STRING" 2972034 T STRING (NIL) -8 NIL NIL NIL) (-1188 2958618 2964127 2964738 "STREAM" 2965932 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1187 2958122 2958205 2958349 "STREAM3" 2958535 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2957086 2957287 2957522 "STREAM2" 2957935 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2956768 2956826 2956919 "STREAM1" 2957028 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2955760 2955965 2956196 "STINPROD" 2956584 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955256 2955508 2955538 "STEP" 2955618 T STEP (NIL) -9 NIL 2955696 NIL) (-1182 2954371 2954745 2954893 "STEPAST" 2955130 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2947427 2954270 2954347 "STBL" 2954352 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2941985 2946590 2946633 "STAGG" 2946786 NIL STAGG (NIL T) -9 NIL 2946875 NIL) (-1179 2939537 2940289 2941161 "STAGG-" 2941166 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2937509 2939307 2939399 "STACK" 2939480 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2929516 2935650 2936106 "SREGSET" 2937139 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2921863 2923310 2924823 "SRDCMPK" 2928122 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2914172 2919222 2919252 "SRAGG" 2920555 T SRAGG (NIL) -9 NIL 2921163 NIL) (-1174 2913123 2913444 2913823 "SRAGG-" 2913828 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2906707 2912070 2912491 "SQMATRIX" 2912749 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900119 2903425 2904152 "SPLTREE" 2906052 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2895944 2896775 2897421 "SPLNODE" 2899545 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2894919 2895224 2895254 "SPFCAT" 2895698 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2893614 2893866 2894130 "SPECOUT" 2894677 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2884260 2886578 2886608 "SPADXPT" 2891286 T SPADXPT (NIL) -9 NIL 2893452 NIL) (-1167 2884015 2884061 2884130 "SPADPRSR" 2884213 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2881618 2883970 2884001 "SPADAST" 2884006 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2873219 2875322 2875365 "SPACEC" 2879738 NIL SPACEC (NIL T) -9 NIL 2881554 NIL) (-1164 2871019 2873151 2873200 "SPACE3" 2873205 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2869751 2869942 2870233 "SORTPAK" 2870824 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2867813 2868146 2868558 "SOLVETRA" 2869415 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2866851 2867085 2867346 "SOLVESER" 2867586 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862083 2863043 2864038 "SOLVERAD" 2865903 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2857808 2858507 2859236 "SOLVEFOR" 2861450 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2851419 2857156 2857253 "SNTSCAT" 2857258 NIL SNTSCAT (NIL T T T T) -9 NIL 2857328 NIL) (-1157 2844963 2849742 2850133 "SMTS" 2851109 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2838678 2844851 2844928 "SMP" 2844933 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2836807 2837138 2837536 "SMITH" 2838375 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2828339 2833386 2833489 "SMATCAT" 2834840 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835390 NIL) (-1153 2825111 2826102 2827280 "SMATCAT-" 2827285 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2822580 2824319 2824362 "SKAGG" 2824623 NIL SKAGG (NIL T) -9 NIL 2824758 NIL) (-1151 2818074 2822053 2822237 "SINT" 2822389 T SINT (NIL) -8 NIL NIL 2822551) (-1150 2817840 2817884 2817950 "SIMPAN" 2818030 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817065 2817375 2817515 "SIG" 2817722 T SIG (NIL) -8 NIL NIL NIL) (-1148 2815885 2816124 2816399 "SIGNRF" 2816824 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1147 2814700 2814869 2815153 "SIGNEF" 2815714 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1146 2813940 2814283 2814407 "SIGAST" 2814598 T SIGAST (NIL) -8 NIL NIL NIL) (-1145 2811592 2812084 2812590 "SHP" 2813481 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2804965 2811493 2811569 "SHDP" 2811574 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2804476 2804716 2804746 "SGROUP" 2804839 T SGROUP (NIL) -9 NIL 2804901 NIL) (-1142 2804328 2804360 2804433 "SGROUP-" 2804438 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801047 2801817 2802540 "SGCF" 2803627 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2794756 2800493 2800590 "SFRTCAT" 2800595 NIL SFRTCAT (NIL T T T T) -9 NIL 2800634 NIL) (-1139 2788075 2789195 2790331 "SFRGCD" 2793739 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781093 2782274 2783460 "SFQCMPK" 2787008 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2780695 2780802 2780913 "SFORT" 2781034 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2779621 2780535 2780656 "SEXOF" 2780661 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2778536 2779502 2779570 "SEX" 2779575 T SEX (NIL) -8 NIL NIL NIL) (-1134 2774125 2775032 2775127 "SEXCAT" 2777749 NIL SEXCAT (NIL T T T T T) -9 NIL 2778309 NIL) (-1133 2770934 2774059 2774107 "SET" 2774112 NIL SET (NIL T) -8 NIL NIL NIL) (-1132 2769056 2769647 2769952 "SETMN" 2770675 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1131 2768586 2768774 2768804 "SETCAT" 2768921 T SETCAT (NIL) -9 NIL 2769006 NIL) (-1130 2768354 2768418 2768517 "SETCAT-" 2768522 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1129 2764457 2766815 2766858 "SETAGG" 2767728 NIL SETAGG (NIL T) -9 NIL 2768068 NIL) (-1128 2763879 2764031 2764268 "SETAGG-" 2764273 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1127 2763262 2763575 2763676 "SEQAST" 2763800 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2762389 2762755 2762816 "SEGXCAT" 2763102 NIL SEGXCAT (NIL T T) -9 NIL 2763222 NIL) (-1125 2761305 2762055 2762237 "SEG" 2762242 NIL SEG (NIL T) -8 NIL NIL NIL) (-1124 2760230 2760498 2760541 "SEGCAT" 2761063 NIL SEGCAT (NIL T) -9 NIL 2761284 NIL) (-1123 2759120 2759593 2759801 "SEGBIND" 2760057 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2758735 2758800 2758913 "SEGBIND2" 2759055 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2758254 2758536 2758613 "SEGAST" 2758680 T SEGAST (NIL) -8 NIL NIL NIL) (-1120 2757463 2757599 2757803 "SEG2" 2758098 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1119 2756696 2757398 2757445 "SDVAR" 2757450 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748047 2756466 2756596 "SDPOL" 2756601 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2746616 2746906 2747225 "SCPKG" 2747762 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2745738 2745952 2746144 "SCOPE" 2746446 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2744934 2745092 2745271 "SCACHE" 2745593 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2744518 2744752 2744782 "SASTCAT" 2744787 T SASTCAT (NIL) -9 NIL 2744800 NIL) (-1113 2743921 2744353 2744429 "SAOS" 2744464 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2743480 2743521 2743694 "SAERFFC" 2743880 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2736507 2743377 2743457 "SAE" 2743462 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2736094 2736135 2736294 "SAEFACT" 2736466 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1109 2734397 2734729 2735130 "RURPK" 2735760 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2732974 2733340 2733645 "RULESET" 2734231 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2730089 2730727 2731185 "RULE" 2732655 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2729659 2729883 2729966 "RULECOLD" 2730041 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1105 2729443 2729477 2729548 "RTVALUE" 2729610 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2728854 2729160 2729254 "RSTRCAST" 2729371 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2723624 2724497 2725417 "RSETGCD" 2728053 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2712195 2717932 2718029 "RSETCAT" 2722148 NIL RSETCAT (NIL T T T T) -9 NIL 2723245 NIL) (-1101 2710014 2710661 2711485 "RSETCAT-" 2711490 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2702322 2703776 2705296 "RSDCMPK" 2708613 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2700191 2700754 2700828 "RRCC" 2701914 NIL RRCC (NIL T T) -9 NIL 2702258 NIL) (-1098 2699512 2699716 2699995 "RRCC-" 2700000 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2698895 2699208 2699309 "RPTAST" 2699433 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2671281 2682007 2682074 "RPOLCAT" 2692740 NIL RPOLCAT (NIL T T T) -9 NIL 2695900 NIL) (-1095 2662251 2665119 2668241 "RPOLCAT-" 2668246 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2652704 2660462 2660944 "ROUTINE" 2661791 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2648753 2652330 2652470 "ROMAN" 2652586 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2646865 2647613 2647873 "ROIRC" 2648558 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2642583 2645354 2645384 "RNS" 2645688 T RNS (NIL) -9 NIL 2645962 NIL) (-1090 2640990 2641475 2642009 "RNS-" 2642084 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640283 2640787 2640817 "RNG" 2640822 T RNG (NIL) -9 NIL 2640843 NIL) (-1088 2639244 2639648 2639850 "RNGBIND" 2640134 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1087 2638539 2639017 2639060 "RMODULE" 2639065 NIL RMODULE (NIL T) -9 NIL 2639092 NIL) (-1086 2637363 2637469 2637805 "RMCAT2" 2638440 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2633865 2636709 2637006 "RMATRIX" 2637125 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2626364 2628952 2629067 "RMATCAT" 2632426 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633408 NIL) (-1083 2625703 2625886 2626193 "RMATCAT-" 2626198 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2625276 2625490 2625533 "RLINSET" 2625595 NIL RLINSET (NIL T) -9 NIL 2625639 NIL) (-1081 2624837 2624918 2625046 "RINTERP" 2625195 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2623761 2624435 2624465 "RING" 2624521 T RING (NIL) -9 NIL 2624613 NIL) (-1079 2623541 2623597 2623694 "RING-" 2623699 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2622352 2622619 2622877 "RIDIST" 2623305 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2612977 2621820 2622026 "RGCHAIN" 2622200 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2612235 2612719 2612760 "RGBCSPC" 2612818 NIL RGBCSPC (NIL T) -9 NIL 2612870 NIL) (-1075 2611301 2611760 2611801 "RGBCMDL" 2612033 NIL RGBCMDL (NIL T) -9 NIL 2612147 NIL) (-1074 2608241 2608909 2609579 "RF" 2610665 NIL RF (NIL T) -7 NIL NIL NIL) (-1073 2607881 2607950 2608053 "RFFACTOR" 2608172 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1072 2607600 2607641 2607738 "RFFACT" 2607840 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1071 2605651 2606081 2606463 "RFDIST" 2607240 T RFDIST (NIL) -7 NIL NIL NIL) (-1070 2605098 2605196 2605359 "RETSOL" 2605553 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2604716 2604814 2604857 "RETRACT" 2604990 NIL RETRACT (NIL T) -9 NIL 2605077 NIL) (-1068 2604559 2604590 2604677 "RETRACT-" 2604682 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604107 2604381 2604451 "RETAST" 2604511 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2596457 2603760 2603887 "RESULT" 2604002 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2594892 2595726 2595925 "RESRING" 2596360 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2594516 2594577 2594675 "RESLATC" 2594829 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2594215 2594256 2594363 "REPSQ" 2594475 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2591595 2592217 2592819 "REP" 2593635 T REP (NIL) -7 NIL NIL NIL) (-1061 2591286 2591327 2591438 "REPDB" 2591554 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1060 2585118 2586575 2587798 "REP2" 2590098 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1059 2581421 2582176 2582984 "REP1" 2584345 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1058 2573429 2579562 2580018 "REGSET" 2581051 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572138 2572577 2572827 "REF" 2573214 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2571503 2571618 2571785 "REDORDER" 2572022 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2566867 2570716 2570943 "RECLOS" 2571331 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2565901 2566100 2566315 "REALSOLV" 2566674 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2565735 2565788 2565818 "REAL" 2565823 T REAL (NIL) -9 NIL 2565858 NIL) (-1052 2562182 2563020 2563904 "REAL0Q" 2564900 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1051 2557735 2558771 2559832 "REAL0" 2561163 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1050 2557146 2557452 2557546 "RDUCEAST" 2557663 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2556545 2556623 2556830 "RDIV" 2557068 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2555595 2555787 2556000 "RDIST" 2556367 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2554180 2554479 2554851 "RDETRS" 2555303 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2551974 2552446 2552984 "RDETR" 2553722 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2550593 2550877 2551274 "RDEEFS" 2551690 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549096 2549408 2549833 "RDEEF" 2550281 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2542573 2546050 2546080 "RCFIELD" 2547375 T RCFIELD (NIL) -9 NIL 2548106 NIL) (-1042 2540529 2541141 2541837 "RCFIELD-" 2541912 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2536581 2538602 2538645 "RCAGG" 2539729 NIL RCAGG (NIL T) -9 NIL 2540194 NIL) (-1040 2536191 2536303 2536466 "RCAGG-" 2536471 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2535508 2535638 2535803 "RATRET" 2536075 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535049 2535128 2535249 "RATFACT" 2535436 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2534327 2534477 2534629 "RANDSRC" 2534919 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534055 2534105 2534178 "RADUTIL" 2534276 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2526179 2532886 2533197 "RADIX" 2533778 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2515773 2526021 2526151 "RADFF" 2526156 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2515402 2515495 2515525 "RADCAT" 2515685 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2515172 2515232 2515332 "RADCAT-" 2515337 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513083 2514942 2515034 "QUEUE" 2515115 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2508922 2513016 2513064 "QUAT" 2513069 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1029 2508547 2508596 2508727 "QUATCT2" 2508873 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1028 2500923 2504970 2505012 "QUATCAT" 2505803 NIL QUATCAT (NIL T) -9 NIL 2506569 NIL) (-1027 2496804 2498099 2499489 "QUATCAT-" 2499585 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1026 2494060 2495852 2495895 "QUAGG" 2496276 NIL QUAGG (NIL T) -9 NIL 2496451 NIL) (-1025 2493608 2493882 2493952 "QQUTAST" 2494012 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2492519 2493121 2493286 "QFORM" 2493489 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2482195 2488366 2488408 "QFCAT" 2489076 NIL QFCAT (NIL T) -9 NIL 2490077 NIL) (-1022 2477510 2478963 2480557 "QFCAT-" 2480653 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477135 2477184 2477315 "QFCAT2" 2477461 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2476566 2476700 2476832 "QEQUAT" 2477025 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2469584 2470765 2471951 "QCMPACK" 2475499 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2467034 2467570 2468000 "QALGSET" 2469239 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2466263 2466445 2466681 "QALGSET2" 2466852 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1016 2464930 2465172 2465491 "PWFFINTB" 2466036 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463075 2463273 2463629 "PUSHVAR" 2464744 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2458802 2460018 2460061 "PTRANFN" 2461972 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457139 2457484 2457808 "PTPACK" 2458513 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2456762 2456825 2456936 "PTFUNC2" 2457076 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2450687 2455551 2455594 "PTCAT" 2455894 NIL PTCAT (NIL T) -9 NIL 2456047 NIL) (-1010 2450336 2450377 2450503 "PSQFR" 2450646 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2448908 2449224 2449560 "PSEUDLIN" 2450034 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2435428 2438003 2440329 "PSETPK" 2446668 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428136 2431164 2431262 "PSETCAT" 2434303 NIL PSETCAT (NIL T T T T) -9 NIL 2435117 NIL) (-1006 2425861 2426603 2427427 "PSETCAT-" 2427432 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2425174 2425369 2425399 "PSCURVE" 2425671 T PSCURVE (NIL) -9 NIL 2425838 NIL) (-1004 2420890 2422664 2422731 "PSCAT" 2423583 NIL PSCAT (NIL T T T) -9 NIL 2423823 NIL) (-1003 2419884 2420166 2420569 "PSCAT-" 2420574 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418083 2418943 2419208 "PRTITION" 2419641 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2417494 2417800 2417894 "PRTDAST" 2418011 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2406338 2408760 2410950 "PRS" 2415356 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2403958 2405660 2405700 "PRQAGG" 2405883 NIL PRQAGG (NIL T) -9 NIL 2405985 NIL) (-998 2403137 2403586 2403614 "PROPLOG" 2403753 T PROPLOG (NIL) -9 NIL 2403868 NIL) (-997 2402735 2402798 2402921 "PROPFUN2" 2403060 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402032 2402171 2402343 "PROPFUN1" 2402596 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400011 2400779 2401076 "PROPFRML" 2401768 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2399456 2399587 2399715 "PROPERTY" 2399903 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2393344 2397622 2398442 "PRODUCT" 2398682 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2390302 2392802 2393036 "PR" 2393155 NIL PR (NIL T T) -8 NIL NIL NIL) (-991 2390092 2390130 2390189 "PRINT" 2390263 T PRINT (NIL) -7 NIL NIL NIL) (-990 2389408 2389549 2389701 "PRIMES" 2389972 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-989 2387455 2387874 2388340 "PRIMELT" 2388987 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-988 2387172 2387233 2387261 "PRIMCAT" 2387385 T PRIMCAT (NIL) -9 NIL NIL NIL) (-987 2382894 2387110 2387155 "PRIMARR" 2387160 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2381883 2382079 2382307 "PRIMARR2" 2382712 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2381520 2381582 2381693 "PREASSOC" 2381821 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-984 2380971 2381128 2381156 "PPCURVE" 2381361 T PPCURVE (NIL) -9 NIL 2381497 NIL) (-983 2380518 2380766 2380849 "PORTNUM" 2380908 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2377855 2378276 2378868 "POLYROOT" 2380099 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2371063 2377459 2377619 "POLY" 2377728 NIL POLY (NIL T) -8 NIL NIL NIL) (-980 2370440 2370504 2370738 "POLYLIFT" 2370999 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-979 2366661 2367164 2367793 "POLYCATQ" 2369985 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-978 2352309 2358408 2358473 "POLYCAT" 2361987 NIL POLYCAT (NIL T T T) -9 NIL 2363865 NIL) (-977 2345428 2347620 2350004 "POLYCAT-" 2350009 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-976 2345009 2345083 2345203 "POLY2UP" 2345354 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-975 2344635 2344698 2344807 "POLY2" 2344946 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-974 2343296 2343559 2343835 "POLUTIL" 2344409 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2341615 2341928 2342259 "POLTOPOL" 2343018 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2336611 2341549 2341596 "POINT" 2341601 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2334744 2335155 2335530 "PNTHEORY" 2336256 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333190 2333499 2333898 "PMTOOLS" 2334442 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2332777 2332861 2332978 "PMSYM" 2333106 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2332279 2332354 2332529 "PMQFCAT" 2332702 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2331622 2331744 2331900 "PMPRED" 2332156 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2331003 2331101 2331263 "PMPREDFS" 2331523 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-965 2329657 2329875 2330253 "PMPLCAT" 2330765 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329183 2329268 2329420 "PMLSAGG" 2329572 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2328650 2328732 2328914 "PMKERNEL" 2329101 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328261 2328342 2328455 "PMINS" 2328569 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2327697 2327772 2327981 "PMFS" 2328186 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2326913 2327043 2327248 "PMDOWN" 2327574 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326056 2326238 2326419 "PMASS" 2326752 T PMASS (NIL) -7 NIL NIL NIL) (-958 2325305 2325439 2325602 "PMASSFS" 2325943 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-957 2324954 2325028 2325122 "PLOTTOOL" 2325231 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2319375 2320765 2321913 "PLOT" 2323826 T PLOT (NIL) -8 NIL NIL NIL) (-955 2315027 2316221 2317143 "PLOT3D" 2318473 T PLOT3D (NIL) -8 NIL NIL NIL) (-954 2313915 2314116 2314351 "PLOT1" 2314831 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-953 2289090 2293981 2298832 "PLEQN" 2309181 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2288396 2288530 2288710 "PINTERP" 2288955 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2288083 2288136 2288239 "PINTERPA" 2288343 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-950 2287179 2287847 2287934 "PI" 2287974 T PI (NIL) -8 NIL NIL 2288041) (-949 2285264 2286437 2286465 "PID" 2286647 T PID (NIL) -9 NIL 2286781 NIL) (-948 2285009 2285052 2285127 "PICOERCE" 2285221 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-947 2284317 2284468 2284644 "PGROEB" 2284865 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2279756 2280715 2281621 "PGE" 2283431 T PGE (NIL) -7 NIL NIL NIL) (-945 2277837 2278126 2278492 "PGCD" 2279473 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277163 2277278 2277439 "PFRPAC" 2277721 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2273413 2275711 2276064 "PFR" 2276842 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2271766 2272046 2272371 "PFOTOOLS" 2273160 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270281 2270538 2270889 "PFOQ" 2271523 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2268764 2268994 2269350 "PFO" 2270065 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2264689 2268653 2268722 "PF" 2268727 NIL PF (NIL NIL) -8 NIL NIL NIL) (-938 2261767 2263280 2263308 "PFECAT" 2263893 T PFECAT (NIL) -9 NIL 2264277 NIL) (-937 2261194 2261366 2261580 "PFECAT-" 2261585 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-936 2259767 2260049 2260350 "PFBRU" 2260943 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-935 2257597 2257985 2258417 "PFBR" 2259418 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-934 2253399 2255106 2255754 "PERM" 2256982 NIL PERM (NIL T) -8 NIL NIL NIL) (-933 2248453 2249606 2250476 "PERMGRP" 2252562 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-932 2246365 2247477 2247518 "PERMCAT" 2247918 NIL PERMCAT (NIL T) -9 NIL 2248216 NIL) (-931 2246012 2246059 2246183 "PERMAN" 2246318 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-930 2243253 2245677 2245799 "PENDTREE" 2245923 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242134 2242397 2242438 "PDSPC" 2242971 NIL PDSPC (NIL T) -9 NIL 2243216 NIL) (-928 2241189 2241455 2241817 "PDSPC-" 2241822 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2239903 2240839 2240880 "PDRING" 2240885 NIL PDRING (NIL T) -9 NIL 2240913 NIL) (-926 2238646 2239408 2239462 "PDMOD" 2239467 NIL PDMOD (NIL T T) -9 NIL 2239571 NIL) (-925 2235813 2236639 2237307 "PDEPROB" 2237998 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2233322 2233862 2234417 "PDEPACK" 2235278 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232210 2232424 2232675 "PDECOMP" 2233121 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2229727 2230618 2230646 "PDECAT" 2231433 T PDECAT (NIL) -9 NIL 2232146 NIL) (-921 2229344 2229411 2229465 "PDDOM" 2229630 NIL PDDOM (NIL T T) -9 NIL 2229710 NIL) (-920 2229157 2229193 2229300 "PDDOM-" 2229305 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2228902 2228941 2229031 "PCOMP" 2229118 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2226942 2227703 2228000 "PBWLB" 2228631 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2219121 2221015 2222353 "PATTERN" 2225625 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-916 2218747 2218810 2218919 "PATTERN2" 2219058 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-915 2216456 2216892 2217349 "PATTERN1" 2218336 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-914 2213722 2214405 2214886 "PATRES" 2216021 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2213280 2213353 2213485 "PATRES2" 2213649 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-912 2211133 2211568 2211975 "PATMATCH" 2212947 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2210587 2210838 2210879 "PATMAB" 2210986 NIL PATMAB (NIL T) -9 NIL 2211069 NIL) (-910 2209033 2209441 2209699 "PATLRES" 2210392 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2208571 2208702 2208743 "PATAB" 2208748 NIL PATAB (NIL T) -9 NIL 2208920 NIL) (-908 2206711 2207148 2207571 "PARTPERM" 2208168 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2206320 2206395 2206497 "PARSURF" 2206642 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2205946 2206009 2206118 "PARSU2" 2206257 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2205704 2205750 2205817 "PARSER" 2205899 T PARSER (NIL) -7 NIL NIL NIL) (-904 2205313 2205388 2205490 "PARSCURV" 2205635 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2204939 2205002 2205111 "PARSC2" 2205250 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2204566 2204636 2204733 "PARPCURV" 2204875 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204192 2204255 2204364 "PARPC2" 2204503 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203181 2203565 2203747 "PARAMAST" 2204030 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2202689 2202787 2202906 "PAN2EXPR" 2203082 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2201382 2201810 2202038 "PALETTE" 2202481 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2199727 2200387 2200747 "PAIR" 2201068 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2192639 2198984 2199179 "PADICRC" 2199581 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2184875 2191983 2192168 "PADICRAT" 2192486 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182884 2184812 2184857 "PADIC" 2184862 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2179674 2181544 2181584 "PADICCT" 2182165 NIL PADICCT (NIL NIL) -9 NIL 2182447 NIL) (-892 2178619 2178831 2179099 "PADEPAC" 2179461 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2177819 2177964 2178170 "PADE" 2178481 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176052 2177027 2177307 "OWP" 2177623 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2175497 2175758 2175855 "OVERSET" 2175975 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2174417 2175102 2175274 "OVAR" 2175365 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2173657 2173802 2173963 "OUT" 2174276 T OUT (NIL) -7 NIL NIL NIL) (-886 2161893 2164766 2166966 "OUTFORM" 2171477 T OUTFORM (NIL) -8 NIL NIL NIL) (-885 2161175 2161490 2161617 "OUTBFILE" 2161786 T OUTBFILE (NIL) -8 NIL NIL NIL) (-884 2160452 2160647 2160675 "OUTBCON" 2160993 T OUTBCON (NIL) -9 NIL 2161159 NIL) (-883 2160035 2160165 2160322 "OUTBCON-" 2160327 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-882 2159331 2159764 2159853 "OSI" 2159966 T OSI (NIL) -8 NIL NIL NIL) (-881 2158750 2159172 2159200 "OSGROUP" 2159205 T OSGROUP (NIL) -9 NIL 2159227 NIL) (-880 2157461 2157722 2158007 "ORTHPOL" 2158497 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2154712 2157296 2157417 "OREUP" 2157422 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2151815 2154403 2154530 "ORESUP" 2154654 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2149315 2149843 2150404 "OREPCTO" 2151304 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2142693 2145188 2145229 "OREPCAT" 2147577 NIL OREPCAT (NIL T) -9 NIL 2148681 NIL) (-875 2139666 2140622 2141680 "OREPCAT-" 2141685 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2138859 2139136 2139164 "ORDTYPE" 2139473 T ORDTYPE (NIL) -9 NIL 2139636 NIL) (-873 2138160 2138376 2138631 "ORDTYPE-" 2138636 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2137516 2137899 2138057 "ORDSTRCT" 2138062 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137014 2137384 2137412 "ORDSET" 2137417 T ORDSET (NIL) -9 NIL 2137439 NIL) (-870 2135372 2136343 2136371 "ORDRING" 2136573 T ORDRING (NIL) -9 NIL 2136698 NIL) (-869 2134993 2135111 2135255 "ORDRING-" 2135260 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2134244 2134809 2134837 "ORDMON" 2134842 T ORDMON (NIL) -9 NIL 2134863 NIL) (-867 2133388 2133553 2133748 "ORDFUNS" 2134093 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2132603 2133118 2133146 "ORDFIN" 2133211 T ORDFIN (NIL) -9 NIL 2133285 NIL) (-865 2128950 2131189 2131598 "ORDCOMP" 2132227 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-864 2128204 2128343 2128529 "ORDCOMP2" 2128810 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2124725 2125695 2126509 "OPTPROB" 2127410 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2121467 2122166 2122870 "OPTPACK" 2124041 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119080 2119906 2119934 "OPTCAT" 2120753 T OPTCAT (NIL) -9 NIL 2121403 NIL) (-860 2118398 2118757 2118862 "OPSIG" 2118995 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118160 2118205 2118271 "OPQUERY" 2118352 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2115069 2116471 2116975 "OP" 2117689 NIL OP (NIL T) -8 NIL NIL NIL) (-857 2114375 2114655 2114696 "OPERCAT" 2114908 NIL OPERCAT (NIL T) -9 NIL 2115005 NIL) (-856 2114118 2114186 2114303 "OPERCAT-" 2114308 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-855 2110731 2112915 2113284 "ONECOMP" 2113782 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-854 2110024 2110151 2110325 "ONECOMP2" 2110603 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-853 2109425 2109549 2109679 "OMSERVER" 2109914 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2105939 2108865 2108905 "OMSAGG" 2108966 NIL OMSAGG (NIL T) -9 NIL 2109030 NIL) (-851 2104514 2104825 2105107 "OMPKG" 2105677 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103920 2104047 2104075 "OM" 2104374 T OM (NIL) -9 NIL NIL NIL) (-849 2102267 2103469 2103638 "OMLO" 2103801 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-848 2101203 2101374 2101594 "OMEXPR" 2102093 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-847 2100440 2100749 2100885 "OMERR" 2101087 T OMERR (NIL) -8 NIL NIL NIL) (-846 2099525 2099861 2100021 "OMERRK" 2100300 T OMERRK (NIL) -8 NIL NIL NIL) (-845 2098916 2099202 2099310 "OMENC" 2099437 T OMENC (NIL) -8 NIL NIL NIL) (-844 2092553 2093996 2095167 "OMDEV" 2097765 T OMDEV (NIL) -8 NIL NIL NIL) (-843 2091586 2091793 2091987 "OMCONN" 2092379 T OMCONN (NIL) -8 NIL NIL NIL) (-842 2089864 2091056 2091084 "OINTDOM" 2091089 T OINTDOM (NIL) -9 NIL 2091110 NIL) (-841 2086938 2088552 2088889 "OFMONOID" 2089559 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086172 2086875 2086920 "ODVAR" 2086925 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2083309 2085917 2086072 "ODR" 2086077 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2074714 2083085 2083211 "ODPOL" 2083216 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068057 2074586 2074691 "ODP" 2074696 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2066799 2067038 2067313 "ODETOOLS" 2067831 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2063742 2064424 2065140 "ODESYS" 2066132 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2058572 2059532 2060557 "ODERTRIC" 2062817 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2057992 2058080 2058274 "ODERED" 2058484 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2054844 2055428 2056105 "ODERAT" 2057415 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2051761 2052268 2052865 "ODEPRRIC" 2054373 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2049656 2050300 2050786 "ODEPROB" 2051295 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046122 2046661 2047308 "ODEPRIM" 2049135 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2045365 2045473 2045733 "ODEPAL" 2046014 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2041467 2042318 2043182 "ODEPACK" 2044521 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2040510 2040635 2040857 "ODEINT" 2041356 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2034575 2036036 2037483 "ODEIFTBL" 2039083 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2029925 2030759 2031711 "ODEEF" 2033734 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2029268 2029363 2029586 "ODECONST" 2029830 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2027331 2028040 2028068 "ODECAT" 2028673 T ODECAT (NIL) -9 NIL 2029204 NIL) (-821 2023824 2027036 2027158 "OCT" 2027241 NIL OCT (NIL T) -8 NIL NIL NIL) (-820 2023456 2023505 2023632 "OCTCT2" 2023775 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-819 2017725 2020499 2020539 "OC" 2021636 NIL OC (NIL T) -9 NIL 2022494 NIL) (-818 2014760 2015700 2016690 "OC-" 2016784 NIL OC- (NIL T T) -8 NIL NIL NIL) (-817 2013983 2014553 2014581 "OCAMON" 2014586 T OCAMON (NIL) -9 NIL 2014607 NIL) (-816 2013403 2013828 2013856 "OASGP" 2013861 T OASGP (NIL) -9 NIL 2013881 NIL) (-815 2012529 2013126 2013154 "OAMONS" 2013194 T OAMONS (NIL) -9 NIL 2013237 NIL) (-814 2011820 2012349 2012377 "OAMON" 2012382 T OAMON (NIL) -9 NIL 2012402 NIL) (-813 2010931 2011569 2011597 "OAGROUP" 2011602 T OAGROUP (NIL) -9 NIL 2011622 NIL) (-812 2010613 2010669 2010758 "NUMTUBE" 2010875 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004132 2005704 2007240 "NUMQUAD" 2009097 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1999852 2000876 2001901 "NUMODE" 2003127 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997133 1998073 1998101 "NUMINT" 1999024 T NUMINT (NIL) -9 NIL 1999788 NIL) (-808 1996045 1996278 1996496 "NUMFMT" 1996935 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982228 1985349 1987881 "NUMERIC" 1993552 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1975939 1981676 1981771 "NTSCAT" 1981776 NIL NTSCAT (NIL T T T T) -9 NIL 1981815 NIL) (-805 1975119 1975298 1975491 "NTPOLFN" 1975778 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1961880 1971944 1972756 "NSUP" 1974340 NIL NSUP (NIL T) -8 NIL NIL NIL) (-803 1961506 1961569 1961678 "NSUP2" 1961817 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-802 1950342 1961280 1961413 "NSMP" 1961418 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1948750 1949075 1949432 "NREP" 1950030 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947329 1947593 1947951 "NPCOEF" 1948493 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946377 1946510 1946726 "NORMRETR" 1947210 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944388 1944708 1945117 "NORMPK" 1946085 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944067 1944101 1944225 "NORMMA" 1944354 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1943831 1944024 1944053 "NONE" 1944058 T NONE (NIL) -8 NIL NIL NIL) (-795 1943614 1943649 1943718 "NONE1" 1943795 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-794 1943105 1943173 1943352 "NODE1" 1943546 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941197 1942228 1942483 "NNI" 1942830 T NNI (NIL) -8 NIL NIL 1943065) (-792 1939593 1939930 1940294 "NLINSOL" 1940865 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1935774 1936829 1937728 "NIPROB" 1938714 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934513 1934765 1935067 "NFINTBAS" 1935536 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1933597 1934163 1934204 "NETCLT" 1934376 NIL NETCLT (NIL T) -9 NIL 1934458 NIL) (-788 1932269 1932536 1932817 "NCODIV" 1933365 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932025 1932068 1932143 "NCNTFRAC" 1932226 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930181 1930569 1930989 "NCEP" 1931650 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1928844 1929791 1929819 "NASRING" 1929929 T NASRING (NIL) -9 NIL 1930009 NIL) (-784 1928627 1928683 1928777 "NASRING-" 1928782 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1927594 1928245 1928273 "NARNG" 1928390 T NARNG (NIL) -9 NIL 1928481 NIL) (-782 1927268 1927353 1927487 "NARNG-" 1927492 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926105 1926354 1926589 "NAGSP" 1927053 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917149 1919061 1920734 "NAGS" 1924452 T NAGS (NIL) -7 NIL NIL NIL) (-779 1915673 1916005 1916336 "NAGF07" 1916838 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910145 1911502 1912809 "NAGF04" 1914386 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903017 1904727 1906360 "NAGF02" 1908532 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898181 1899341 1900458 "NAGF01" 1901920 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1891761 1893375 1894960 "NAGE04" 1896616 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1882822 1885051 1887181 "NAGE02" 1889651 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1878715 1879722 1880686 "NAGE01" 1881878 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876492 1877044 1877602 "NAGD03" 1878177 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868188 1870170 1872124 "NAGD02" 1874558 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1861927 1863424 1864864 "NAGD01" 1866768 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858064 1858958 1859795 "NAGC06" 1861110 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856511 1856861 1857217 "NAGC05" 1857728 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1855875 1856006 1856150 "NAGC02" 1856387 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1854676 1855403 1855443 "NAALG" 1855522 NIL NAALG (NIL T) -9 NIL 1855583 NIL) (-765 1854505 1854540 1854630 "NAALG-" 1854635 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848377 1849563 1850750 "MULTSQFR" 1853401 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1847684 1847771 1847955 "MULTFACT" 1848289 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1839829 1844267 1844320 "MTSCAT" 1845390 NIL MTSCAT (NIL T T) -9 NIL 1845906 NIL) (-761 1839535 1839595 1839687 "MTHING" 1839769 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839321 1839360 1839420 "MSYSCMD" 1839495 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1835035 1838076 1838396 "MSET" 1839034 NIL MSET (NIL T) -8 NIL NIL NIL) (-758 1831780 1834596 1834637 "MSETAGG" 1834642 NIL MSETAGG (NIL T) -9 NIL 1834676 NIL) (-757 1827372 1829159 1829904 "MRING" 1831080 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1826932 1827005 1827136 "MRF2" 1827299 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826544 1826585 1826729 "MRATFAC" 1826891 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824114 1824451 1824882 "MPRFF" 1826249 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817441 1823968 1824065 "MPOLY" 1824070 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1816925 1816966 1817174 "MPCPF" 1817400 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816433 1816482 1816666 "MPC3" 1816876 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1815616 1815709 1815930 "MPC2" 1816348 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1813893 1814254 1814644 "MONOTOOL" 1815276 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813038 1813421 1813449 "MONOID" 1813668 T MONOID (NIL) -9 NIL 1813815 NIL) (-747 1812554 1812703 1812884 "MONOID-" 1812889 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801508 1808374 1808433 "MONOGEN" 1809107 NIL MONOGEN (NIL T T) -9 NIL 1809563 NIL) (-745 1798558 1799461 1800461 "MONOGEN-" 1800580 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797275 1797823 1797851 "MONADWU" 1798243 T MONADWU (NIL) -9 NIL 1798481 NIL) (-743 1796605 1796806 1797054 "MONADWU-" 1797059 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1795890 1796194 1796222 "MONAD" 1796429 T MONAD (NIL) -9 NIL 1796541 NIL) (-741 1795557 1795653 1795785 "MONAD-" 1795790 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1793696 1794470 1794749 "MOEBIUS" 1795310 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1792864 1793364 1793404 "MODULE" 1793409 NIL MODULE (NIL T) -9 NIL 1793448 NIL) (-738 1792402 1792528 1792718 "MODULE-" 1792723 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1789932 1790766 1791093 "MODRING" 1792226 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1786654 1788037 1788558 "MODOP" 1789461 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785140 1785721 1785998 "MODMONOM" 1786517 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1773880 1783431 1783845 "MODMON" 1784777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1770706 1772724 1773000 "MODFIELD" 1773755 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1769617 1769987 1770177 "MMLFORM" 1770536 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769137 1769186 1769365 "MMAP" 1769568 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767030 1767969 1768010 "MLO" 1768433 NIL MLO (NIL T) -9 NIL 1768675 NIL) (-729 1764378 1764912 1765514 "MLIFT" 1766511 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1763757 1763853 1764007 "MKUCFUNC" 1764289 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763350 1763426 1763549 "MKRECORD" 1763680 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762373 1762559 1762787 "MKFUNC" 1763161 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1761749 1761865 1762021 "MKFLCFN" 1762256 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761014 1761128 1761313 "MKBCFUNC" 1761642 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1756997 1760568 1760704 "MINT" 1760898 T MINT (NIL) -8 NIL NIL NIL) (-722 1755779 1756052 1756329 "MHROWRED" 1756752 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1750523 1754314 1754719 "MFLOAT" 1755394 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1749868 1749956 1750127 "MFINFACT" 1750435 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746147 1747031 1747915 "MESH" 1749004 T MESH (NIL) -7 NIL NIL NIL) (-718 1744501 1744849 1745202 "MDDFACT" 1745834 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741037 1743632 1743673 "MDAGG" 1743928 NIL MDAGG (NIL T) -9 NIL 1744071 NIL) (-716 1728739 1740330 1740537 "MCMPLX" 1740850 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1727858 1728022 1728223 "MCDEN" 1728588 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1725706 1726018 1726398 "MCALCFN" 1727588 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1724583 1724871 1725104 "MAYBE" 1725512 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722141 1722718 1723280 "MATSTOR" 1724054 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1717563 1721513 1721761 "MATRIX" 1721926 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713263 1714036 1714772 "MATLIN" 1716920 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1702609 1706320 1706397 "MATCAT" 1711429 NIL MATCAT (NIL T T T) -9 NIL 1712901 NIL) (-708 1698562 1699872 1701285 "MATCAT-" 1701290 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-707 1697138 1697309 1697642 "MATCAT2" 1698397 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1695214 1695574 1695958 "MAPPKG3" 1696813 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694171 1694368 1694590 "MAPPKG2" 1695038 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1692628 1692954 1693281 "MAPPKG1" 1693877 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1691629 1692034 1692211 "MAPPAST" 1692471 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691234 1691298 1691421 "MAPHACK3" 1691565 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1690814 1690887 1691001 "MAPHACK2" 1691166 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690240 1690355 1690497 "MAPHACK1" 1690705 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688163 1688940 1689244 "MAGMA" 1689968 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1687582 1687887 1687978 "MACROAST" 1688092 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1683825 1685821 1686282 "M3D" 1687154 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677305 1682136 1682177 "LZSTAGG" 1682959 NIL LZSTAGG (NIL T) -9 NIL 1683254 NIL) (-695 1672987 1674436 1675893 "LZSTAGG-" 1675898 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1669900 1670878 1671365 "LWORD" 1672532 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669422 1669704 1669779 "LSTAST" 1669845 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661350 1669193 1669327 "LSQM" 1669332 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1660568 1660713 1660941 "LSPP" 1661205 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658350 1658681 1659137 "LSMP" 1660257 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-689 1655087 1655803 1656533 "LSMP1" 1657652 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-688 1648223 1654177 1654218 "LSAGG" 1654280 NIL LSAGG (NIL T) -9 NIL 1654358 NIL) (-687 1644732 1645842 1647055 "LSAGG-" 1647060 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642027 1643876 1644125 "LPOLY" 1644527 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1641603 1641694 1641817 "LPEFRAC" 1641936 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1639780 1640697 1640950 "LO" 1641435 NIL LO (NIL T T T) -8 NIL NIL NIL) (-683 1639463 1639542 1639570 "LOGIC" 1639681 T LOGIC (NIL) -9 NIL 1639763 NIL) (-682 1639319 1639348 1639419 "LOGIC-" 1639424 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-681 1638494 1638652 1638845 "LODOOPS" 1639175 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-680 1635589 1638410 1638476 "LODO" 1638481 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-679 1634113 1634362 1634715 "LODOF" 1635336 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1629989 1632748 1632789 "LODOCAT" 1633227 NIL LODOCAT (NIL T) -9 NIL 1633438 NIL) (-677 1629704 1629780 1629907 "LODOCAT-" 1629912 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1626690 1629545 1629663 "LODO2" 1629668 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1623797 1626627 1626672 "LODO1" 1626677 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1622666 1622843 1623148 "LODEEF" 1623620 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-673 1617638 1620832 1620873 "LNAGG" 1621735 NIL LNAGG (NIL T) -9 NIL 1622170 NIL) (-672 1616731 1616999 1617341 "LNAGG-" 1617346 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1612711 1613656 1614295 "LMOPS" 1616146 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612010 1612488 1612529 "LMODULE" 1612534 NIL LMODULE (NIL T) -9 NIL 1612560 NIL) (-669 1608965 1611655 1611778 "LMDICT" 1611920 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608541 1608755 1608796 "LLINSET" 1608857 NIL LLINSET (NIL T) -9 NIL 1608901 NIL) (-667 1608186 1608449 1608509 "LITERAL" 1608514 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1600640 1607120 1607424 "LIST" 1607915 NIL LIST (NIL T) -8 NIL NIL NIL) (-665 1600159 1600239 1600378 "LIST3" 1600560 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-664 1599148 1599344 1599572 "LIST2" 1599977 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597246 1597594 1597993 "LIST2MAP" 1598795 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1596829 1597065 1597106 "LINSET" 1597111 NIL LINSET (NIL T) -9 NIL 1597145 NIL) (-661 1595643 1596337 1596504 "LINFORM" 1596714 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1593942 1594670 1594711 "LINEXP" 1595201 NIL LINEXP (NIL T) -9 NIL 1595474 NIL) (-659 1592518 1593422 1593603 "LINELT" 1593813 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591075 1591355 1591666 "LINDEP" 1592270 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590211 1590807 1590917 "LINBASIS" 1591005 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1586948 1587697 1588474 "LIMITRF" 1589466 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585233 1585547 1585956 "LIMITPS" 1586643 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1579253 1584744 1584972 "LIE" 1585054 NIL LIE (NIL T T) -8 NIL NIL NIL) (-653 1578081 1578656 1578696 "LIECAT" 1578836 NIL LIECAT (NIL T) -9 NIL 1578987 NIL) (-652 1577916 1577949 1578037 "LIECAT-" 1578042 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-651 1570103 1577456 1577612 "LIB" 1577780 T LIB (NIL) -8 NIL NIL NIL) (-650 1565672 1566621 1567556 "LGROBP" 1569220 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1563610 1563944 1564294 "LF" 1565393 NIL LF (NIL T T) -7 NIL NIL NIL) (-648 1562234 1563142 1563170 "LFCAT" 1563377 T LFCAT (NIL) -9 NIL 1563516 NIL) (-647 1559094 1559766 1560454 "LEXTRIPK" 1561598 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1555682 1556664 1557167 "LEXP" 1558674 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555098 1555403 1555495 "LETAST" 1555610 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553484 1553809 1554210 "LEADCDET" 1554780 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552662 1552748 1552977 "LAZM3PK" 1553405 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547173 1550739 1551277 "LAUPOL" 1552174 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1546746 1546796 1546957 "LAPLACE" 1547123 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1544483 1545847 1546098 "LA" 1546579 NIL LA (NIL T T T) -8 NIL NIL NIL) (-639 1543331 1544047 1544088 "LALG" 1544150 NIL LALG (NIL T) -9 NIL 1544209 NIL) (-638 1543027 1543104 1543240 "LALG-" 1543245 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-637 1542856 1542886 1542927 "KVTFROM" 1542989 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541613 1542223 1542408 "KTVLOGIC" 1542691 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541442 1541472 1541513 "KRCFROM" 1541575 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540334 1540533 1540832 "KOVACIC" 1541242 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540163 1540193 1540234 "KONVERT" 1540296 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1539992 1540022 1540063 "KOERCE" 1540125 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1537679 1538585 1538962 "KERNEL" 1539648 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-630 1537163 1537256 1537388 "KERNEL2" 1537593 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-629 1530634 1535640 1535694 "KDAGG" 1536071 NIL KDAGG (NIL T T) -9 NIL 1536277 NIL) (-628 1530145 1530287 1530492 "KDAGG-" 1530497 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1522845 1529806 1529961 "KAFILE" 1530023 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522449 1522734 1522797 "JVMOP" 1522802 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521185 1521689 1521938 "JVMMDACC" 1522220 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520121 1520575 1520780 "JVMFDACC" 1521000 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1518702 1519197 1519497 "JVMCSTTG" 1519841 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1517838 1518242 1518403 "JVMCFACC" 1518561 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517516 1517755 1517804 "JVMBCODE" 1517809 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511536 1517027 1517255 "JORDAN" 1517337 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1510849 1511185 1511306 "JOINAST" 1511435 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1506884 1509026 1509080 "IXAGG" 1510009 NIL IXAGG (NIL T T) -9 NIL 1510468 NIL) (-617 1505737 1506109 1506528 "IXAGG-" 1506533 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1500826 1505659 1505718 "IVECTOR" 1505723 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499550 1499829 1500095 "ITUPLE" 1500593 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498022 1498229 1498524 "ITRIGMNP" 1499372 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1496749 1496971 1497254 "ITFUN3" 1497798 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496375 1496438 1496547 "ITFUN2" 1496686 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1495480 1495855 1496029 "ITFORM" 1496221 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493249 1494500 1494778 "ITAYLOR" 1495235 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481646 1487386 1488549 "ISUPS" 1492119 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1480738 1480890 1481126 "ISUMP" 1481493 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475588 1480683 1480724 "ISTRING" 1480729 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475004 1475309 1475401 "ISAST" 1475516 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474201 1474295 1474511 "IRURPK" 1474918 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473113 1473338 1473578 "IRSN" 1473981 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471158 1471539 1471968 "IRRF2F" 1472751 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1470899 1470943 1471019 "IRREDFFX" 1471114 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469472 1469773 1470072 "IROOT" 1470632 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1465912 1467156 1467848 "IR" 1468812 NIL IR (NIL T) -8 NIL NIL NIL) (-599 1465051 1465405 1465556 "IRFORM" 1465781 T IRFORM (NIL) -8 NIL NIL NIL) (-598 1462640 1463159 1463725 "IR2" 1464529 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1461722 1461853 1462067 "IR2F" 1462523 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1461507 1461547 1461607 "IPRNTPK" 1461682 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457460 1461396 1461465 "IPF" 1461470 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455481 1457385 1457442 "IPADIC" 1457447 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1454739 1455041 1455171 "IP4ADDR" 1455371 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454077 1454368 1454500 "IOMODE" 1454627 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453048 1453674 1453801 "IOBFILE" 1453970 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452458 1452952 1452980 "IOBCON" 1452985 T IOBCON (NIL) -9 NIL 1453006 NIL) (-589 1451963 1452027 1452210 "INVLAPLA" 1452394 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441533 1443965 1446351 "INTTR" 1449627 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1437826 1438610 1439475 "INTTOOLS" 1440718 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437406 1437503 1437620 "INTSLPE" 1437729 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1434873 1437329 1437388 "INTRVL" 1437393 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432451 1432987 1433562 "INTRF" 1434358 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1431844 1431959 1432101 "INTRET" 1432349 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1429817 1430230 1430700 "INTRAT" 1431452 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427062 1427663 1428282 "INTPM" 1429302 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1423779 1424406 1425144 "INTPAF" 1426448 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1418880 1419920 1420971 "INTPACK" 1422748 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1415068 1418677 1418786 "INT" 1418791 T INT (NIL) -8 NIL NIL NIL) (-577 1414314 1414472 1414680 "INTHERTR" 1414910 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-576 1413747 1413833 1414021 "INTHERAL" 1414228 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-575 1411515 1412036 1412493 "INTHEORY" 1413310 T INTHEORY (NIL) -7 NIL NIL NIL) (-574 1402847 1404542 1406314 "INTG0" 1409867 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-573 1383372 1388210 1393020 "INTFTBL" 1398057 T INTFTBL (NIL) -8 NIL NIL NIL) (-572 1382597 1382759 1382932 "INTFACT" 1383231 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-571 1379994 1380470 1381027 "INTEF" 1382151 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-570 1378191 1379086 1379114 "INTDOM" 1379415 T INTDOM (NIL) -9 NIL 1379622 NIL) (-569 1377530 1377734 1377976 "INTDOM-" 1377981 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-568 1373404 1375819 1375873 "INTCAT" 1376672 NIL INTCAT (NIL T) -9 NIL 1376993 NIL) (-567 1372858 1372979 1373107 "INTBIT" 1373296 T INTBIT (NIL) -7 NIL NIL NIL) (-566 1371539 1371711 1372018 "INTALG" 1372703 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-565 1371016 1371112 1371269 "INTAF" 1371443 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-564 1363983 1370826 1370966 "INTABL" 1370971 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-563 1363220 1363782 1363847 "INT8" 1363881 T INT8 (NIL) -8 NIL NIL 1363926) (-562 1362456 1363018 1363083 "INT64" 1363117 T INT64 (NIL) -8 NIL NIL 1363162) (-561 1361692 1362254 1362319 "INT32" 1362353 T INT32 (NIL) -8 NIL NIL 1362398) (-560 1360928 1361490 1361555 "INT16" 1361589 T INT16 (NIL) -8 NIL NIL 1361634) (-559 1355029 1358476 1358504 "INS" 1359438 T INS (NIL) -9 NIL 1360103 NIL) (-558 1352083 1353040 1354014 "INS-" 1354087 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1350840 1351085 1351383 "INPSIGN" 1351836 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1349934 1350075 1350272 "INPRODPF" 1350720 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1348804 1348945 1349182 "INPRODFF" 1349814 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1347792 1347956 1348216 "INNMFACT" 1348640 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1346971 1347086 1347274 "INMODGCD" 1347691 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345455 1345724 1346048 "INFSP" 1346716 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1344615 1344756 1344939 "INFPROD0" 1345335 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1341182 1342680 1343195 "INFORM" 1344108 T INFORM (NIL) -8 NIL NIL NIL) (-549 1340780 1340852 1340950 "INFORM1" 1341117 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-548 1340285 1340392 1340506 "INFINITY" 1340686 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339359 1340005 1340106 "INETCLTS" 1340204 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1337957 1338225 1338546 "INEP" 1339107 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337018 1337854 1337919 "INDE" 1337924 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1336570 1336650 1336767 "INCRMAPS" 1336945 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335292 1335839 1336045 "INBFILE" 1336384 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330471 1331528 1332472 "INBFF" 1334380 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329325 1329648 1329676 "INBCON" 1330189 T INBCON (NIL) -9 NIL 1330455 NIL) (-540 1328535 1328800 1329076 "INBCON-" 1329081 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1327954 1328259 1328350 "INAST" 1328464 T INAST (NIL) -8 NIL NIL NIL) (-538 1327321 1327633 1327739 "IMPTAST" 1327868 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323242 1327165 1327269 "IMATRIX" 1327274 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1321934 1322073 1322389 "IMATQF" 1323098 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320114 1320381 1320718 "IMATLIN" 1321690 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314029 1320038 1320096 "ILIST" 1320101 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1311695 1313889 1314002 "IIARRAY2" 1314007 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306495 1311606 1311670 "IFF" 1311675 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1305776 1306112 1306228 "IFAST" 1306399 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300288 1305068 1305256 "IFARRAY" 1305633 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299326 1300192 1300265 "IFAMON" 1300270 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1298898 1298975 1299029 "IEVALAB" 1299236 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1298561 1298641 1298801 "IEVALAB-" 1298806 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1297942 1298476 1298538 "IDPO" 1298543 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-525 1297006 1297831 1297906 "IDPOAMS" 1297911 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-524 1296139 1296895 1296970 "IDPOAM" 1296975 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-523 1294619 1295146 1295198 "IDPC" 1295710 NIL IDPC (NIL T T) -9 NIL 1295991 NIL) (-522 1293951 1294511 1294584 "IDPAM" 1294589 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293166 1293843 1293916 "IDPAG" 1293921 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1292710 1292972 1293062 "IDENT" 1293096 T IDENT (NIL) -8 NIL NIL NIL) (-519 1288929 1289813 1290708 "IDECOMP" 1291867 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281564 1282852 1283899 "IDEAL" 1287965 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1280706 1280836 1281036 "ICDEN" 1281448 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1279681 1280186 1280333 "ICARD" 1280579 T ICARD (NIL) -8 NIL NIL NIL) (-515 1277711 1278054 1278459 "IBPTOOLS" 1279358 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1272826 1277331 1277444 "IBITS" 1277630 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269501 1270125 1270820 "IBATOOL" 1272243 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267262 1267742 1268275 "IBACHIN" 1269036 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1264852 1267108 1267211 "IARRAY2" 1267216 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260565 1264778 1264835 "IARRAY1" 1264840 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1253575 1258977 1259458 "IAN" 1260104 T IAN (NIL) -8 NIL NIL NIL) (-508 1253080 1253143 1253316 "IALGFACT" 1253512 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1252572 1252721 1252749 "HYPCAT" 1252956 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252074 1252227 1252413 "HYPCAT-" 1252418 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1251621 1251869 1251952 "HOSTNAME" 1252011 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251454 1251503 1251544 "HOMOTOP" 1251549 NIL HOMOTOP (NIL T) -9 NIL 1251582 NIL) (-503 1247887 1249386 1249427 "HOAGG" 1250408 NIL HOAGG (NIL T) -9 NIL 1251137 NIL) (-502 1246403 1246880 1247406 "HOAGG-" 1247411 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239439 1245996 1246146 "HEXADEC" 1246273 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238151 1238409 1238672 "HEUGCD" 1239216 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237083 1237988 1238118 "HELLFDIV" 1238123 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235093 1236860 1236948 "HEAP" 1237027 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234290 1234645 1234779 "HEADAST" 1234979 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1227677 1234205 1234267 "HDP" 1234272 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1220689 1227312 1227464 "HDMP" 1227578 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1219995 1220153 1220317 "HB" 1220545 T HB (NIL) -7 NIL NIL NIL) (-493 1213005 1219841 1219945 "HASHTBL" 1219950 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212421 1212726 1212818 "HASAST" 1212933 T HASAST (NIL) -8 NIL NIL NIL) (-491 1209827 1212043 1212225 "HACKPI" 1212259 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1204999 1209680 1209793 "GTSET" 1209798 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198038 1204877 1204975 "GSTBL" 1204980 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1189787 1197203 1197459 "GSERIES" 1197838 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1188818 1189331 1189359 "GROUP" 1189562 T GROUP (NIL) -9 NIL 1189696 NIL) (-486 1188142 1188343 1188594 "GROUP-" 1188599 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186491 1186830 1187217 "GROEBSOL" 1187819 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185319 1185679 1185730 "GRMOD" 1186259 NIL GRMOD (NIL T T) -9 NIL 1186427 NIL) (-483 1185075 1185123 1185251 "GRMOD-" 1185256 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180215 1181429 1182429 "GRIMAGE" 1184095 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1178609 1178942 1179266 "GRDEF" 1179911 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178041 1178169 1178310 "GRAY" 1178488 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177118 1177620 1177671 "GRALG" 1177824 NIL GRALG (NIL T T) -9 NIL 1177917 NIL) (-478 1176755 1176852 1177015 "GRALG-" 1177020 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173236 1176338 1176517 "GPOLSET" 1176661 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1172584 1172647 1172905 "GOSPER" 1173173 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168154 1169022 1169548 "GMODPOL" 1172283 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167141 1167343 1167581 "GHENSEL" 1167966 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161213 1162140 1163160 "GENUPS" 1166225 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1160904 1160961 1161050 "GENUFACT" 1161156 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160304 1160393 1160558 "GENPGCD" 1160822 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1159772 1159813 1160026 "GENMFACT" 1160263 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158308 1158595 1158902 "GENEEZ" 1159515 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151480 1157919 1158081 "GDMP" 1158231 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140219 1145251 1146357 "GCNAALG" 1150463 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138346 1139394 1139422 "GCDDOM" 1139677 T GCDDOM (NIL) -9 NIL 1139834 NIL) (-465 1137786 1137943 1138158 "GCDDOM-" 1138163 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1136436 1136643 1136947 "GB" 1137565 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-463 1124908 1127382 1129774 "GBINTERN" 1134127 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-462 1122709 1123037 1123458 "GBF" 1124583 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-461 1121466 1121655 1121922 "GBEUCLID" 1122525 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-460 1120797 1120940 1121089 "GAUSSFAC" 1121337 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119118 1119466 1119780 "GALUTIL" 1120516 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117378 1117700 1118024 "GALPOLYU" 1118845 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1114677 1115033 1115440 "GALFACTU" 1117075 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106291 1107982 1109590 "GALFACT" 1113109 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1103577 1104337 1104365 "FVFUN" 1105521 T FVFUN (NIL) -9 NIL 1106241 NIL) (-454 1102807 1103025 1103053 "FVC" 1103344 T FVC (NIL) -9 NIL 1103527 NIL) (-453 1102408 1102632 1102700 "FUNDESC" 1102759 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1101981 1102205 1102286 "FUNCTION" 1102360 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1099611 1100303 1100769 "FT" 1101535 T FT (NIL) -8 NIL NIL NIL) (-450 1098288 1098912 1099115 "FTEM" 1099428 T FTEM (NIL) -8 NIL NIL NIL) (-449 1096557 1096868 1097265 "FSUPFACT" 1097979 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1094876 1095243 1095575 "FST" 1096245 T FST (NIL) -8 NIL NIL NIL) (-447 1094057 1094181 1094369 "FSRED" 1094758 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1092746 1093012 1093359 "FSPRMELT" 1093772 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1089956 1090490 1090976 "FSPECF" 1092309 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1070183 1079730 1079771 "FS" 1083655 NIL FS (NIL T) -9 NIL 1085944 NIL) (-443 1058244 1061819 1065876 "FS-" 1066176 NIL FS- (NIL T T) -8 NIL NIL NIL) (-442 1057766 1057826 1057996 "FSINT" 1058185 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1055902 1056759 1057062 "FSERIES" 1057545 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1054926 1055060 1055284 "FSCINT" 1055782 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1050790 1053870 1053911 "FSAGG" 1054281 NIL FSAGG (NIL T) -9 NIL 1054540 NIL) (-438 1048390 1049153 1049949 "FSAGG-" 1050044 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-437 1047414 1047575 1047802 "FSAGG2" 1048243 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-436 1045074 1045372 1045920 "FS2UPS" 1047132 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1044702 1044751 1044880 "FS2" 1045025 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-434 1043568 1043751 1044053 "FS2EXPXP" 1044527 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-433 1042982 1043109 1043261 "FRUTIL" 1043448 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1033899 1038477 1039835 "FR" 1041656 NIL FR (NIL T) -8 NIL NIL NIL) (-431 1028417 1031588 1031628 "FRNAALG" 1032948 NIL FRNAALG (NIL T) -9 NIL 1033546 NIL) (-430 1023898 1025166 1026441 "FRNAALG-" 1027191 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-429 1023530 1023579 1023706 "FRNAAF2" 1023849 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-428 1021817 1022379 1022675 "FRMOD" 1023342 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-427 1019422 1020192 1020510 "FRIDEAL" 1021608 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1018607 1018700 1018991 "FRIDEAL2" 1019329 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1017698 1018154 1018195 "FRETRCT" 1018200 NIL FRETRCT (NIL T) -9 NIL 1018376 NIL) (-424 1016756 1017041 1017392 "FRETRCT-" 1017397 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-423 1013570 1015040 1015099 "FRAMALG" 1015981 NIL FRAMALG (NIL T T) -9 NIL 1016273 NIL) (-422 1011608 1012159 1012789 "FRAMALG-" 1013012 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-421 1004579 1011081 1011358 "FRAC" 1011363 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1004209 1004272 1004379 "FRAC2" 1004516 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1003839 1003902 1004009 "FR2" 1004146 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-418 997756 1001218 1001246 "FPS" 1002365 T FPS (NIL) -9 NIL 1002922 NIL) (-417 997181 997314 997478 "FPS-" 997624 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994133 996138 996166 "FPC" 996391 T FPC (NIL) -9 NIL 996533 NIL) (-415 993914 993966 994063 "FPC-" 994068 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 992672 993402 993443 "FPATMAB" 993448 NIL FPATMAB (NIL T) -9 NIL 993600 NIL) (-413 990815 991414 991761 "FPARFRAC" 992388 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986107 986707 987389 "FORTRAN" 990247 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 983793 984323 984862 "FORT" 985588 T FORT (NIL) -7 NIL NIL NIL) (-410 981367 982031 982059 "FORTFN" 983119 T FORTFN (NIL) -9 NIL 983743 NIL) (-409 981119 981181 981209 "FORTCAT" 981268 T FORTCAT (NIL) -9 NIL 981330 NIL) (-408 979123 979735 980125 "FORMULA" 980749 T FORMULA (NIL) -8 NIL NIL NIL) (-407 978905 978941 979010 "FORMULA1" 979087 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-406 978422 978480 978653 "FORDER" 978847 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977482 977682 977875 "FOP" 978249 T FOP (NIL) -7 NIL NIL NIL) (-404 975895 976762 976936 "FNLA" 977364 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974514 975025 975053 "FNCAT" 975513 T FNCAT (NIL) -9 NIL 975773 NIL) (-402 973957 974473 974501 "FNAME" 974506 T FNAME (NIL) -8 NIL NIL NIL) (-401 972283 973456 973484 "FMTC" 973489 T FMTC (NIL) -9 NIL 973525 NIL) (-400 970831 972219 972265 "FMONOID" 972270 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967420 968786 968827 "FMONCAT" 970044 NIL FMONCAT (NIL T) -9 NIL 970649 NIL) (-398 966438 967162 967311 "FM" 967316 NIL FM (NIL T T) -8 NIL NIL NIL) (-397 963760 964508 964536 "FMFUN" 965680 T FMFUN (NIL) -9 NIL 966388 NIL) (-396 962993 963210 963238 "FMC" 963528 T FMC (NIL) -9 NIL 963710 NIL) (-395 959866 960918 960972 "FMCAT" 962167 NIL FMCAT (NIL T T) -9 NIL 962662 NIL) (-394 958534 959632 959732 "FM1" 959811 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-393 956272 956724 957218 "FLOATRP" 958085 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 948928 954001 954622 "FLOAT" 955671 T FLOAT (NIL) -8 NIL NIL NIL) (-391 946330 946866 947444 "FLOATCP" 948395 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-390 944848 945922 945963 "FLINEXP" 945968 NIL FLINEXP (NIL T) -9 NIL 946061 NIL) (-389 943978 944237 944565 "FLINEXP-" 944570 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943036 943198 943422 "FLASORT" 943830 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 939954 941006 941058 "FLALG" 942285 NIL FLALG (NIL T T) -9 NIL 942752 NIL) (-386 933218 937363 937404 "FLAGG" 938666 NIL FLAGG (NIL T) -9 NIL 939318 NIL) (-385 931872 932283 932773 "FLAGG-" 932778 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-384 930896 931057 931284 "FLAGG2" 931725 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-383 927527 928741 928800 "FINRALG" 929928 NIL FINRALG (NIL T T) -9 NIL 930436 NIL) (-382 926651 926916 927255 "FINRALG-" 927260 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 925957 926256 926284 "FINITE" 926480 T FINITE (NIL) -9 NIL 926587 NIL) (-380 917908 920487 920527 "FINAALG" 924194 NIL FINAALG (NIL T) -9 NIL 925647 NIL) (-379 913024 914290 915434 "FINAALG-" 916813 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912302 912779 912882 "FILE" 912954 NIL FILE (NIL T) -8 NIL NIL NIL) (-377 910862 911284 911338 "FILECAT" 912022 NIL FILECAT (NIL T T) -9 NIL 912238 NIL) (-376 908258 910092 910120 "FIELD" 910160 T FIELD (NIL) -9 NIL 910240 NIL) (-375 906800 907263 907774 "FIELD-" 907779 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904482 905435 905782 "FGROUP" 906486 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 903554 903736 903956 "FGLMICPK" 904314 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 898788 903479 903536 "FFX" 903541 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898383 898450 898585 "FFSLPE" 898721 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 894259 895155 895951 "FFPOLY" 897619 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-369 893757 893799 894008 "FFPOLY2" 894217 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-368 889005 893676 893739 "FFP" 893744 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 883805 888916 888980 "FF" 888985 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-366 878315 883148 883338 "FFNBX" 883659 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-365 872627 877450 877708 "FFNBP" 878169 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-364 866644 871911 872122 "FFNB" 872460 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-363 865464 865674 865989 "FFINTBAS" 866441 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-362 861040 863711 863739 "FFIELDC" 864359 T FFIELDC (NIL) -9 NIL 864735 NIL) (-361 859618 860073 860570 "FFIELDC-" 860575 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-360 859175 859233 859357 "FFHOM" 859560 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-359 856834 857357 857874 "FFF" 858690 NIL FFF (NIL T) -7 NIL NIL NIL) (-358 851848 856576 856677 "FFCGX" 856777 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-357 846866 851580 851687 "FFCGP" 851791 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-356 841445 846593 846701 "FFCG" 846802 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-355 820108 831177 831263 "FFCAT" 836428 NIL FFCAT (NIL T T T) -9 NIL 837879 NIL) (-354 815119 816353 817667 "FFCAT-" 818897 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 814524 814573 814808 "FFCAT2" 815070 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-352 803177 807496 808716 "FEXPR" 813376 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802105 802574 802615 "FEVALAB" 802699 NIL FEVALAB (NIL T) -9 NIL 802960 NIL) (-350 801222 801474 801812 "FEVALAB-" 801817 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 799632 800605 800808 "FDIV" 801121 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-348 796494 797379 797494 "FDIVCAT" 799062 NIL FDIVCAT (NIL T T T T) -9 NIL 799499 NIL) (-347 796250 796283 796453 "FDIVCAT-" 796458 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-346 795464 795557 795834 "FDIV2" 796157 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-345 794372 794759 794961 "FCTRDATA" 795282 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793028 793317 793606 "FCPAK1" 794103 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792031 792528 792669 "FCOMP" 792919 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 775346 779181 782719 "FC" 788513 T FC (NIL) -8 NIL NIL NIL) (-341 767041 771667 771707 "FAXF" 773509 NIL FAXF (NIL T) -9 NIL 774201 NIL) (-340 764162 764975 765800 "FAXF-" 766265 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 758731 763538 763714 "FARRAY" 764019 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753295 755678 755731 "FAMR" 756754 NIL FAMR (NIL T T) -9 NIL 757214 NIL) (-337 752119 752487 752922 "FAMR-" 752927 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751146 752041 752094 "FAMONOID" 752099 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 748776 749628 749681 "FAMONC" 750622 NIL FAMONC (NIL T T) -9 NIL 751008 NIL) (-334 747250 748530 748667 "FAGROUP" 748672 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745003 745364 745767 "FACUTIL" 746931 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744090 744287 744509 "FACTFUNC" 744813 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 735848 743393 743592 "EXPUPXS" 743946 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 733301 733871 734457 "EXPRTUBE" 735282 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 729512 730164 730894 "EXPRODE" 732640 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 713806 728161 728590 "EXPR" 729116 NIL EXPR (NIL T) -8 NIL NIL NIL) (-327 708240 708947 709753 "EXPR2UPS" 713104 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-326 707866 707929 708038 "EXPR2" 708177 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-325 698183 707017 707308 "EXPEXPAN" 707702 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 697947 698140 698169 "EXIT" 698174 T EXIT (NIL) -8 NIL NIL NIL) (-323 697367 697671 697762 "EXITAST" 697876 T EXITAST (NIL) -8 NIL NIL NIL) (-322 696988 697056 697169 "EVALCYC" 697299 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 696505 696647 696688 "EVALAB" 696858 NIL EVALAB (NIL T) -9 NIL 696962 NIL) (-320 695962 696108 696329 "EVALAB-" 696334 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693070 694618 694646 "EUCDOM" 695201 T EUCDOM (NIL) -9 NIL 695551 NIL) (-318 691409 691917 692507 "EUCDOM-" 692512 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 678726 681707 684457 "ESTOOLS" 688679 T ESTOOLS (NIL) -7 NIL NIL NIL) (-316 678352 678415 678524 "ESTOOLS2" 678663 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-315 678097 678145 678225 "ESTOOLS1" 678304 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-314 671798 673728 673756 "ES" 676524 T ES (NIL) -9 NIL 677934 NIL) (-313 666475 668032 669849 "ES-" 670013 NIL ES- (NIL T) -8 NIL NIL NIL) (-312 662783 663610 664390 "ESCONT" 665715 T ESCONT (NIL) -7 NIL NIL NIL) (-311 662522 662560 662642 "ESCONT1" 662745 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-310 662191 662247 662347 "ES2" 662466 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-309 661815 661879 661988 "ES1" 662127 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-308 661007 661160 661336 "ERROR" 661659 T ERROR (NIL) -7 NIL NIL NIL) (-307 654023 660866 660957 "EQTBL" 660962 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 646282 649337 650786 "EQ" 652607 NIL -1544 (NIL T) -8 NIL NIL NIL) (-305 645908 645971 646080 "EQ2" 646219 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-304 641151 642246 643339 "EP" 644847 NIL EP (NIL T) -7 NIL NIL NIL) (-303 639691 640042 640348 "ENV" 640865 T ENV (NIL) -8 NIL NIL NIL) (-302 638651 639325 639353 "ENTIRER" 639358 T ENTIRER (NIL) -9 NIL 639404 NIL) (-301 635063 636833 637194 "EMR" 638459 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634167 634378 634432 "ELTAGG" 634812 NIL ELTAGG (NIL T T) -9 NIL 635023 NIL) (-299 633874 633948 634089 "ELTAGG-" 634094 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 633632 633667 633721 "ELTAB" 633805 NIL ELTAB (NIL T T) -9 NIL 633857 NIL) (-297 632734 632904 633103 "ELFUTS" 633483 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 632458 632532 632560 "ELEMFUN" 632665 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 632322 632349 632417 "ELEMFUN-" 632422 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 626739 630364 630405 "ELAGG" 631345 NIL ELAGG (NIL T) -9 NIL 631808 NIL) (-293 624916 625458 626121 "ELAGG-" 626126 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624198 624365 624521 "ELABOR" 624780 T ELABOR (NIL) -8 NIL NIL NIL) (-291 622805 623138 623432 "ELABEXPR" 623924 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 615317 617442 618271 "EFUPXS" 622080 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 608443 610566 611377 "EFULS" 614592 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 605880 606286 606758 "EFSTRUC" 608075 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 595317 597237 598785 "EF" 604395 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 594295 594802 594951 "EAB" 595188 T EAB (NIL) -8 NIL NIL NIL) (-285 593417 594254 594282 "E04UCFA" 594287 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 592539 593376 593404 "E04NAFA" 593409 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 591661 592498 592526 "E04MBFA" 592531 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 590783 591620 591648 "E04JAFA" 591653 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 589907 590742 590770 "E04GCFA" 590775 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589031 589866 589894 "E04FDFA" 589899 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588153 588990 589018 "E04DGFA" 589023 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582230 583678 585042 "E04AGNT" 586809 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 580850 581531 581571 "DVARCAT" 581912 NIL DVARCAT (NIL T) -9 NIL 582075 NIL) (-276 580000 580266 580580 "DVARCAT-" 580585 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 571961 579799 579928 "DSMP" 579933 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 570312 571103 571144 "DSEXT" 571507 NIL DSEXT (NIL T) -9 NIL 571801 NIL) (-273 568501 569025 569691 "DSEXT-" 569696 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563084 564446 565514 "DROPT" 567453 T DROPT (NIL) -8 NIL NIL NIL) (-271 562743 562808 562906 "DROPT1" 563019 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-270 557762 558984 560121 "DROPT0" 561626 T DROPT0 (NIL) -7 NIL NIL NIL) (-269 556071 556432 556818 "DRAWPT" 557396 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 550562 551581 552660 "DRAW" 555045 NIL DRAW (NIL T) -7 NIL NIL NIL) (-267 550189 550248 550366 "DRAWHACK" 550503 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-266 548890 549189 549480 "DRAWCX" 549918 T DRAWCX (NIL) -7 NIL NIL NIL) (-265 548399 548474 548625 "DRAWCURV" 548816 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-264 538717 540829 542944 "DRAWCFUN" 546304 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-263 535188 537382 537423 "DQAGG" 538052 NIL DQAGG (NIL T) -9 NIL 538326 NIL) (-262 521771 529399 529482 "DPOLCAT" 531334 NIL DPOLCAT (NIL T T T T) -9 NIL 531879 NIL) (-261 516290 517956 519914 "DPOLCAT-" 519919 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509147 516151 516249 "DPMO" 516254 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 501901 508927 509094 "DPMM" 509099 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 501423 501685 501774 "DOMTMPLT" 501832 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 500772 501225 501305 "DOMCTOR" 501363 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 499924 500252 500403 "DOMAIN" 500641 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 492936 499559 499711 "DMP" 499825 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 490713 492003 492044 "DMEXT" 492049 NIL DMEXT (NIL T) -9 NIL 492225 NIL) (-253 490307 490369 490513 "DLP" 490651 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 483430 489634 489824 "DLIST" 490149 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 479968 482255 482296 "DLAGG" 482846 NIL DLAGG (NIL T) -9 NIL 483076 NIL) (-250 478480 479294 479322 "DIVRING" 479414 T DIVRING (NIL) -9 NIL 479497 NIL) (-249 477663 477907 478207 "DIVRING-" 478212 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 475705 476122 476528 "DISPLAY" 477277 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 469112 475619 475682 "DIRPROD" 475687 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-246 467942 468163 468428 "DIRPROD2" 468905 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-245 456161 462653 462706 "DIRPCAT" 462964 NIL DIRPCAT (NIL NIL T) -9 NIL 463839 NIL) (-244 453361 454129 455010 "DIRPCAT-" 455347 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 452642 452808 452994 "DIOSP" 453195 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449056 451526 451567 "DIOPS" 452001 NIL DIOPS (NIL T) -9 NIL 452230 NIL) (-241 448575 448719 448910 "DIOPS-" 448915 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 447482 448254 448282 "DIFRING" 448287 T DIFRING (NIL) -9 NIL 448309 NIL) (-239 447130 447228 447256 "DIFFSPC" 447375 T DIFFSPC (NIL) -9 NIL 447450 NIL) (-238 446751 446853 447005 "DIFFSPC-" 447010 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 445687 446285 446326 "DIFFMOD" 446331 NIL DIFFMOD (NIL T) -9 NIL 446429 NIL) (-236 445383 445440 445481 "DIFFDOM" 445602 NIL DIFFDOM (NIL T) -9 NIL 445670 NIL) (-235 445230 445260 445344 "DIFFDOM-" 445349 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 442970 444434 444475 "DIFEXT" 444480 NIL DIFEXT (NIL T) -9 NIL 444633 NIL) (-233 440004 442474 442515 "DIAGG" 442520 NIL DIAGG (NIL T) -9 NIL 442540 NIL) (-232 439352 439545 439797 "DIAGG-" 439802 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434202 438311 438588 "DHMATRIX" 439121 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 429670 430723 431733 "DFSFUN" 433212 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 423904 428601 428913 "DFLOAT" 429378 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422143 422448 422837 "DFINTTLS" 423612 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 418962 420164 420564 "DERHAM" 421809 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 416498 418737 418826 "DEQUEUE" 418906 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 415740 415885 416068 "DEGRED" 416360 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412146 412915 413761 "DEFINTRF" 414968 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 409683 410170 410762 "DEFINTEF" 411665 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 408967 409303 409418 "DEFAST" 409588 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402003 408560 408710 "DECIMAL" 408837 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 399461 399973 400479 "DDFACT" 401547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399051 399100 399251 "DBLRESP" 399412 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398252 398821 398912 "DBASIS" 399000 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396036 396482 396843 "DBASE" 398018 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395224 395516 395662 "DATAARY" 395935 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394282 395183 395211 "D03FAFA" 395216 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 393341 394241 394269 "D03EEFA" 394274 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391267 391757 392246 "D03AGNT" 392872 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 390508 391226 391254 "D02EJFA" 391259 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 389749 390467 390495 "D02CJFA" 390500 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 388990 389708 389736 "D02BHFA" 389741 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388231 388949 388977 "D02BBFA" 388982 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 381362 383017 384623 "D02AGNT" 386645 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379112 379653 380199 "D01WGTS" 380836 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378119 379071 379099 "D01TRNS" 379104 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377127 378078 378106 "D01GBFA" 378111 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376135 377086 377114 "D01FCFA" 377119 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375143 376094 376122 "D01ASFA" 376127 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374151 375102 375130 "D01AQFA" 375135 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373159 374110 374138 "D01APFA" 374143 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372167 373118 373146 "D01ANFA" 373151 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371175 372126 372154 "D01AMFA" 372159 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370183 371134 371162 "D01ALFA" 371167 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369191 370142 370170 "D01AKFA" 370175 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368199 369150 369178 "D01AJFA" 369183 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 361422 363047 364608 "D01AGNT" 366658 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 360741 360887 361039 "CYCLOTOM" 361290 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 357396 358189 358916 "CYCLES" 360034 T CYCLES (NIL) -7 NIL NIL NIL) (-192 356696 356842 357013 "CVMP" 357257 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 354483 354795 355164 "CTRIGMNP" 356424 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 353841 354277 354350 "CTOR" 354430 T CTOR (NIL) -8 NIL NIL NIL) (-189 353314 353572 353673 "CTORKIND" 353760 T CTORKIND (NIL) -8 NIL NIL NIL) (-188 352519 352907 352935 "CTORCAT" 353117 T CTORCAT (NIL) -9 NIL 353230 NIL) (-187 352093 352228 352387 "CTORCAT-" 352392 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-186 351507 351767 351875 "CTORCALL" 352017 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-185 350863 350980 351133 "CSTTOOLS" 351404 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 346560 347319 348077 "CRFP" 350175 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 345975 346281 346373 "CRCEAST" 346488 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 344998 345207 345435 "CRAPACK" 345779 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 344378 344483 344687 "CPMATCH" 344874 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344097 344131 344237 "CPIMA" 344344 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 340355 341117 341836 "COORDSYS" 343432 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 339743 339888 340030 "CONTOUR" 340233 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335208 337746 338238 "CONTFRAC" 339283 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335082 335109 335137 "CONDUIT" 335174 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334036 334710 334738 "COMRING" 334743 T COMRING (NIL) -9 NIL 334795 NIL) (-174 333018 333394 333578 "COMPPROP" 333872 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 332673 332714 332842 "COMPLPAT" 332977 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 321056 332482 332591 "COMPLEX" 332596 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-171 320686 320749 320856 "COMPLEX2" 320993 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-170 320007 320146 320306 "COMPILER" 320546 T COMPILER (NIL) -8 NIL NIL NIL) (-169 319719 319760 319858 "COMPFACT" 319966 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301094 313423 313463 "COMPCAT" 314467 NIL COMPCAT (NIL T) -9 NIL 315815 NIL) (-167 289982 293533 297160 "COMPCAT-" 297516 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 289705 289739 289842 "COMMUPC" 289948 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 289493 289533 289592 "COMMONOP" 289666 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289001 289244 289331 "COMM" 289426 T COMM (NIL) -8 NIL NIL NIL) (-163 288523 288805 288880 "COMMAAST" 288946 T COMMAAST (NIL) -8 NIL NIL NIL) (-162 287718 287966 287994 "COMBOPC" 288332 T COMBOPC (NIL) -9 NIL 288507 NIL) (-161 286572 286824 287066 "COMBINAT" 287508 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 282915 283603 284230 "COMBF" 285994 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 281577 282031 282266 "COLOR" 282700 T COLOR (NIL) -8 NIL NIL NIL) (-158 280993 281298 281390 "COLONAST" 281505 T COLONAST (NIL) -8 NIL NIL NIL) (-157 280627 280680 280805 "CMPLXRT" 280940 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280015 280327 280426 "CLLCTAST" 280548 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 275475 276545 277625 "CLIP" 278955 T CLIP (NIL) -7 NIL NIL NIL) (-154 273648 274576 274816 "CLIF" 275302 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 269630 271766 271807 "CLAGG" 272736 NIL CLAGG (NIL T) -9 NIL 273272 NIL) (-152 267974 268509 269092 "CLAGG-" 269097 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 267512 267603 267743 "CINTSLPE" 267883 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 264977 265484 266032 "CHVAR" 267040 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264017 264691 264719 "CHARZ" 264724 T CHARZ (NIL) -9 NIL 264739 NIL) (-148 263765 263811 263889 "CHARPOL" 263971 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 262683 263396 263424 "CHARNZ" 263471 T CHARNZ (NIL) -9 NIL 263527 NIL) (-146 260427 261337 261690 "CHAR" 262350 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247376 248635 249379 "CARTEN" 251790 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-137 246472 246632 246853 "CARTEN2" 247223 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 241151 241908 242057 "BYTE" 242220 T BYTE (NIL) -8 NIL NIL 242349) (-130 236078 240656 240828 "BYTEBUF" 240999 T BYTEBUF (NIL) -8 NIL NIL NIL) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197235 198679 199591 "BOP" 201361 T BOP (NIL) -8 NIL NIL NIL) (-115 194962 195420 195895 "BOP1" 196793 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-114 194555 194712 194740 "BOOLE" 194851 T BOOLE (NIL) -9 NIL 194932 NIL) (-113 194423 194450 194516 "BOOLE-" 194521 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-112 193088 194011 194153 "BOOLEAN" 194301 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137620 138341 138451 "ASP1" 138561 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 136455 137294 137413 "ASP19" 137532 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 136174 136259 136335 "ASP12" 136410 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135773 135917 "ASP10" 136061 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 127890 132178 132292 "ARRAY1" 132447 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 126904 127095 127316 "ARRAY12" 127713 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115193 115486 115606 "ANY" 115791 T ANY (NIL) -8 NIL NIL NIL) (-51 114447 114594 114751 "ANY1" 115067 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) \ No newline at end of file
+((-3 3472614 3472619 3472624 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472599 3472604 3472609 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472584 3472589 3472594 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472569 3472574 3472579 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471556 3472444 3472521 "ZMOD" 3472526 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470592 3470774 3470997 "ZLINDEP" 3471388 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459754 3461660 3463632 "ZDSOLVE" 3468722 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3458988 3459141 3459330 "YSTREAM" 3459600 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458348 3458657 3458772 "YDIAGRAM" 3458895 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455796 3457649 3457853 "XRPOLY" 3458191 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452063 3453667 3454242 "XPR" 3455268 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449458 3451394 3451598 "XPOLY" 3451894 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1319 3446789 3448465 3448520 "XPOLYC" 3448808 NIL XPOLYC (NIL T T) -9 NIL 3448921 NIL) (-1318 3442735 3445306 3445694 "XPBWPOLY" 3446447 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3438004 3440711 3440753 "XF" 3441374 NIL XF (NIL T) -9 NIL 3441774 NIL) (-1316 3437601 3437713 3437882 "XF-" 3437887 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1315 3432493 3434072 3434127 "XFALG" 3436299 NIL XFALG (NIL T T) -9 NIL 3437088 NIL) (-1314 3431608 3431730 3431935 "XEXPPKG" 3432385 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429349 3431458 3431554 "XDPOLY" 3431559 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428004 3428742 3428785 "XALG" 3428790 NIL XALG (NIL T) -9 NIL 3428901 NIL) (-1311 3420914 3425981 3426475 "WUTSET" 3427596 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419016 3419966 3420289 "WP" 3420725 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418564 3418838 3418908 "WHILEAST" 3418968 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3417976 3418281 3418375 "WHEREAST" 3418492 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416850 3417060 3417355 "WFFINTBS" 3417773 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414718 3415181 3415643 "WEIER" 3416422 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413642 3414200 3414242 "VSPACE" 3414378 NIL VSPACE (NIL T) -9 NIL 3414452 NIL) (-1304 3413474 3413507 3413598 "VSPACE-" 3413603 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413271 3413325 3413393 "VOID" 3413428 T VOID (NIL) -8 NIL NIL NIL) (-1302 3411371 3411766 3412172 "VIEW" 3412887 T VIEW (NIL) -7 NIL NIL NIL) (-1301 3407639 3408434 3409171 "VIEWDEF" 3410656 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1300 3396583 3399187 3401360 "VIEW3D" 3405488 T VIEW3D (NIL) -8 NIL NIL NIL) (-1299 3388600 3390494 3392073 "VIEW2D" 3395026 T VIEW2D (NIL) -8 NIL NIL NIL) (-1298 3383506 3388370 3388462 "VECTOR" 3388543 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3382059 3382342 3382660 "VECTOR2" 3383236 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1296 3375013 3379763 3379806 "VECTCAT" 3380801 NIL VECTCAT (NIL T) -9 NIL 3381388 NIL) (-1295 3373955 3374281 3374671 "VECTCAT-" 3374676 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373361 3373606 3373726 "VARIABLE" 3373870 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373294 3373299 3373329 "UTYPE" 3373334 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372102 3372278 3372540 "UTSODETL" 3373120 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369494 3370002 3370526 "UTSODE" 3371643 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3360804 3367255 3367735 "UTS" 3369072 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1289 3350811 3356737 3356780 "UTSCAT" 3357892 NIL UTSCAT (NIL T) -9 NIL 3358650 NIL) (-1288 3347937 3348881 3349870 "UTSCAT-" 3349875 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1287 3347558 3347607 3347740 "UTS2" 3347888 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1286 3341425 3344368 3344411 "URAGG" 3346481 NIL URAGG (NIL T) -9 NIL 3347204 NIL) (-1285 3338148 3339227 3340350 "URAGG-" 3340355 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333517 3336783 3337248 "UPXSSING" 3337812 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3324995 3332899 3333163 "UPXS" 3333311 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1282 3317410 3324899 3324971 "UPXSCONS" 3324976 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1281 3306158 3313612 3313674 "UPXSCCA" 3314248 NIL UPXSCCA (NIL T T) -9 NIL 3314481 NIL) (-1280 3305778 3305881 3306055 "UPXSCCA-" 3306060 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1279 3294426 3301605 3301648 "UPXSCAT" 3302296 NIL UPXSCAT (NIL T) -9 NIL 3302905 NIL) (-1278 3293850 3293935 3294114 "UPXS2" 3294341 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1277 3292486 3292757 3293108 "UPSQFREE" 3293593 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285314 3288752 3288807 "UPSCAT" 3289887 NIL UPSCAT (NIL T T) -9 NIL 3290653 NIL) (-1275 3284470 3284725 3285052 "UPSCAT-" 3285057 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3268604 3277597 3277640 "UPOLYC" 3279741 NIL UPOLYC (NIL T) -9 NIL 3280962 NIL) (-1273 3259452 3262358 3265505 "UPOLYC-" 3265510 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3259073 3259122 3259255 "UPOLYC2" 3259403 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1271 3249648 3258756 3258885 "UP" 3258992 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1270 3248969 3249094 3249258 "UPMP" 3249537 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1269 3248516 3248603 3248742 "UPDIVP" 3248882 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1268 3247054 3247333 3247649 "UPDECOMP" 3248265 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1267 3246267 3246397 3246583 "UPCDEN" 3246938 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1266 3245780 3245855 3246004 "UP2" 3246192 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1265 3244133 3244984 3245261 "UNISEG" 3245538 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3243338 3243475 3243680 "UNISEG2" 3243976 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1263 3242380 3242578 3242804 "UNIFACT" 3243154 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3224190 3241692 3241934 "ULS" 3242196 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3210900 3224094 3224166 "ULSCONS" 3224171 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3190700 3203980 3204042 "ULSCCAT" 3204680 NIL ULSCCAT (NIL T T) -9 NIL 3204969 NIL) (-1259 3189696 3189995 3190383 "ULSCCAT-" 3190388 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1258 3178141 3185242 3185285 "ULSCAT" 3186148 NIL ULSCAT (NIL T) -9 NIL 3186879 NIL) (-1257 3177565 3177650 3177829 "ULS2" 3178056 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3176480 3177180 3177294 "UINT8" 3177405 T UINT8 (NIL) -8 NIL NIL 3177497) (-1255 3175394 3176094 3176208 "UINT64" 3176319 T UINT64 (NIL) -8 NIL NIL 3176411) (-1254 3174308 3175008 3175122 "UINT32" 3175233 T UINT32 (NIL) -8 NIL NIL 3175325) (-1253 3173222 3173922 3174036 "UINT16" 3174147 T UINT16 (NIL) -8 NIL NIL 3174239) (-1252 3171301 3172468 3172498 "UFD" 3172710 T UFD (NIL) -9 NIL 3172824 NIL) (-1251 3171083 3171141 3171236 "UFD-" 3171241 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170141 3170348 3170564 "UDVO" 3170889 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3167907 3168366 3168837 "UDPO" 3169705 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167840 3167845 3167875 "TYPE" 3167880 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3167552 3167795 3167826 "TYPEAST" 3167831 T TYPEAST (NIL) -8 NIL NIL NIL) (-1246 3166505 3166725 3166965 "TWOFACT" 3167346 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165480 3165914 3166149 "TUPLE" 3166305 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163117 3163690 3164229 "TUBETOOL" 3164963 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3161923 3162164 3162406 "TUBE" 3162910 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3156102 3160895 3161178 "TS" 3161675 NIL TS (NIL T) -8 NIL NIL NIL) (-1241 3144244 3148859 3148956 "TSETCAT" 3154225 NIL TSETCAT (NIL T T T T) -9 NIL 3155757 NIL) (-1240 3138712 3140576 3142467 "TSETCAT-" 3142472 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3133185 3134198 3135127 "TRMANIP" 3137848 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132614 3132689 3132852 "TRIMAT" 3133117 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130426 3130717 3131074 "TRIGMNIP" 3132363 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3129910 3130059 3130089 "TRIGCAT" 3130302 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129555 3129658 3129799 "TRIGCAT-" 3129804 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126169 3128413 3128694 "TREE" 3129309 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125275 3125971 3126001 "TRANFUN" 3126036 T TRANFUN (NIL) -9 NIL 3126102 NIL) (-1232 3124494 3124745 3125025 "TRANFUN-" 3125030 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124292 3124330 3124391 "TOPSP" 3124455 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123622 3123755 3123909 "TOOLSIGN" 3124173 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122136 3122799 3123038 "TEXTFILE" 3123405 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3119940 3120589 3121018 "TEX" 3121729 T TEX (NIL) -8 NIL NIL NIL) (-1227 3119715 3119752 3119824 "TEX1" 3119903 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3119351 3119426 3119516 "TEMUTL" 3119647 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117445 3117785 3118110 "TBCMPPK" 3119074 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108772 3115531 3115587 "TBAGG" 3115987 NIL TBAGG (NIL T T) -9 NIL 3116198 NIL) (-1223 3103656 3105330 3107084 "TBAGG-" 3107089 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103022 3103147 3103292 "TANEXP" 3103545 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102473 3102797 3102887 "TALGOP" 3102967 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3095487 3102330 3102423 "TABLE" 3102428 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3094881 3094998 3095136 "TABLEAU" 3095384 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3089411 3090709 3091957 "TABLBUMP" 3093667 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088621 3088780 3088961 "SYSTEM" 3089252 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085026 3085779 3086562 "SYSSOLP" 3087872 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084788 3084981 3085012 "SYSPTR" 3085017 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083623 3084315 3084441 "SYSNNI" 3084627 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084719) (-1213 3082826 3083381 3083460 "SYSINT" 3083520 NIL SYSINT (NIL NIL) -8 NIL NIL 3083565) (-1212 3078924 3080104 3080814 "SYNTAX" 3082138 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076004 3076684 3077316 "SYMTAB" 3078314 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071103 3072155 3073138 "SYMS" 3075043 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068002 3070554 3070787 "SYMPOLY" 3070905 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067507 3067594 3067717 "SYMFUNC" 3067914 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063305 3064819 3065632 "SYMBOL" 3066716 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056778 3058533 3060253 "SWITCH" 3061607 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049532 3055734 3056028 "SUTS" 3056542 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041010 3048914 3049178 "SUPXS" 3049326 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3031533 3040628 3040754 "SUP" 3040919 NIL SUP (NIL T) -8 NIL NIL NIL) (-1202 3030680 3030819 3031036 "SUPFRACF" 3031401 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3030295 3030360 3030473 "SUP2" 3030615 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3028719 3029017 3029373 "SUMRF" 3029994 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028042 3028120 3028312 "SUMFS" 3028640 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3009887 3027354 3027596 "SULS" 3027858 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009435 3009709 3009779 "SUCHTAST" 3009839 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008676 3008960 3009100 "SUCH" 3009343 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002315 3003582 3004541 "SUBSPACE" 3007764 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001735 3001835 3001999 "SUBRESP" 3002203 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2994929 2996400 2997711 "STTF" 3000471 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2988940 2990222 2991369 "STTFNC" 2993829 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2980057 2982122 2983916 "STTAYLOR" 2987181 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972811 2979921 2980004 "STRTBL" 2980009 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967208 2972520 2972619 "STRING" 2972734 T STRING (NIL) -8 NIL NIL NIL) (-1188 2959318 2964827 2965438 "STREAM" 2966632 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1187 2958822 2958905 2959049 "STREAM3" 2959235 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2957786 2957987 2958222 "STREAM2" 2958635 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2957468 2957526 2957619 "STREAM1" 2957728 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2956460 2956665 2956896 "STINPROD" 2957284 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955956 2956208 2956238 "STEP" 2956318 T STEP (NIL) -9 NIL 2956396 NIL) (-1182 2955071 2955445 2955593 "STEPAST" 2955830 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2948127 2954970 2955047 "STBL" 2955052 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942685 2947290 2947333 "STAGG" 2947486 NIL STAGG (NIL T) -9 NIL 2947575 NIL) (-1179 2940237 2940989 2941861 "STAGG-" 2941866 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938209 2940007 2940099 "STACK" 2940180 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930216 2936350 2936806 "SREGSET" 2937839 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922563 2924010 2925523 "SRDCMPK" 2928822 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2914872 2919922 2919952 "SRAGG" 2921255 T SRAGG (NIL) -9 NIL 2921863 NIL) (-1174 2913823 2914144 2914523 "SRAGG-" 2914528 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907407 2912770 2913191 "SQMATRIX" 2913449 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900819 2904125 2904852 "SPLTREE" 2906752 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896644 2897475 2898121 "SPLNODE" 2900245 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895619 2895924 2895954 "SPFCAT" 2896398 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894314 2894566 2894830 "SPECOUT" 2895377 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2884960 2887278 2887308 "SPADXPT" 2891986 T SPADXPT (NIL) -9 NIL 2894152 NIL) (-1167 2884715 2884761 2884830 "SPADPRSR" 2884913 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882318 2884670 2884701 "SPADAST" 2884706 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2873919 2876022 2876065 "SPACEC" 2880438 NIL SPACEC (NIL T) -9 NIL 2882254 NIL) (-1164 2871719 2873851 2873900 "SPACE3" 2873905 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870451 2870642 2870933 "SORTPAK" 2871524 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868513 2868846 2869258 "SOLVETRA" 2870115 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867551 2867785 2868046 "SOLVESER" 2868286 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862783 2863743 2864738 "SOLVERAD" 2866603 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858508 2859207 2859936 "SOLVEFOR" 2862150 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852119 2857856 2857953 "SNTSCAT" 2857958 NIL SNTSCAT (NIL T T T T) -9 NIL 2858028 NIL) (-1157 2845663 2850442 2850833 "SMTS" 2851809 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839378 2845551 2845628 "SMP" 2845633 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837507 2837838 2838236 "SMITH" 2839075 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829039 2834086 2834189 "SMATCAT" 2835540 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836090 NIL) (-1153 2825811 2826802 2827980 "SMATCAT-" 2827985 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823280 2825019 2825062 "SKAGG" 2825323 NIL SKAGG (NIL T) -9 NIL 2825458 NIL) (-1151 2818774 2822753 2822937 "SINT" 2823089 T SINT (NIL) -8 NIL NIL 2823251) (-1150 2818540 2818584 2818650 "SIMPAN" 2818730 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817765 2818075 2818215 "SIG" 2818422 T SIG (NIL) -8 NIL NIL NIL) (-1148 2816585 2816824 2817099 "SIGNRF" 2817524 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1147 2815400 2815569 2815853 "SIGNEF" 2816414 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1146 2814640 2814983 2815107 "SIGAST" 2815298 T SIGAST (NIL) -8 NIL NIL NIL) (-1145 2812292 2812784 2813290 "SHP" 2814181 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805665 2812193 2812269 "SHDP" 2812274 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805176 2805416 2805446 "SGROUP" 2805539 T SGROUP (NIL) -9 NIL 2805601 NIL) (-1142 2805028 2805060 2805133 "SGROUP-" 2805138 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801747 2802517 2803240 "SGCF" 2804327 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795456 2801193 2801290 "SFRTCAT" 2801295 NIL SFRTCAT (NIL T T T T) -9 NIL 2801334 NIL) (-1139 2788775 2789895 2791031 "SFRGCD" 2794439 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781793 2782974 2784160 "SFQCMPK" 2787708 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781395 2781502 2781613 "SFORT" 2781734 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780321 2781235 2781356 "SEXOF" 2781361 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2779236 2780202 2780270 "SEX" 2780275 T SEX (NIL) -8 NIL NIL NIL) (-1134 2774825 2775732 2775827 "SEXCAT" 2778449 NIL SEXCAT (NIL T T T T T) -9 NIL 2779009 NIL) (-1133 2771634 2774759 2774807 "SET" 2774812 NIL SET (NIL T) -8 NIL NIL NIL) (-1132 2769756 2770347 2770652 "SETMN" 2771375 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1131 2769286 2769474 2769504 "SETCAT" 2769621 T SETCAT (NIL) -9 NIL 2769706 NIL) (-1130 2769054 2769118 2769217 "SETCAT-" 2769222 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1129 2765157 2767515 2767558 "SETAGG" 2768428 NIL SETAGG (NIL T) -9 NIL 2768768 NIL) (-1128 2764579 2764731 2764968 "SETAGG-" 2764973 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1127 2763962 2764275 2764376 "SEQAST" 2764500 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763089 2763455 2763516 "SEGXCAT" 2763802 NIL SEGXCAT (NIL T T) -9 NIL 2763922 NIL) (-1125 2762005 2762755 2762937 "SEG" 2762942 NIL SEG (NIL T) -8 NIL NIL NIL) (-1124 2760930 2761198 2761241 "SEGCAT" 2761763 NIL SEGCAT (NIL T) -9 NIL 2761984 NIL) (-1123 2759820 2760293 2760501 "SEGBIND" 2760757 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759435 2759500 2759613 "SEGBIND2" 2759755 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2758954 2759236 2759313 "SEGAST" 2759380 T SEGAST (NIL) -8 NIL NIL NIL) (-1120 2758163 2758299 2758503 "SEG2" 2758798 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1119 2757396 2758098 2758145 "SDVAR" 2758150 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748747 2757166 2757296 "SDPOL" 2757301 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747316 2747606 2747925 "SCPKG" 2748462 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746438 2746652 2746844 "SCOPE" 2747146 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745634 2745792 2745971 "SCACHE" 2746293 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745218 2745452 2745482 "SASTCAT" 2745487 T SASTCAT (NIL) -9 NIL 2745500 NIL) (-1113 2744621 2745053 2745129 "SAOS" 2745164 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744180 2744221 2744394 "SAERFFC" 2744580 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2737207 2744077 2744157 "SAE" 2744162 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1110 2736794 2736835 2736994 "SAEFACT" 2737166 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1109 2735097 2735429 2735830 "RURPK" 2736460 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733674 2734040 2734345 "RULESET" 2734931 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2730789 2731427 2731885 "RULE" 2733355 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1106 2730359 2730583 2730666 "RULECOLD" 2730741 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1105 2730143 2730177 2730248 "RTVALUE" 2730310 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729554 2729860 2729954 "RSTRCAST" 2730071 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724324 2725197 2726117 "RSETGCD" 2728753 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2712895 2718632 2718729 "RSETCAT" 2722848 NIL RSETCAT (NIL T T T T) -9 NIL 2723945 NIL) (-1101 2710714 2711361 2712185 "RSETCAT-" 2712190 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703022 2704476 2705996 "RSDCMPK" 2709313 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2700891 2701454 2701528 "RRCC" 2702614 NIL RRCC (NIL T T) -9 NIL 2702958 NIL) (-1098 2700212 2700416 2700695 "RRCC-" 2700700 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699595 2699908 2700009 "RPTAST" 2700133 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2671981 2682707 2682774 "RPOLCAT" 2693440 NIL RPOLCAT (NIL T T T) -9 NIL 2696600 NIL) (-1095 2662951 2665819 2668941 "RPOLCAT-" 2668946 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653404 2661162 2661644 "ROUTINE" 2662491 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649453 2653030 2653170 "ROMAN" 2653286 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647565 2648313 2648573 "ROIRC" 2649258 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643283 2646054 2646084 "RNS" 2646388 T RNS (NIL) -9 NIL 2646662 NIL) (-1090 2641690 2642175 2642709 "RNS-" 2642784 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640983 2641487 2641517 "RNG" 2641522 T RNG (NIL) -9 NIL 2641543 NIL) (-1088 2639944 2640348 2640550 "RNGBIND" 2640834 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1087 2639239 2639717 2639760 "RMODULE" 2639765 NIL RMODULE (NIL T) -9 NIL 2639792 NIL) (-1086 2638063 2638169 2638505 "RMCAT2" 2639140 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634565 2637409 2637706 "RMATRIX" 2637825 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627064 2629652 2629767 "RMATCAT" 2633126 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634108 NIL) (-1083 2626403 2626586 2626893 "RMATCAT-" 2626898 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2625976 2626190 2626233 "RLINSET" 2626295 NIL RLINSET (NIL T) -9 NIL 2626339 NIL) (-1081 2625537 2625618 2625746 "RINTERP" 2625895 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624461 2625135 2625165 "RING" 2625221 T RING (NIL) -9 NIL 2625313 NIL) (-1079 2624241 2624297 2624394 "RING-" 2624399 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623052 2623319 2623577 "RIDIST" 2624005 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613677 2622520 2622726 "RGCHAIN" 2622900 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2612935 2613419 2613460 "RGBCSPC" 2613518 NIL RGBCSPC (NIL T) -9 NIL 2613570 NIL) (-1075 2612001 2612460 2612501 "RGBCMDL" 2612733 NIL RGBCMDL (NIL T) -9 NIL 2612847 NIL) (-1074 2608941 2609609 2610279 "RF" 2611365 NIL RF (NIL T) -7 NIL NIL NIL) (-1073 2608581 2608650 2608753 "RFFACTOR" 2608872 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1072 2608300 2608341 2608438 "RFFACT" 2608540 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1071 2606351 2606781 2607163 "RFDIST" 2607940 T RFDIST (NIL) -7 NIL NIL NIL) (-1070 2605798 2605896 2606059 "RETSOL" 2606253 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605416 2605514 2605557 "RETRACT" 2605690 NIL RETRACT (NIL T) -9 NIL 2605777 NIL) (-1068 2605259 2605290 2605377 "RETRACT-" 2605382 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604807 2605081 2605151 "RETAST" 2605211 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597157 2604460 2604587 "RESULT" 2604702 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595592 2596426 2596625 "RESRING" 2597060 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595216 2595277 2595375 "RESLATC" 2595529 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2594915 2594956 2595063 "REPSQ" 2595175 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2592295 2592917 2593519 "REP" 2594335 T REP (NIL) -7 NIL NIL NIL) (-1061 2591986 2592027 2592138 "REPDB" 2592254 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1060 2585818 2587275 2588498 "REP2" 2590798 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1059 2582121 2582876 2583684 "REP1" 2585045 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1058 2574129 2580262 2580718 "REGSET" 2581751 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572838 2573277 2573527 "REF" 2573914 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572203 2572318 2572485 "REDORDER" 2572722 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567567 2571416 2571643 "RECLOS" 2572031 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566601 2566800 2567015 "REALSOLV" 2567374 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2566435 2566488 2566518 "REAL" 2566523 T REAL (NIL) -9 NIL 2566558 NIL) (-1052 2562882 2563720 2564604 "REAL0Q" 2565600 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1051 2558435 2559471 2560532 "REAL0" 2561863 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1050 2557846 2558152 2558246 "RDUCEAST" 2558363 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557245 2557323 2557530 "RDIV" 2557768 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556295 2556487 2556700 "RDIST" 2557067 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2554880 2555179 2555551 "RDETRS" 2556003 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552674 2553146 2553684 "RDETR" 2554422 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551293 2551577 2551974 "RDEEFS" 2552390 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549796 2550108 2550533 "RDEEF" 2550981 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543273 2546750 2546780 "RCFIELD" 2548075 T RCFIELD (NIL) -9 NIL 2548806 NIL) (-1042 2541229 2541841 2542537 "RCFIELD-" 2542612 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537281 2539302 2539345 "RCAGG" 2540429 NIL RCAGG (NIL T) -9 NIL 2540894 NIL) (-1040 2536891 2537003 2537166 "RCAGG-" 2537171 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536208 2536338 2536503 "RATRET" 2536775 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535749 2535828 2535949 "RATFACT" 2536136 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535027 2535177 2535329 "RANDSRC" 2535619 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534755 2534805 2534878 "RADUTIL" 2534976 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2526879 2533586 2533897 "RADIX" 2534478 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516473 2526721 2526851 "RADFF" 2526856 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516102 2516195 2516225 "RADCAT" 2516385 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2515872 2515932 2516032 "RADCAT-" 2516037 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513783 2515642 2515734 "QUEUE" 2515815 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2509622 2513716 2513764 "QUAT" 2513769 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1029 2509247 2509296 2509427 "QUATCT2" 2509573 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1028 2501623 2505670 2505712 "QUATCAT" 2506503 NIL QUATCAT (NIL T) -9 NIL 2507269 NIL) (-1027 2497504 2498799 2500189 "QUATCAT-" 2500285 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1026 2494760 2496552 2496595 "QUAGG" 2496976 NIL QUAGG (NIL T) -9 NIL 2497151 NIL) (-1025 2494308 2494582 2494652 "QQUTAST" 2494712 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493219 2493821 2493986 "QFORM" 2494189 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2482895 2489066 2489108 "QFCAT" 2489776 NIL QFCAT (NIL T) -9 NIL 2490777 NIL) (-1022 2478210 2479663 2481257 "QFCAT-" 2481353 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1021 2477835 2477884 2478015 "QFCAT2" 2478161 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2477266 2477400 2477532 "QEQUAT" 2477725 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470284 2471465 2472651 "QCMPACK" 2476199 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2467734 2468270 2468700 "QALGSET" 2469939 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1017 2466963 2467145 2467381 "QALGSET2" 2467552 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1016 2465630 2465872 2466191 "PWFFINTB" 2466736 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463775 2463973 2464329 "PUSHVAR" 2465444 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459502 2460718 2460761 "PTRANFN" 2462672 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457839 2458184 2458508 "PTPACK" 2459213 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457462 2457525 2457636 "PTFUNC2" 2457776 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451387 2456251 2456294 "PTCAT" 2456594 NIL PTCAT (NIL T) -9 NIL 2456747 NIL) (-1010 2451036 2451077 2451203 "PSQFR" 2451346 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449608 2449924 2450260 "PSEUDLIN" 2450734 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436128 2438703 2441029 "PSETPK" 2447368 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428836 2431864 2431962 "PSETCAT" 2435003 NIL PSETCAT (NIL T T T T) -9 NIL 2435817 NIL) (-1006 2426561 2427303 2428127 "PSETCAT-" 2428132 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2425874 2426069 2426099 "PSCURVE" 2426371 T PSCURVE (NIL) -9 NIL 2426538 NIL) (-1004 2421590 2423364 2423431 "PSCAT" 2424283 NIL PSCAT (NIL T T T) -9 NIL 2424523 NIL) (-1003 2420584 2420866 2421269 "PSCAT-" 2421274 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418783 2419643 2419908 "PRTITION" 2420341 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418194 2418500 2418594 "PRTDAST" 2418711 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407038 2409460 2411650 "PRS" 2416056 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404658 2406360 2406400 "PRQAGG" 2406583 NIL PRQAGG (NIL T) -9 NIL 2406685 NIL) (-998 2403837 2404286 2404314 "PROPLOG" 2404453 T PROPLOG (NIL) -9 NIL 2404568 NIL) (-997 2403435 2403498 2403621 "PROPFUN2" 2403760 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402732 2402871 2403043 "PROPFUN1" 2403296 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400711 2401479 2401776 "PROPFRML" 2402468 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400156 2400287 2400415 "PROPERTY" 2400603 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394044 2398322 2399142 "PRODUCT" 2399382 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2391002 2393502 2393736 "PR" 2393855 NIL PR (NIL T T) -8 NIL NIL NIL) (-991 2390792 2390830 2390889 "PRINT" 2390963 T PRINT (NIL) -7 NIL NIL NIL) (-990 2390108 2390249 2390401 "PRIMES" 2390672 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-989 2388155 2388574 2389040 "PRIMELT" 2389687 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-988 2387872 2387933 2387961 "PRIMCAT" 2388085 T PRIMCAT (NIL) -9 NIL NIL NIL) (-987 2383594 2387810 2387855 "PRIMARR" 2387860 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2382583 2382779 2383007 "PRIMARR2" 2383412 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2382220 2382282 2382393 "PREASSOC" 2382521 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-984 2381671 2381828 2381856 "PPCURVE" 2382061 T PPCURVE (NIL) -9 NIL 2382197 NIL) (-983 2381218 2381466 2381549 "PORTNUM" 2381608 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378555 2378976 2379568 "POLYROOT" 2380799 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2371763 2378159 2378319 "POLY" 2378428 NIL POLY (NIL T) -8 NIL NIL NIL) (-980 2371140 2371204 2371438 "POLYLIFT" 2371699 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-979 2367361 2367864 2368493 "POLYCATQ" 2370685 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-978 2353009 2359108 2359173 "POLYCAT" 2362687 NIL POLYCAT (NIL T T T) -9 NIL 2364565 NIL) (-977 2346128 2348320 2350704 "POLYCAT-" 2350709 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-976 2345709 2345783 2345903 "POLY2UP" 2346054 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-975 2345335 2345398 2345507 "POLY2" 2345646 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-974 2343996 2344259 2344535 "POLUTIL" 2345109 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342315 2342628 2342959 "POLTOPOL" 2343718 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337311 2342249 2342296 "POINT" 2342301 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335444 2335855 2336230 "PNTHEORY" 2336956 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333890 2334199 2334598 "PMTOOLS" 2335142 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333477 2333561 2333678 "PMSYM" 2333806 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2332979 2333054 2333229 "PMQFCAT" 2333402 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332322 2332444 2332600 "PMPRED" 2332856 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-966 2331703 2331801 2331963 "PMPREDFS" 2332223 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-965 2330357 2330575 2330953 "PMPLCAT" 2331465 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329883 2329968 2330120 "PMLSAGG" 2330272 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329350 2329432 2329614 "PMKERNEL" 2329801 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328961 2329042 2329155 "PMINS" 2329269 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328397 2328472 2328681 "PMFS" 2328886 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327613 2327743 2327948 "PMDOWN" 2328274 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326756 2326938 2327119 "PMASS" 2327452 T PMASS (NIL) -7 NIL NIL NIL) (-958 2326005 2326139 2326302 "PMASSFS" 2326643 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-957 2325654 2325728 2325822 "PLOTTOOL" 2325931 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320075 2321465 2322613 "PLOT" 2324526 T PLOT (NIL) -8 NIL NIL NIL) (-955 2315727 2316921 2317843 "PLOT3D" 2319173 T PLOT3D (NIL) -8 NIL NIL NIL) (-954 2314615 2314816 2315051 "PLOT1" 2315531 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-953 2289790 2294681 2299532 "PLEQN" 2309881 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289096 2289230 2289410 "PINTERP" 2289655 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-951 2288783 2288836 2288939 "PINTERPA" 2289043 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-950 2287879 2288547 2288634 "PI" 2288674 T PI (NIL) -8 NIL NIL 2288741) (-949 2285964 2287137 2287165 "PID" 2287347 T PID (NIL) -9 NIL 2287481 NIL) (-948 2285709 2285752 2285827 "PICOERCE" 2285921 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-947 2285017 2285168 2285344 "PGROEB" 2285565 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280456 2281415 2282321 "PGE" 2284131 T PGE (NIL) -7 NIL NIL NIL) (-945 2278537 2278826 2279192 "PGCD" 2280173 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277863 2277978 2278139 "PFRPAC" 2278421 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274113 2276411 2276764 "PFR" 2277542 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272466 2272746 2273071 "PFOTOOLS" 2273860 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270981 2271238 2271589 "PFOQ" 2272223 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269464 2269694 2270050 "PFO" 2270765 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2265389 2269353 2269422 "PF" 2269427 NIL PF (NIL NIL) -8 NIL NIL NIL) (-938 2262467 2263980 2264008 "PFECAT" 2264593 T PFECAT (NIL) -9 NIL 2264977 NIL) (-937 2261894 2262066 2262280 "PFECAT-" 2262285 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-936 2260467 2260749 2261050 "PFBRU" 2261643 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-935 2258297 2258685 2259117 "PFBR" 2260118 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-934 2254099 2255806 2256454 "PERM" 2257682 NIL PERM (NIL T) -8 NIL NIL NIL) (-933 2249153 2250306 2251176 "PERMGRP" 2253262 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-932 2247065 2248177 2248218 "PERMCAT" 2248618 NIL PERMCAT (NIL T) -9 NIL 2248916 NIL) (-931 2246712 2246759 2246883 "PERMAN" 2247018 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-930 2243953 2246377 2246499 "PENDTREE" 2246623 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242834 2243097 2243138 "PDSPC" 2243671 NIL PDSPC (NIL T) -9 NIL 2243916 NIL) (-928 2241889 2242155 2242517 "PDSPC-" 2242522 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240603 2241539 2241580 "PDRING" 2241585 NIL PDRING (NIL T) -9 NIL 2241613 NIL) (-926 2239346 2240108 2240162 "PDMOD" 2240167 NIL PDMOD (NIL T T) -9 NIL 2240271 NIL) (-925 2236513 2237339 2238007 "PDEPROB" 2238698 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234022 2234562 2235117 "PDEPACK" 2235978 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232910 2233124 2233375 "PDECOMP" 2233821 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230427 2231318 2231346 "PDECAT" 2232133 T PDECAT (NIL) -9 NIL 2232846 NIL) (-921 2230044 2230111 2230165 "PDDOM" 2230330 NIL PDDOM (NIL T T) -9 NIL 2230410 NIL) (-920 2229857 2229893 2230000 "PDDOM-" 2230005 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229602 2229641 2229731 "PCOMP" 2229818 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227642 2228403 2228700 "PBWLB" 2229331 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2219821 2221715 2223053 "PATTERN" 2226325 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-916 2219447 2219510 2219619 "PATTERN2" 2219758 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-915 2217156 2217592 2218049 "PATTERN1" 2219036 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-914 2214422 2215105 2215586 "PATRES" 2216721 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-913 2213980 2214053 2214185 "PATRES2" 2214349 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-912 2211833 2212268 2212675 "PATMATCH" 2213647 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211287 2211538 2211579 "PATMAB" 2211686 NIL PATMAB (NIL T) -9 NIL 2211769 NIL) (-910 2209733 2210141 2210399 "PATLRES" 2211092 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209271 2209402 2209443 "PATAB" 2209448 NIL PATAB (NIL T) -9 NIL 2209620 NIL) (-908 2207411 2207848 2208271 "PARTPERM" 2208868 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207020 2207095 2207197 "PARSURF" 2207342 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206646 2206709 2206818 "PARSU2" 2206957 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206404 2206450 2206517 "PARSER" 2206599 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206013 2206088 2206190 "PARSCURV" 2206335 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205639 2205702 2205811 "PARSC2" 2205950 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205266 2205336 2205433 "PARPCURV" 2205575 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204892 2204955 2205064 "PARPC2" 2205203 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203881 2204265 2204447 "PARAMAST" 2204730 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203389 2203487 2203606 "PAN2EXPR" 2203782 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202082 2202510 2202738 "PALETTE" 2203181 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200427 2201087 2201447 "PAIR" 2201768 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193339 2199684 2199879 "PADICRC" 2200281 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185575 2192683 2192868 "PADICRAT" 2193186 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2183584 2185512 2185557 "PADIC" 2185562 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-893 2180374 2182244 2182284 "PADICCT" 2182865 NIL PADICCT (NIL NIL) -9 NIL 2183147 NIL) (-892 2179319 2179531 2179799 "PADEPAC" 2180161 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178519 2178664 2178870 "PADE" 2179181 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176752 2177727 2178007 "OWP" 2178323 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176197 2176458 2176555 "OVERSET" 2176675 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175117 2175802 2175974 "OVAR" 2176065 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2174357 2174502 2174663 "OUT" 2174976 T OUT (NIL) -7 NIL NIL NIL) (-886 2162593 2165466 2167666 "OUTFORM" 2172177 T OUTFORM (NIL) -8 NIL NIL NIL) (-885 2161875 2162190 2162317 "OUTBFILE" 2162486 T OUTBFILE (NIL) -8 NIL NIL NIL) (-884 2161152 2161347 2161375 "OUTBCON" 2161693 T OUTBCON (NIL) -9 NIL 2161859 NIL) (-883 2160735 2160865 2161022 "OUTBCON-" 2161027 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-882 2160031 2160464 2160553 "OSI" 2160666 T OSI (NIL) -8 NIL NIL NIL) (-881 2159450 2159872 2159900 "OSGROUP" 2159905 T OSGROUP (NIL) -9 NIL 2159927 NIL) (-880 2158161 2158422 2158707 "ORTHPOL" 2159197 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155412 2157996 2158117 "OREUP" 2158122 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152515 2155103 2155230 "ORESUP" 2155354 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150015 2150543 2151104 "OREPCTO" 2152004 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143393 2145888 2145929 "OREPCAT" 2148277 NIL OREPCAT (NIL T) -9 NIL 2149381 NIL) (-875 2140366 2141322 2142380 "OREPCAT-" 2142385 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139559 2139836 2139864 "ORDTYPE" 2140173 T ORDTYPE (NIL) -9 NIL 2140336 NIL) (-873 2138860 2139076 2139331 "ORDTYPE-" 2139336 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138216 2138599 2138757 "ORDSTRCT" 2138762 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137714 2138084 2138112 "ORDSET" 2138117 T ORDSET (NIL) -9 NIL 2138139 NIL) (-870 2136072 2137043 2137071 "ORDRING" 2137273 T ORDRING (NIL) -9 NIL 2137398 NIL) (-869 2135693 2135811 2135955 "ORDRING-" 2135960 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2134944 2135509 2135537 "ORDMON" 2135542 T ORDMON (NIL) -9 NIL 2135563 NIL) (-867 2134088 2134253 2134448 "ORDFUNS" 2134793 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133303 2133818 2133846 "ORDFIN" 2133911 T ORDFIN (NIL) -9 NIL 2133985 NIL) (-865 2129650 2131889 2132298 "ORDCOMP" 2132927 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-864 2128904 2129043 2129229 "ORDCOMP2" 2129510 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2125425 2126395 2127209 "OPTPROB" 2128110 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122167 2122866 2123570 "OPTPACK" 2124741 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119780 2120606 2120634 "OPTCAT" 2121453 T OPTCAT (NIL) -9 NIL 2122103 NIL) (-860 2119098 2119457 2119562 "OPSIG" 2119695 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118860 2118905 2118971 "OPQUERY" 2119052 T 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NIL) (-846 2100225 2100561 2100721 "OMERRK" 2101000 T OMERRK (NIL) -8 NIL NIL NIL) (-845 2099616 2099902 2100010 "OMENC" 2100137 T OMENC (NIL) -8 NIL NIL NIL) (-844 2093253 2094696 2095867 "OMDEV" 2098465 T OMDEV (NIL) -8 NIL NIL NIL) (-843 2092286 2092493 2092687 "OMCONN" 2093079 T OMCONN (NIL) -8 NIL NIL NIL) (-842 2090564 2091756 2091784 "OINTDOM" 2091789 T OINTDOM (NIL) -9 NIL 2091810 NIL) (-841 2087638 2089252 2089589 "OFMONOID" 2090259 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086872 2087575 2087620 "ODVAR" 2087625 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084009 2086617 2086772 "ODR" 2086777 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075414 2083785 2083911 "ODPOL" 2083916 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068757 2075286 2075391 "ODP" 2075396 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067499 2067738 2068013 "ODETOOLS" 2068531 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064442 2065124 2065840 "ODESYS" 2066832 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059272 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-7 NIL NIL NIL) (-822 2028031 2028740 2028768 "ODECAT" 2029373 T ODECAT (NIL) -9 NIL 2029904 NIL) (-821 2024524 2027736 2027858 "OCT" 2027941 NIL OCT (NIL T) -8 NIL NIL NIL) (-820 2024156 2024205 2024332 "OCTCT2" 2024475 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-819 2018425 2021199 2021239 "OC" 2022336 NIL OC (NIL T) -9 NIL 2023194 NIL) (-818 2015460 2016400 2017390 "OC-" 2017484 NIL OC- (NIL T T) -8 NIL NIL NIL) (-817 2014683 2015253 2015281 "OCAMON" 2015286 T OCAMON (NIL) -9 NIL 2015307 NIL) (-816 2014103 2014528 2014556 "OASGP" 2014561 T OASGP (NIL) -9 NIL 2014581 NIL) (-815 2013229 2013826 2013854 "OAMONS" 2013894 T OAMONS (NIL) -9 NIL 2013937 NIL) (-814 2012520 2013049 2013077 "OAMON" 2013082 T OAMON (NIL) -9 NIL 2013102 NIL) (-813 2011631 2012269 2012297 "OAGROUP" 2012302 T OAGROUP (NIL) -9 NIL 2012322 NIL) (-812 2011313 2011369 2011458 "NUMTUBE" 2011575 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004832 2006404 2007940 "NUMQUAD" 2009797 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000552 2001576 2002601 "NUMODE" 2003827 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997833 1998773 1998801 "NUMINT" 1999724 T NUMINT (NIL) -9 NIL 2000488 NIL) (-808 1996745 1996978 1997196 "NUMFMT" 1997635 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982928 1986049 1988581 "NUMERIC" 1994252 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976639 1982376 1982471 "NTSCAT" 1982476 NIL NTSCAT (NIL T T T T) -9 NIL 1982515 NIL) (-805 1975819 1975998 1976191 "NTPOLFN" 1976478 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1962580 1972644 1973456 "NSUP" 1975040 NIL NSUP (NIL T) -8 NIL NIL NIL) (-803 1962206 1962269 1962378 "NSUP2" 1962517 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-802 1951042 1961980 1962113 "NSMP" 1962118 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949450 1949775 1950132 "NREP" 1950730 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948029 1948293 1948651 "NPCOEF" 1949193 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947077 1947210 1947426 "NORMRETR" 1947910 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945088 1945408 1945817 "NORMPK" 1946785 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944767 1944801 1944925 "NORMMA" 1945054 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944531 1944724 1944753 "NONE" 1944758 T NONE (NIL) -8 NIL NIL NIL) (-795 1944314 1944349 1944418 "NONE1" 1944495 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-794 1943805 1943873 1944052 "NODE1" 1944246 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941897 1942928 1943183 "NNI" 1943530 T NNI (NIL) -8 NIL NIL 1943765) (-792 1940293 1940630 1940994 "NLINSOL" 1941565 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936474 1937529 1938428 "NIPROB" 1939414 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935213 1935465 1935767 "NFINTBAS" 1936236 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934297 1934863 1934904 "NETCLT" 1935076 NIL NETCLT (NIL T) -9 NIL 1935158 NIL) (-788 1932969 1933236 1933517 "NCODIV" 1934065 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932725 1932768 1932843 "NCNTFRAC" 1932926 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930881 1931269 1931689 "NCEP" 1932350 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929544 1930491 1930519 "NASRING" 1930629 T NASRING (NIL) -9 NIL 1930709 NIL) (-784 1929327 1929383 1929477 "NASRING-" 1929482 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928294 1928945 1928973 "NARNG" 1929090 T NARNG (NIL) -9 NIL 1929181 NIL) (-782 1927968 1928053 1928187 "NARNG-" 1928192 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926805 1927054 1927289 "NAGSP" 1927753 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917849 1919761 1921434 "NAGS" 1925152 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916373 1916705 1917036 "NAGF07" 1917538 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910845 1912202 1913509 "NAGF04" 1915086 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903717 1905427 1907060 "NAGF02" 1909232 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898881 1900041 1901158 "NAGF01" 1902620 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892461 1894075 1895660 "NAGE04" 1897316 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883522 1885751 1887881 "NAGE02" 1890351 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879415 1880422 1881386 "NAGE01" 1882578 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877192 1877744 1878302 "NAGD03" 1878877 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868888 1870870 1872824 "NAGD02" 1875258 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862627 1864124 1865564 "NAGD01" 1867468 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858764 1859658 1860495 "NAGC06" 1861810 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857211 1857561 1857917 "NAGC05" 1858428 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856575 1856706 1856850 "NAGC02" 1857087 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855376 1856103 1856143 "NAALG" 1856222 NIL NAALG (NIL T) -9 NIL 1856283 NIL) (-765 1855205 1855240 1855330 "NAALG-" 1855335 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849077 1850263 1851450 "MULTSQFR" 1854101 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848384 1848471 1848655 "MULTFACT" 1848989 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840529 1844967 1845020 "MTSCAT" 1846090 NIL MTSCAT (NIL T T) -9 NIL 1846606 NIL) (-761 1840235 1840295 1840387 "MTHING" 1840469 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840021 1840060 1840120 "MSYSCMD" 1840195 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1835735 1838776 1839096 "MSET" 1839734 NIL MSET (NIL T) -8 NIL NIL NIL) (-758 1832480 1835296 1835337 "MSETAGG" 1835342 NIL MSETAGG (NIL T) -9 NIL 1835376 NIL) (-757 1828072 1829859 1830604 "MRING" 1831780 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827632 1827705 1827836 "MRF2" 1827999 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827244 1827285 1827429 "MRATFAC" 1827591 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824814 1825151 1825582 "MPRFF" 1826949 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818141 1824668 1824765 "MPOLY" 1824770 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817625 1817666 1817874 "MPCPF" 1818100 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817133 1817182 1817366 "MPC3" 1817576 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816316 1816409 1816630 "MPC2" 1817048 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814593 1814954 1815344 "MONOTOOL" 1815976 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813738 1814121 1814149 "MONOID" 1814368 T MONOID (NIL) -9 NIL 1814515 NIL) (-747 1813254 1813403 1813584 "MONOID-" 1813589 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802208 1809074 1809133 "MONOGEN" 1809807 NIL MONOGEN (NIL T T) -9 NIL 1810263 NIL) (-745 1799258 1800161 1801161 "MONOGEN-" 1801280 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797975 1798523 1798551 "MONADWU" 1798943 T MONADWU (NIL) -9 NIL 1799181 NIL) (-743 1797305 1797506 1797754 "MONADWU-" 1797759 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796590 1796894 1796922 "MONAD" 1797129 T MONAD (NIL) -9 NIL 1797241 NIL) (-741 1796257 1796353 1796485 "MONAD-" 1796490 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794396 1795170 1795449 "MOEBIUS" 1796010 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793564 1794064 1794104 "MODULE" 1794109 NIL MODULE (NIL T) -9 NIL 1794148 NIL) (-738 1793102 1793228 1793418 "MODULE-" 1793423 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790632 1791466 1791793 "MODRING" 1792926 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787354 1788737 1789258 "MODOP" 1790161 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785840 1786421 1786698 "MODMONOM" 1787217 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774580 1784131 1784545 "MODMON" 1785477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771406 1773424 1773700 "MODFIELD" 1774455 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770317 1770687 1770877 "MMLFORM" 1771236 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769837 1769886 1770065 "MMAP" 1770268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767730 1768669 1768710 "MLO" 1769133 NIL MLO (NIL T) -9 NIL 1769375 NIL) (-729 1765078 1765612 1766214 "MLIFT" 1767211 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764457 1764553 1764707 "MKUCFUNC" 1764989 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764050 1764126 1764249 "MKRECORD" 1764380 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763073 1763259 1763487 "MKFUNC" 1763861 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762449 1762565 1762721 "MKFLCFN" 1762956 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761714 1761828 1762013 "MKBCFUNC" 1762342 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757697 1761268 1761404 "MINT" 1761598 T MINT (NIL) -8 NIL NIL NIL) (-722 1756479 1756752 1757029 "MHROWRED" 1757452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751223 1755014 1755419 "MFLOAT" 1756094 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750568 1750656 1750827 "MFINFACT" 1751135 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746847 1747731 1748615 "MESH" 1749704 T MESH (NIL) -7 NIL NIL NIL) (-718 1745201 1745549 1745902 "MDDFACT" 1746534 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741737 1744332 1744373 "MDAGG" 1744628 NIL MDAGG (NIL T) -9 NIL 1744771 NIL) (-716 1729439 1741030 1741237 "MCMPLX" 1741550 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728558 1728722 1728923 "MCDEN" 1729288 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726406 1726718 1727098 "MCALCFN" 1728288 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725283 1725571 1725804 "MAYBE" 1726212 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722841 1723418 1723980 "MATSTOR" 1724754 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718263 1722213 1722461 "MATRIX" 1722626 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713963 1714736 1715472 "MATLIN" 1717620 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1703309 1707020 1707097 "MATCAT" 1712129 NIL MATCAT (NIL T T T) -9 NIL 1713601 NIL) (-708 1699262 1700572 1701985 "MATCAT-" 1701990 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-707 1697838 1698009 1698342 "MATCAT2" 1699097 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1695914 1696274 1696658 "MAPPKG3" 1697513 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694871 1695068 1695290 "MAPPKG2" 1695738 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693328 1693654 1693981 "MAPPKG1" 1694577 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692329 1692734 1692911 "MAPPAST" 1693171 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691934 1691998 1692121 "MAPHACK3" 1692265 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691514 1691587 1691701 "MAPHACK2" 1691866 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690940 1691055 1691197 "MAPHACK1" 1691405 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688863 1689640 1689944 "MAGMA" 1690668 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688282 1688587 1688678 "MACROAST" 1688792 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684525 1686521 1686982 "M3D" 1687854 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678005 1682836 1682877 "LZSTAGG" 1683659 NIL LZSTAGG (NIL T) -9 NIL 1683954 NIL) (-695 1673687 1675136 1676593 "LZSTAGG-" 1676598 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670600 1671578 1672065 "LWORD" 1673232 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670122 1670404 1670479 "LSTAST" 1670545 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662050 1669893 1670027 "LSQM" 1670032 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661268 1661413 1661641 "LSPP" 1661905 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1659050 1659381 1659837 "LSMP" 1660957 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-689 1655787 1656503 1657233 "LSMP1" 1658352 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-688 1648923 1654877 1654918 "LSAGG" 1654980 NIL LSAGG (NIL T) -9 NIL 1655058 NIL) (-687 1645432 1646542 1647755 "LSAGG-" 1647760 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642727 1644576 1644825 "LPOLY" 1645227 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642303 1642394 1642517 "LPEFRAC" 1642636 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1640480 1641397 1641650 "LO" 1642135 NIL LO (NIL T T T) -8 NIL NIL NIL) (-683 1640163 1640242 1640270 "LOGIC" 1640381 T LOGIC (NIL) -9 NIL 1640463 NIL) (-682 1640019 1640048 1640119 "LOGIC-" 1640124 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-681 1639194 1639352 1639545 "LODOOPS" 1639875 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-680 1636289 1639110 1639176 "LODO" 1639181 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-679 1634813 1635062 1635415 "LODOF" 1636036 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1630689 1633448 1633489 "LODOCAT" 1633927 NIL LODOCAT (NIL T) -9 NIL 1634138 NIL) (-677 1630404 1630480 1630607 "LODOCAT-" 1630612 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1627390 1630245 1630363 "LODO2" 1630368 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1624497 1627327 1627372 "LODO1" 1627377 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1623366 1623543 1623848 "LODEEF" 1624320 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-673 1618338 1621532 1621573 "LNAGG" 1622435 NIL LNAGG (NIL T) -9 NIL 1622870 NIL) (-672 1617431 1617699 1618041 "LNAGG-" 1618046 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613411 1614356 1614995 "LMOPS" 1616846 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612710 1613188 1613229 "LMODULE" 1613234 NIL LMODULE (NIL T) -9 NIL 1613260 NIL) (-669 1609665 1612355 1612478 "LMDICT" 1612620 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609241 1609455 1609496 "LLINSET" 1609557 NIL LLINSET (NIL T) -9 NIL 1609601 NIL) (-667 1608886 1609149 1609209 "LITERAL" 1609214 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1601340 1607820 1608124 "LIST" 1608615 NIL LIST (NIL T) -8 NIL NIL NIL) (-665 1600859 1600939 1601078 "LIST3" 1601260 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-664 1599848 1600044 1600272 "LIST2" 1600677 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597946 1598294 1598693 "LIST2MAP" 1599495 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1597529 1597765 1597806 "LINSET" 1597811 NIL LINSET (NIL T) -9 NIL 1597845 NIL) (-661 1596343 1597037 1597204 "LINFORM" 1597414 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594642 1595370 1595411 "LINEXP" 1595901 NIL LINEXP (NIL T) -9 NIL 1596174 NIL) (-659 1593218 1594122 1594303 "LINELT" 1594513 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591775 1592055 1592366 "LINDEP" 1592970 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590911 1591507 1591617 "LINBASIS" 1591705 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587648 1588397 1589174 "LIMITRF" 1590166 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585933 1586247 1586656 "LIMITPS" 1587343 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1579953 1585444 1585672 "LIE" 1585754 NIL LIE (NIL T T) -8 NIL NIL NIL) (-653 1578781 1579356 1579396 "LIECAT" 1579536 NIL LIECAT (NIL T) -9 NIL 1579687 NIL) (-652 1578616 1578649 1578737 "LIECAT-" 1578742 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-651 1570803 1578156 1578312 "LIB" 1578480 T LIB (NIL) -8 NIL NIL NIL) (-650 1566372 1567321 1568256 "LGROBP" 1569920 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564310 1564644 1564994 "LF" 1566093 NIL LF (NIL T T) -7 NIL NIL NIL) (-648 1562934 1563842 1563870 "LFCAT" 1564077 T LFCAT (NIL) -9 NIL 1564216 NIL) (-647 1559794 1560466 1561154 "LEXTRIPK" 1562298 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556382 1557364 1557867 "LEXP" 1559374 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555798 1556103 1556195 "LETAST" 1556310 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554184 1554509 1554910 "LEADCDET" 1555480 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553362 1553448 1553677 "LAZM3PK" 1554105 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547873 1551439 1551977 "LAUPOL" 1552874 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547446 1547496 1547657 "LAPLACE" 1547823 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545183 1546547 1546798 "LA" 1547279 NIL LA (NIL T T T) -8 NIL NIL NIL) (-639 1544031 1544747 1544788 "LALG" 1544850 NIL LALG (NIL T) -9 NIL 1544909 NIL) (-638 1543727 1543804 1543940 "LALG-" 1543945 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-637 1543556 1543586 1543627 "KVTFROM" 1543689 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542313 1542923 1543108 "KTVLOGIC" 1543391 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542142 1542172 1542213 "KRCFROM" 1542275 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541034 1541233 1541532 "KOVACIC" 1541942 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540863 1540893 1540934 "KONVERT" 1540996 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540692 1540722 1540763 "KOERCE" 1540825 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1538379 1539285 1539662 "KERNEL" 1540348 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-630 1537863 1537956 1538088 "KERNEL2" 1538293 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-629 1531334 1536340 1536394 "KDAGG" 1536771 NIL KDAGG (NIL T T) -9 NIL 1536977 NIL) (-628 1530845 1530987 1531192 "KDAGG-" 1531197 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523545 1530506 1530661 "KAFILE" 1530723 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523149 1523434 1523497 "JVMOP" 1523502 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521885 1522389 1522638 "JVMMDACC" 1522920 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520821 1521275 1521480 "JVMFDACC" 1521700 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519402 1519897 1520197 "JVMCSTTG" 1520541 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518538 1518942 1519103 "JVMCFACC" 1519261 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518216 1518455 1518504 "JVMBCODE" 1518509 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512236 1517727 1517955 "JORDAN" 1518037 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511549 1511885 1512006 "JOINAST" 1512135 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507584 1509726 1509780 "IXAGG" 1510709 NIL IXAGG (NIL T T) -9 NIL 1511168 NIL) (-617 1506437 1506809 1507228 "IXAGG-" 1507233 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501526 1506359 1506418 "IVECTOR" 1506423 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500250 1500529 1500795 "ITUPLE" 1501293 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498722 1498929 1499224 "ITRIGMNP" 1500072 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497449 1497671 1497954 "ITFUN3" 1498498 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497075 1497138 1497247 "ITFUN2" 1497386 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496180 1496555 1496729 "ITFORM" 1496921 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493949 1495200 1495478 "ITAYLOR" 1495935 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482346 1488086 1489249 "ISUPS" 1492819 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481438 1481590 1481826 "ISUMP" 1482193 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476288 1481383 1481424 "ISTRING" 1481429 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475704 1476009 1476101 "ISAST" 1476216 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474901 1474995 1475211 "IRURPK" 1475618 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473813 1474038 1474278 "IRSN" 1474681 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471858 1472239 1472668 "IRRF2F" 1473451 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471599 1471643 1471719 "IRREDFFX" 1471814 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470172 1470473 1470772 "IROOT" 1471332 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1466612 1467856 1468548 "IR" 1469512 NIL IR (NIL T) -8 NIL NIL NIL) (-599 1465751 1466105 1466256 "IRFORM" 1466481 T IRFORM (NIL) -8 NIL NIL NIL) (-598 1463340 1463859 1464425 "IR2" 1465229 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462422 1462553 1462767 "IR2F" 1463223 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1462207 1462247 1462307 "IPRNTPK" 1462382 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458160 1462096 1462165 "IPF" 1462170 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456181 1458085 1458142 "IPADIC" 1458147 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455439 1455741 1455871 "IP4ADDR" 1456071 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454777 1455068 1455200 "IOMODE" 1455327 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453748 1454374 1454501 "IOBFILE" 1454670 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453158 1453652 1453680 "IOBCON" 1453685 T IOBCON (NIL) -9 NIL 1453706 NIL) (-589 1452663 1452727 1452910 "INVLAPLA" 1453094 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442233 1444665 1447051 "INTTR" 1450327 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438526 1439310 1440175 "INTTOOLS" 1441418 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438106 1438203 1438320 "INTSLPE" 1438429 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435573 1438029 1438088 "INTRVL" 1438093 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433151 1433687 1434262 "INTRF" 1435058 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432544 1432659 1432801 "INTRET" 1433049 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430517 1430930 1431400 "INTRAT" 1432152 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427762 1428363 1428982 "INTPM" 1430002 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424479 1425106 1425844 "INTPAF" 1427148 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419580 1420620 1421671 "INTPACK" 1423448 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1415768 1419377 1419486 "INT" 1419491 T INT (NIL) -8 NIL NIL NIL) (-577 1415014 1415172 1415380 "INTHERTR" 1415610 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-576 1414447 1414533 1414721 "INTHERAL" 1414928 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-575 1412215 1412736 1413193 "INTHEORY" 1414010 T INTHEORY (NIL) -7 NIL NIL NIL) (-574 1403547 1405242 1407014 "INTG0" 1410567 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-573 1384072 1388910 1393720 "INTFTBL" 1398757 T INTFTBL (NIL) -8 NIL NIL NIL) (-572 1383297 1383459 1383632 "INTFACT" 1383931 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-571 1380694 1381170 1381727 "INTEF" 1382851 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-570 1378891 1379786 1379814 "INTDOM" 1380115 T INTDOM (NIL) -9 NIL 1380322 NIL) (-569 1378230 1378434 1378676 "INTDOM-" 1378681 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-568 1374104 1376519 1376573 "INTCAT" 1377372 NIL INTCAT (NIL T) -9 NIL 1377693 NIL) (-567 1373558 1373679 1373807 "INTBIT" 1373996 T INTBIT (NIL) -7 NIL NIL NIL) (-566 1372239 1372411 1372718 "INTALG" 1373403 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-565 1371716 1371812 1371969 "INTAF" 1372143 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-564 1364683 1371526 1371666 "INTABL" 1371671 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-563 1363920 1364482 1364547 "INT8" 1364581 T INT8 (NIL) -8 NIL NIL 1364626) (-562 1363156 1363718 1363783 "INT64" 1363817 T INT64 (NIL) -8 NIL NIL 1363862) (-561 1362392 1362954 1363019 "INT32" 1363053 T INT32 (NIL) -8 NIL NIL 1363098) (-560 1361628 1362190 1362255 "INT16" 1362289 T INT16 (NIL) -8 NIL NIL 1362334) (-559 1355729 1359176 1359204 "INS" 1360138 T INS (NIL) -9 NIL 1360803 NIL) (-558 1352783 1353740 1354714 "INS-" 1354787 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351540 1351785 1352083 "INPSIGN" 1352536 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350634 1350775 1350972 "INPRODPF" 1351420 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349504 1349645 1349882 "INPRODFF" 1350514 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348492 1348656 1348916 "INNMFACT" 1349340 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347671 1347786 1347974 "INMODGCD" 1348391 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346155 1346424 1346748 "INFSP" 1347416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345315 1345456 1345639 "INFPROD0" 1346035 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1341882 1343380 1343895 "INFORM" 1344808 T INFORM (NIL) -8 NIL NIL NIL) (-549 1341480 1341552 1341650 "INFORM1" 1341817 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-548 1340985 1341092 1341206 "INFINITY" 1341386 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340059 1340705 1340806 "INETCLTS" 1340904 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338657 1338925 1339246 "INEP" 1339807 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337718 1338554 1338619 "INDE" 1338624 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337270 1337350 1337467 "INCRMAPS" 1337645 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335992 1336539 1336745 "INBFILE" 1337084 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331171 1332228 1333172 "INBFF" 1335080 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330025 1330348 1330376 "INBCON" 1330889 T INBCON (NIL) -9 NIL 1331155 NIL) (-540 1329235 1329500 1329776 "INBCON-" 1329781 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328654 1328959 1329050 "INAST" 1329164 T INAST (NIL) -8 NIL NIL NIL) (-538 1328021 1328333 1328439 "IMPTAST" 1328568 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323942 1327865 1327969 "IMATRIX" 1327974 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322634 1322773 1323089 "IMATQF" 1323798 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320814 1321081 1321418 "IMATLIN" 1322390 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314729 1320738 1320796 "ILIST" 1320801 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312395 1314589 1314702 "IIARRAY2" 1314707 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307195 1312306 1312370 "IFF" 1312375 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306476 1306812 1306928 "IFAST" 1307099 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300988 1305768 1305956 "IFARRAY" 1306333 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300026 1300892 1300965 "IFAMON" 1300970 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299598 1299675 1299729 "IEVALAB" 1299936 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299261 1299341 1299501 "IEVALAB-" 1299506 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298642 1299176 1299238 "IDPO" 1299243 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-525 1297706 1298531 1298606 "IDPOAMS" 1298611 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-524 1296839 1297595 1297670 "IDPOAM" 1297675 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-523 1295319 1295846 1295898 "IDPC" 1296410 NIL IDPC (NIL T T) -9 NIL 1296691 NIL) (-522 1294651 1295211 1295284 "IDPAM" 1295289 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293866 1294543 1294616 "IDPAG" 1294621 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293410 1293672 1293762 "IDENT" 1293796 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289629 1290513 1291408 "IDECOMP" 1292567 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282264 1283552 1284599 "IDEAL" 1288665 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281406 1281536 1281736 "ICDEN" 1282148 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280381 1280886 1281033 "ICARD" 1281279 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278411 1278754 1279159 "IBPTOOLS" 1280058 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273526 1278031 1278144 "IBITS" 1278330 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270201 1270825 1271520 "IBATOOL" 1272943 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267962 1268442 1268975 "IBACHIN" 1269736 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265552 1267808 1267911 "IARRAY2" 1267916 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261265 1265478 1265535 "IARRAY1" 1265540 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254275 1259677 1260158 "IAN" 1260804 T IAN (NIL) -8 NIL NIL NIL) (-508 1253780 1253843 1254016 "IALGFACT" 1254212 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253272 1253421 1253449 "HYPCAT" 1253656 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252774 1252927 1253113 "HYPCAT-" 1253118 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252321 1252569 1252652 "HOSTNAME" 1252711 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252154 1252203 1252244 "HOMOTOP" 1252249 NIL HOMOTOP (NIL T) -9 NIL 1252282 NIL) (-503 1248587 1250086 1250127 "HOAGG" 1251108 NIL HOAGG (NIL T) -9 NIL 1251837 NIL) (-502 1247103 1247580 1248106 "HOAGG-" 1248111 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240139 1246696 1246846 "HEXADEC" 1246973 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238851 1239109 1239372 "HEUGCD" 1239916 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237783 1238688 1238818 "HELLFDIV" 1238823 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235793 1237560 1237648 "HEAP" 1237727 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234990 1235345 1235479 "HEADAST" 1235679 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228377 1234905 1234967 "HDP" 1234972 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221389 1228012 1228164 "HDMP" 1228278 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220695 1220853 1221017 "HB" 1221245 T HB (NIL) -7 NIL NIL NIL) (-493 1213705 1220541 1220645 "HASHTBL" 1220650 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213121 1213426 1213518 "HASAST" 1213633 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210527 1212743 1212925 "HACKPI" 1212959 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205699 1210380 1210493 "GTSET" 1210498 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198738 1205577 1205675 "GSTBL" 1205680 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190487 1197903 1198159 "GSERIES" 1198538 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189518 1190031 1190059 "GROUP" 1190262 T GROUP (NIL) -9 NIL 1190396 NIL) (-486 1188842 1189043 1189294 "GROUP-" 1189299 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187191 1187530 1187917 "GROEBSOL" 1188519 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186019 1186379 1186430 "GRMOD" 1186959 NIL GRMOD (NIL T T) -9 NIL 1187127 NIL) (-483 1185775 1185823 1185951 "GRMOD-" 1185956 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180915 1182129 1183129 "GRIMAGE" 1184795 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179309 1179642 1179966 "GRDEF" 1180611 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178741 1178869 1179010 "GRAY" 1179188 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177818 1178320 1178371 "GRALG" 1178524 NIL GRALG (NIL T T) -9 NIL 1178617 NIL) (-478 1177455 1177552 1177715 "GRALG-" 1177720 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173936 1177038 1177217 "GPOLSET" 1177361 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173284 1173347 1173605 "GOSPER" 1173873 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168854 1169722 1170248 "GMODPOL" 1172983 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167841 1168043 1168281 "GHENSEL" 1168666 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161913 1162840 1163860 "GENUPS" 1166925 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161604 1161661 1161750 "GENUFACT" 1161856 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161004 1161093 1161258 "GENPGCD" 1161522 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160472 1160513 1160726 "GENMFACT" 1160963 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159008 1159295 1159602 "GENEEZ" 1160215 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152180 1158619 1158781 "GDMP" 1158931 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140919 1145951 1147057 "GCNAALG" 1151163 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139046 1140094 1140122 "GCDDOM" 1140377 T GCDDOM (NIL) -9 NIL 1140534 NIL) (-465 1138486 1138643 1138858 "GCDDOM-" 1138863 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1137136 1137343 1137647 "GB" 1138265 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-463 1125608 1128082 1130474 "GBINTERN" 1134827 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-462 1123409 1123737 1124158 "GBF" 1125283 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-461 1122166 1122355 1122622 "GBEUCLID" 1123225 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-460 1121497 1121640 1121789 "GAUSSFAC" 1122037 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119818 1120166 1120480 "GALUTIL" 1121216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118078 1118400 1118724 "GALPOLYU" 1119545 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115377 1115733 1116140 "GALFACTU" 1117775 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106991 1108682 1110290 "GALFACT" 1113809 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104277 1105037 1105065 "FVFUN" 1106221 T FVFUN (NIL) -9 NIL 1106941 NIL) (-454 1103507 1103725 1103753 "FVC" 1104044 T FVC (NIL) -9 NIL 1104227 NIL) (-453 1103108 1103332 1103400 "FUNDESC" 1103459 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102681 1102905 1102986 "FUNCTION" 1103060 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100311 1101003 1101469 "FT" 1102235 T FT (NIL) -8 NIL NIL NIL) (-450 1098988 1099612 1099815 "FTEM" 1100128 T FTEM (NIL) -8 NIL NIL NIL) (-449 1097257 1097568 1097965 "FSUPFACT" 1098679 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095576 1095943 1096275 "FST" 1096945 T FST (NIL) -8 NIL NIL NIL) (-447 1094757 1094881 1095069 "FSRED" 1095458 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093446 1093712 1094059 "FSPRMELT" 1094472 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090656 1091190 1091676 "FSPECF" 1093009 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1070883 1080430 1080471 "FS" 1084355 NIL FS (NIL T) -9 NIL 1086644 NIL) (-443 1058944 1062519 1066576 "FS-" 1066876 NIL FS- (NIL T T) -8 NIL NIL NIL) (-442 1058466 1058526 1058696 "FSINT" 1058885 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1056602 1057459 1057762 "FSERIES" 1058245 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1055626 1055760 1055984 "FSCINT" 1056482 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1051490 1054570 1054611 "FSAGG" 1054981 NIL FSAGG (NIL T) -9 NIL 1055240 NIL) (-438 1049090 1049853 1050649 "FSAGG-" 1050744 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-437 1048114 1048275 1048502 "FSAGG2" 1048943 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-436 1045774 1046072 1046620 "FS2UPS" 1047832 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1045402 1045451 1045580 "FS2" 1045725 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-434 1044268 1044451 1044753 "FS2EXPXP" 1045227 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-433 1043682 1043809 1043961 "FRUTIL" 1044148 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1034599 1039177 1040535 "FR" 1042356 NIL FR (NIL T) -8 NIL NIL NIL) (-431 1029117 1032288 1032328 "FRNAALG" 1033648 NIL FRNAALG (NIL T) -9 NIL 1034246 NIL) (-430 1024598 1025866 1027141 "FRNAALG-" 1027891 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-429 1024230 1024279 1024406 "FRNAAF2" 1024549 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-428 1022517 1023079 1023375 "FRMOD" 1024042 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-427 1020122 1020892 1021210 "FRIDEAL" 1022308 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1019307 1019400 1019691 "FRIDEAL2" 1020029 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018398 1018854 1018895 "FRETRCT" 1018900 NIL FRETRCT (NIL T) -9 NIL 1019076 NIL) (-424 1017456 1017741 1018092 "FRETRCT-" 1018097 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-423 1014270 1015740 1015799 "FRAMALG" 1016681 NIL FRAMALG (NIL T T) -9 NIL 1016973 NIL) (-422 1012308 1012859 1013489 "FRAMALG-" 1013712 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-421 1005279 1011781 1012058 "FRAC" 1012063 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1004909 1004972 1005079 "FRAC2" 1005216 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004539 1004602 1004709 "FR2" 1004846 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-418 998456 1001918 1001946 "FPS" 1003065 T FPS (NIL) -9 NIL 1003622 NIL) (-417 997881 998014 998178 "FPS-" 998324 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994833 996838 996866 "FPC" 997091 T FPC (NIL) -9 NIL 997233 NIL) (-415 994614 994666 994763 "FPC-" 994768 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993372 994102 994143 "FPATMAB" 994148 NIL FPATMAB (NIL T) -9 NIL 994300 NIL) (-413 991515 992114 992461 "FPARFRAC" 993088 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986807 987407 988089 "FORTRAN" 990947 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984493 985023 985562 "FORT" 986288 T FORT (NIL) -7 NIL NIL NIL) (-410 982067 982731 982759 "FORTFN" 983819 T FORTFN (NIL) -9 NIL 984443 NIL) (-409 981819 981881 981909 "FORTCAT" 981968 T FORTCAT (NIL) -9 NIL 982030 NIL) (-408 979823 980435 980825 "FORMULA" 981449 T FORMULA (NIL) -8 NIL NIL NIL) (-407 979605 979641 979710 "FORMULA1" 979787 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-406 979122 979180 979353 "FORDER" 979547 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978182 978382 978575 "FOP" 978949 T FOP (NIL) -7 NIL NIL NIL) (-404 976595 977462 977636 "FNLA" 978064 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975214 975725 975753 "FNCAT" 976213 T FNCAT (NIL) -9 NIL 976473 NIL) (-402 974657 975173 975201 "FNAME" 975206 T FNAME (NIL) -8 NIL NIL NIL) (-401 972983 974156 974184 "FMTC" 974189 T FMTC (NIL) -9 NIL 974225 NIL) (-400 971531 972919 972965 "FMONOID" 972970 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968120 969486 969527 "FMONCAT" 970744 NIL FMONCAT (NIL T) -9 NIL 971349 NIL) (-398 967138 967862 968011 "FM" 968016 NIL FM (NIL T T) -8 NIL NIL NIL) (-397 964460 965208 965236 "FMFUN" 966380 T FMFUN (NIL) -9 NIL 967088 NIL) (-396 963693 963910 963938 "FMC" 964228 T FMC (NIL) -9 NIL 964410 NIL) (-395 960566 961618 961672 "FMCAT" 962867 NIL FMCAT (NIL T T) -9 NIL 963362 NIL) (-394 959234 960332 960432 "FM1" 960511 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-393 956972 957424 957918 "FLOATRP" 958785 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 949628 954701 955322 "FLOAT" 956371 T FLOAT (NIL) -8 NIL NIL NIL) (-391 947030 947566 948144 "FLOATCP" 949095 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-390 945548 946622 946663 "FLINEXP" 946668 NIL FLINEXP (NIL T) -9 NIL 946761 NIL) (-389 944678 944937 945265 "FLINEXP-" 945270 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943736 943898 944122 "FLASORT" 944530 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940654 941706 941758 "FLALG" 942985 NIL FLALG (NIL T T) -9 NIL 943452 NIL) (-386 933918 938063 938104 "FLAGG" 939366 NIL FLAGG (NIL T) -9 NIL 940018 NIL) (-385 932572 932983 933473 "FLAGG-" 933478 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-384 931596 931757 931984 "FLAGG2" 932425 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-383 928227 929441 929500 "FINRALG" 930628 NIL FINRALG (NIL T T) -9 NIL 931136 NIL) (-382 927351 927616 927955 "FINRALG-" 927960 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926657 926956 926984 "FINITE" 927180 T FINITE (NIL) -9 NIL 927287 NIL) (-380 918608 921187 921227 "FINAALG" 924894 NIL FINAALG (NIL T) -9 NIL 926347 NIL) (-379 913724 914990 916134 "FINAALG-" 917513 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 913002 913479 913582 "FILE" 913654 NIL FILE (NIL T) -8 NIL NIL NIL) (-377 911562 911984 912038 "FILECAT" 912722 NIL FILECAT (NIL T T) -9 NIL 912938 NIL) (-376 908958 910792 910820 "FIELD" 910860 T FIELD (NIL) -9 NIL 910940 NIL) (-375 907500 907963 908474 "FIELD-" 908479 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905182 906135 906482 "FGROUP" 907186 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904254 904436 904656 "FGLMICPK" 905014 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899488 904179 904236 "FFX" 904241 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899083 899150 899285 "FFSLPE" 899421 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 894959 895855 896651 "FFPOLY" 898319 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-369 894457 894499 894708 "FFPOLY2" 894917 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-368 889705 894376 894439 "FFP" 894444 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884505 889616 889680 "FF" 889685 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-366 879015 883848 884038 "FFNBX" 884359 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-365 873327 878150 878408 "FFNBP" 878869 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-364 867344 872611 872822 "FFNB" 873160 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-363 866164 866374 866689 "FFINTBAS" 867141 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-362 861740 864411 864439 "FFIELDC" 865059 T FFIELDC (NIL) -9 NIL 865435 NIL) (-361 860318 860773 861270 "FFIELDC-" 861275 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-360 859875 859933 860057 "FFHOM" 860260 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-359 857534 858057 858574 "FFF" 859390 NIL FFF (NIL T) -7 NIL NIL NIL) (-358 852548 857276 857377 "FFCGX" 857477 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-357 847566 852280 852387 "FFCGP" 852491 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-356 842145 847293 847401 "FFCG" 847502 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-355 820808 831877 831963 "FFCAT" 837128 NIL FFCAT (NIL T T T) -9 NIL 838579 NIL) (-354 815819 817053 818367 "FFCAT-" 819597 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815224 815273 815508 "FFCAT2" 815770 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-352 803877 808196 809416 "FEXPR" 814076 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802805 803274 803315 "FEVALAB" 803399 NIL FEVALAB (NIL T) -9 NIL 803660 NIL) (-350 801922 802174 802512 "FEVALAB-" 802517 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 800332 801305 801508 "FDIV" 801821 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-348 797194 798079 798194 "FDIVCAT" 799762 NIL FDIVCAT (NIL T T T T) -9 NIL 800199 NIL) (-347 796950 796983 797153 "FDIVCAT-" 797158 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-346 796164 796257 796534 "FDIV2" 796857 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-345 795072 795459 795661 "FCTRDATA" 795982 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793728 794017 794306 "FCPAK1" 794803 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792731 793228 793369 "FCOMP" 793619 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776046 779881 783419 "FC" 789213 T FC (NIL) -8 NIL NIL NIL) (-341 767741 772367 772407 "FAXF" 774209 NIL FAXF (NIL T) -9 NIL 774901 NIL) (-340 764862 765675 766500 "FAXF-" 766965 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759431 764238 764414 "FARRAY" 764719 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753995 756378 756431 "FAMR" 757454 NIL FAMR (NIL T T) -9 NIL 757914 NIL) (-337 752819 753187 753622 "FAMR-" 753627 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751846 752741 752794 "FAMONOID" 752799 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749476 750328 750381 "FAMONC" 751322 NIL FAMONC (NIL T T) -9 NIL 751708 NIL) (-334 747950 749230 749367 "FAGROUP" 749372 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745703 746064 746467 "FACUTIL" 747631 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744790 744987 745209 "FACTFUNC" 745513 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736548 744093 744292 "EXPUPXS" 744646 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734001 734571 735157 "EXPRTUBE" 735982 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730212 730864 731594 "EXPRODE" 733340 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 714506 728861 729290 "EXPR" 729816 NIL EXPR (NIL T) -8 NIL NIL NIL) (-327 708940 709647 710453 "EXPR2UPS" 713804 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-326 708566 708629 708738 "EXPR2" 708877 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-325 698883 707717 708008 "EXPEXPAN" 708402 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698647 698840 698869 "EXIT" 698874 T EXIT (NIL) -8 NIL NIL NIL) (-323 698067 698371 698462 "EXITAST" 698576 T EXITAST (NIL) -8 NIL NIL NIL) (-322 697688 697756 697869 "EVALCYC" 697999 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697205 697347 697388 "EVALAB" 697558 NIL EVALAB (NIL T) -9 NIL 697662 NIL) (-320 696662 696808 697029 "EVALAB-" 697034 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693770 695318 695346 "EUCDOM" 695901 T EUCDOM (NIL) -9 NIL 696251 NIL) (-318 692109 692617 693207 "EUCDOM-" 693212 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 679426 682407 685157 "ESTOOLS" 689379 T ESTOOLS (NIL) -7 NIL NIL NIL) (-316 679052 679115 679224 "ESTOOLS2" 679363 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-315 678797 678845 678925 "ESTOOLS1" 679004 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-314 672498 674428 674456 "ES" 677224 T ES (NIL) -9 NIL 678634 NIL) (-313 667175 668732 670549 "ES-" 670713 NIL ES- (NIL T) -8 NIL NIL NIL) (-312 663483 664310 665090 "ESCONT" 666415 T ESCONT (NIL) -7 NIL NIL NIL) (-311 663222 663260 663342 "ESCONT1" 663445 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-310 662891 662947 663047 "ES2" 663166 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-309 662515 662579 662688 "ES1" 662827 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-308 661707 661860 662036 "ERROR" 662359 T ERROR (NIL) -7 NIL NIL NIL) (-307 654723 661566 661657 "EQTBL" 661662 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 646982 650037 651486 "EQ" 653307 NIL -1512 (NIL T) -8 NIL NIL NIL) (-305 646608 646671 646780 "EQ2" 646919 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-304 641851 642946 644039 "EP" 645547 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640391 640742 641048 "ENV" 641565 T ENV (NIL) -8 NIL NIL NIL) (-302 639351 640025 640053 "ENTIRER" 640058 T ENTIRER (NIL) -9 NIL 640104 NIL) (-301 635763 637533 637894 "EMR" 639159 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634867 635078 635132 "ELTAGG" 635512 NIL ELTAGG (NIL T T) -9 NIL 635723 NIL) (-299 634574 634648 634789 "ELTAGG-" 634794 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634332 634367 634421 "ELTAB" 634505 NIL ELTAB (NIL T T) -9 NIL 634557 NIL) (-297 633434 633604 633803 "ELFUTS" 634183 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633158 633232 633260 "ELEMFUN" 633365 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633022 633049 633117 "ELEMFUN-" 633122 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627439 631064 631105 "ELAGG" 632045 NIL ELAGG (NIL T) -9 NIL 632508 NIL) (-293 625616 626158 626821 "ELAGG-" 626826 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624898 625065 625221 "ELABOR" 625480 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623505 623838 624132 "ELABEXPR" 624624 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616017 618142 618971 "EFUPXS" 622780 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609143 611266 612077 "EFULS" 615292 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606580 606986 607458 "EFSTRUC" 608775 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596017 597937 599485 "EF" 605095 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 594995 595502 595651 "EAB" 595888 T EAB (NIL) -8 NIL NIL NIL) (-285 594117 594954 594982 "E04UCFA" 594987 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593239 594076 594104 "E04NAFA" 594109 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592361 593198 593226 "E04MBFA" 593231 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591483 592320 592348 "E04JAFA" 592353 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590607 591442 591470 "E04GCFA" 591475 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589731 590566 590594 "E04FDFA" 590599 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588853 589690 589718 "E04DGFA" 589723 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582930 584378 585742 "E04AGNT" 587509 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581550 582231 582271 "DVARCAT" 582612 NIL DVARCAT (NIL T) -9 NIL 582775 NIL) (-276 580700 580966 581280 "DVARCAT-" 581285 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572661 580499 580628 "DSMP" 580633 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571012 571803 571844 "DSEXT" 572207 NIL DSEXT (NIL T) -9 NIL 572501 NIL) (-273 569201 569725 570391 "DSEXT-" 570396 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563784 565146 566214 "DROPT" 568153 T DROPT (NIL) -8 NIL NIL NIL) (-271 563443 563508 563606 "DROPT1" 563719 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-270 558462 559684 560821 "DROPT0" 562326 T DROPT0 (NIL) -7 NIL NIL NIL) (-269 556771 557132 557518 "DRAWPT" 558096 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 551262 552281 553360 "DRAW" 555745 NIL DRAW (NIL T) -7 NIL NIL NIL) (-267 550889 550948 551066 "DRAWHACK" 551203 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-266 549590 549889 550180 "DRAWCX" 550618 T DRAWCX (NIL) -7 NIL NIL NIL) (-265 549099 549174 549325 "DRAWCURV" 549516 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-264 539417 541529 543644 "DRAWCFUN" 547004 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-263 535888 538082 538123 "DQAGG" 538752 NIL DQAGG (NIL T) -9 NIL 539026 NIL) (-262 522471 530099 530182 "DPOLCAT" 532034 NIL DPOLCAT (NIL T T T T) -9 NIL 532579 NIL) (-261 516990 518656 520614 "DPOLCAT-" 520619 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509847 516851 516949 "DPMO" 516954 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502601 509627 509794 "DPMM" 509799 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502123 502385 502474 "DOMTMPLT" 502532 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501472 501925 502005 "DOMCTOR" 502063 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500624 500952 501103 "DOMAIN" 501341 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493636 500259 500411 "DMP" 500525 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491413 492703 492744 "DMEXT" 492749 NIL DMEXT (NIL T) -9 NIL 492925 NIL) (-253 491007 491069 491213 "DLP" 491351 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484130 490334 490524 "DLIST" 490849 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480668 482955 482996 "DLAGG" 483546 NIL DLAGG (NIL T) -9 NIL 483776 NIL) (-250 479180 479994 480022 "DIVRING" 480114 T DIVRING (NIL) -9 NIL 480197 NIL) (-249 478363 478607 478907 "DIVRING-" 478912 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476405 476822 477228 "DISPLAY" 477977 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 469812 476319 476382 "DIRPROD" 476387 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-246 468642 468863 469128 "DIRPROD2" 469605 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-245 456861 463353 463406 "DIRPCAT" 463664 NIL DIRPCAT (NIL NIL T) -9 NIL 464539 NIL) (-244 454061 454829 455710 "DIRPCAT-" 456047 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453342 453508 453694 "DIOSP" 453895 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449756 452226 452267 "DIOPS" 452701 NIL DIOPS (NIL T) -9 NIL 452930 NIL) (-241 449275 449419 449610 "DIOPS-" 449615 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448182 448954 448982 "DIFRING" 448987 T DIFRING (NIL) -9 NIL 449009 NIL) (-239 447830 447928 447956 "DIFFSPC" 448075 T DIFFSPC (NIL) -9 NIL 448150 NIL) (-238 447451 447553 447705 "DIFFSPC-" 447710 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446387 446985 447026 "DIFFMOD" 447031 NIL DIFFMOD (NIL T) -9 NIL 447129 NIL) (-236 446083 446140 446181 "DIFFDOM" 446302 NIL DIFFDOM (NIL T) -9 NIL 446370 NIL) (-235 445930 445960 446044 "DIFFDOM-" 446049 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443670 445134 445175 "DIFEXT" 445180 NIL DIFEXT (NIL T) -9 NIL 445333 NIL) (-233 440704 443174 443215 "DIAGG" 443220 NIL DIAGG (NIL T) -9 NIL 443240 NIL) (-232 440052 440245 440497 "DIAGG-" 440502 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434902 439011 439288 "DHMATRIX" 439821 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430370 431423 432433 "DFSFUN" 433912 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424604 429301 429613 "DFLOAT" 430078 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422843 423148 423537 "DFINTTLS" 424312 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419662 420864 421264 "DERHAM" 422509 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417198 419437 419526 "DEQUEUE" 419606 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416440 416585 416768 "DEGRED" 417060 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412846 413615 414461 "DEFINTRF" 415668 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410383 410870 411462 "DEFINTEF" 412365 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409667 410003 410118 "DEFAST" 410288 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402703 409260 409410 "DECIMAL" 409537 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400161 400673 401179 "DDFACT" 402247 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399751 399800 399951 "DBLRESP" 400112 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398952 399521 399612 "DBASIS" 399700 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396736 397182 397543 "DBASE" 398718 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395924 396216 396362 "DATAARY" 396635 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394982 395883 395911 "D03FAFA" 395916 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394041 394941 394969 "D03EEFA" 394974 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391967 392457 392946 "D03AGNT" 393572 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391208 391926 391954 "D02EJFA" 391959 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390449 391167 391195 "D02CJFA" 391200 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389690 390408 390436 "D02BHFA" 390441 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388931 389649 389677 "D02BBFA" 389682 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382062 383717 385323 "D02AGNT" 387345 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379812 380353 380899 "D01WGTS" 381536 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378819 379771 379799 "D01TRNS" 379804 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377827 378778 378806 "D01GBFA" 378811 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376835 377786 377814 "D01FCFA" 377819 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375843 376794 376822 "D01ASFA" 376827 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374851 375802 375830 "D01AQFA" 375835 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373859 374810 374838 "D01APFA" 374843 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372867 373818 373846 "D01ANFA" 373851 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371875 372826 372854 "D01AMFA" 372859 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370883 371834 371862 "D01ALFA" 371867 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369891 370842 370870 "D01AKFA" 370875 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368899 369850 369878 "D01AJFA" 369883 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362122 363747 365308 "D01AGNT" 367358 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361441 361587 361739 "CYCLOTOM" 361990 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358096 358889 359616 "CYCLES" 360734 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357396 357542 357713 "CVMP" 357957 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355183 355495 355864 "CTRIGMNP" 357124 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354541 354977 355050 "CTOR" 355130 T CTOR (NIL) -8 NIL NIL NIL) (-189 354014 354272 354373 "CTORKIND" 354460 T CTORKIND (NIL) -8 NIL NIL NIL) (-188 353219 353607 353635 "CTORCAT" 353817 T CTORCAT (NIL) -9 NIL 353930 NIL) (-187 352793 352928 353087 "CTORCAT-" 353092 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-186 352207 352467 352575 "CTORCALL" 352717 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-185 351563 351680 351833 "CSTTOOLS" 352104 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347260 348019 348777 "CRFP" 350875 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346675 346981 347073 "CRCEAST" 347188 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345698 345907 346135 "CRAPACK" 346479 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345078 345183 345387 "CPMATCH" 345574 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344797 344831 344937 "CPIMA" 345044 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341055 341817 342536 "COORDSYS" 344132 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340443 340588 340730 "CONTOUR" 340933 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335908 338446 338938 "CONTFRAC" 339983 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335782 335809 335837 "CONDUIT" 335874 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334736 335410 335438 "COMRING" 335443 T COMRING (NIL) -9 NIL 335495 NIL) (-174 333718 334094 334278 "COMPPROP" 334572 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333373 333414 333542 "COMPLPAT" 333677 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 321756 333182 333291 "COMPLEX" 333296 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-171 321386 321449 321556 "COMPLEX2" 321693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-170 320707 320846 321006 "COMPILER" 321246 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320419 320460 320558 "COMPFACT" 320666 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301794 314123 314163 "COMPCAT" 315167 NIL COMPCAT (NIL T) -9 NIL 316515 NIL) (-167 290682 294233 297860 "COMPCAT-" 298216 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290405 290439 290542 "COMMUPC" 290648 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290193 290233 290292 "COMMONOP" 290366 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289701 289944 290031 "COMM" 290126 T COMM (NIL) -8 NIL NIL NIL) (-163 289223 289505 289580 "COMMAAST" 289646 T COMMAAST (NIL) -8 NIL NIL NIL) (-162 288418 288666 288694 "COMBOPC" 289032 T COMBOPC (NIL) -9 NIL 289207 NIL) (-161 287272 287524 287766 "COMBINAT" 288208 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283615 284303 284930 "COMBF" 286694 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282277 282731 282966 "COLOR" 283400 T COLOR (NIL) -8 NIL NIL NIL) (-158 281693 281998 282090 "COLONAST" 282205 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281327 281380 281505 "CMPLXRT" 281640 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280715 281027 281126 "CLLCTAST" 281248 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276175 277245 278325 "CLIP" 279655 T CLIP (NIL) -7 NIL NIL NIL) (-154 274348 275276 275516 "CLIF" 276002 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270330 272466 272507 "CLAGG" 273436 NIL CLAGG (NIL T) -9 NIL 273972 NIL) (-152 268674 269209 269792 "CLAGG-" 269797 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268212 268303 268443 "CINTSLPE" 268583 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265677 266184 266732 "CHVAR" 267740 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264717 265391 265419 "CHARZ" 265424 T CHARZ (NIL) -9 NIL 265439 NIL) (-148 264465 264511 264589 "CHARPOL" 264671 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263383 264096 264124 "CHARNZ" 264171 T CHARNZ (NIL) -9 NIL 264227 NIL) (-146 260427 261512 262019 "CHAR" 262896 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247376 248635 249379 "CARTEN" 251790 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-137 246472 246632 246853 "CARTEN2" 247223 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 241151 241908 242057 "BYTE" 242220 T BYTE (NIL) -8 NIL NIL 242349) (-130 236078 240656 240828 "BYTEBUF" 240999 T BYTEBUF (NIL) -8 NIL NIL NIL) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197235 198679 199591 "BOP" 201361 T BOP (NIL) -8 NIL NIL NIL) (-115 194962 195420 195895 "BOP1" 196793 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-114 194555 194712 194740 "BOOLE" 194851 T BOOLE (NIL) -9 NIL 194932 NIL) (-113 194423 194450 194516 "BOOLE-" 194521 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-112 193088 194011 194153 "BOOLEAN" 194301 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137620 138341 138451 "ASP1" 138561 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 136455 137294 137413 "ASP19" 137532 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 136174 136259 136335 "ASP12" 136410 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135773 135917 "ASP10" 136061 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 127890 132178 132292 "ARRAY1" 132447 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 126904 127095 127316 "ARRAY12" 127713 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115193 115486 115606 "ANY" 115791 T ANY (NIL) -8 NIL NIL NIL) (-51 114447 114594 114751 "ANY1" 115067 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) \ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index cbe5ca07..a3541134 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,1842 +1,2127 @@
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+ (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1131)) (-4 *4 (-1131))
+ (-5 *2 (-2 (|:| -2338 *3) (|:| -2078 *4))))))
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+ (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871))
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+ (-12 (-4 *4 (-570))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3383 *4)))
+ (-5 *1 (-1000 *4 *3)) (-4 *3 (-1274 *4)))))
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+ (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4))
+ (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))
+ ((*1 *2 *3)
+ (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815))
+ (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6))))
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-793)) (-4 *1 (-277 *2)) (-4 *2 (-871)))))
+(((*1 *2 *3)
+ (-12 (-4 *4 (-570)) (-5 *2 (-666 *3)) (-5 *1 (-43 *4 *3))
+ (-4 *3 (-431 *4)))))
(((*1 *2 *1)
(-12 (-4 *1 (-1241 *3 *4 *5 *6)) (-4 *3 (-570)) (-4 *4 (-815))
(-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-112))))
@@ -2026,13 +2406,120 @@
(-12 (-4 *1 (-1241 *4 *5 *6 *3)) (-4 *4 (-570)) (-4 *5 (-815))
(-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-5 *2 (-112)))))
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- (-4 *2 (-709 *3 *4 *5)))))
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- (-12 (-5 *3 (-950)) (-5 *1 (-1061 *2))
- (-4 *2 (-13 (-1131) (-10 -8 (-15 -2471 ($ $ $))))))))
-(((*1 *1) (-5 *1 (-1300))))
+ (-12 (-4 *3 (-362)) (-4 *4 (-341 *3)) (-4 *5 (-1274 *4))
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+ (-2
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+ (|:| |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| (-1188 (-229)))
+ (|:| |notEvaluated|
+ "Internal singularities not yet evaluated")))
+ (|:| -1868
+ (-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 (-573))))
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+ (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-13 (-871) (-633 (-1207))))
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+ (-12 (-5 *3 (-1 (-392) (-392))) (-5 *4 (-392))
+ (-5 *2
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+ (|:| |success| (-112))))
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(((*1 *2 *2 *3)
(-12 (-5 *3 (-421 (-578))) (-4 *4 (-1069 (-578))) (-4 *4 (-570))
(-5 *1 (-32 *4 *2)) (-4 *2 (-444 *4))))
@@ -2104,24 +2591,218 @@
(-5 *1 (-1193 *3))))
((*1 *1 *1 *2)
(-12 (-4 *1 (-1289 *2)) (-4 *2 (-1080)) (-4 *2 (-376)))))
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- (-4 *2 (-13 (-444 *3) (-1233))))))
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+ *4 *6 *4)
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+ (-5 *3 (-229)) (-5 *2 (-1066)) (-5 *1 (-772)))))
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+ (-4 *3 (-13 (-1233) (-988) (-29 *7)))
+ (-5 *2
+ (-3 (|:| |f1| (-865 *3)) (|:| |f2| (-666 (-865 *3)))
+ (|:| |fail| "failed") (|:| |pole| "potentialPole")))
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(-4 *3 (-1131)))))
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- (-12 (-5 *3 (-666 (-1207))) (-5 *2 (-1303)) (-5 *1 (-1250))))
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- (-12 (-5 *2 (-1188 *4)) (-5 *3 (-578)) (-4 *4 (-1080))
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+ (-12 (-4 *4 (-570)) (-4 *5 (-1023 *4))
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((*1 *2 *3)
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((*1 *2 *3 *4)
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((*1 *2 *3 *4)
- (-12 (-4 *5 (-1131)) (-5 *2 (-666 (-306 (-981 *3))))
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- (-4 *4 (-633 (-917 *5)))))
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+ ((*1 *2 *3 *1)
+ (-12 (-5 *3 (-578)) (-5 *2 (-1303)) (-5 *1 (-1188 *4))
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+ (-4 *2 (-13 (-444 *3) (-1033))))))
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+ (-4 *3 (-1248)))))
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+ (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-666 (-793)))))
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+ ((*1 *1 *1)
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+ ((*1 *1 *1) (-12 (-5 *1 (-841 *2)) (-4 *2 (-871))))
+ ((*1 *1 *1)
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+ (-12 (-5 *1 (-609 *2)) (-4 *2 (-38 (-421 (-578)))) (-4 *2 (-1080)))))
+(((*1 *2 *3) (-12 (-5 *3 (-950)) (-5 *2 (-933 (-578))) (-5 *1 (-946))))
+ ((*1 *2 *3)
+ (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946)))))
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+(((*1 *1) (-5 *1 (-622))))
+(((*1 *2 *3 *4 *5)
+ (-12 (-5 *4 (-1 (-666 *7) *7 (-1203 *7))) (-5 *5 (-1 (-432 *7) *7))
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+ (-5 *2 (-666 (-2 (|:| |frac| (-421 *7)) (|:| -1481 *3))))
+ (-5 *1 (-831 *6 *7 *3 *8)) (-4 *3 (-678 *7))
+ (-4 *8 (-678 (-421 *7)))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-1131)) (-5 *2 (-914 *5 *3)) (-5 *1 (-912 *5 *3 *4))
- (-2309 (-4 *3 (-1069 (-1207)))) (-2309 (-4 *3 (-1080)))
- (-4 *3 (-911 *5)) (-4 *4 (-633 (-917 *5))))))
-(((*1 *2) (-12 (-5 *2 (-1207)) (-5 *1 (-1210)))))
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- ((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230))))
- ((*1 *2 *2)
- (-12 (-4 *3 (-570)) (-5 *1 (-445 *3 *2)) (-4 *2 (-444 *3))))
- ((*1 *1 *1) (-4 *1 (-1170))))
+ (-12 (-5 *4 (-1 (-432 *6) *6)) (-4 *6 (-1274 *5))
+ (-4 *5 (-13 (-376) (-149) (-1069 (-578)) (-1069 (-421 (-578)))))
+ (-5 *2
+ (-666 (-2 (|:| |frac| (-421 *6)) (|:| -1481 (-676 *6 (-421 *6))))))
+ (-5 *1 (-834 *5 *6)) (-5 *3 (-676 *6 (-421 *6))))))
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+ (-12 (-4 *1 (-348 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1274 *3))
+ (-4 *5 (-1274 (-421 *4))) (-4 *6 (-355 *3 *4 *5)) (-5 *2 (-112)))))
+(((*1 *2 *2 *3)
+ (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1289 *3)))))
+(((*1 *2 *3)
+ (|partial| -12
+ (-5 *3
+ (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229)))
+ (|:| -1868 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
+ (|:| |relerr| (-229))))
+ (-5 *2
+ (-2
+ (|:| |endPointContinuity|
+ (-3 (|:| |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|
+ (-3 (|:| |str| (-1188 (-229)))
+ (|:| |notEvaluated|
+ "Internal singularities not yet evaluated")))
+ (|:| -1868
+ (-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 (-573)))))
+(((*1 *2 *2 *3) (-12 (-5 *3 (-578)) (-5 *1 (-1222 *2)) (-4 *2 (-376)))))
+(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1217)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-841 *4)) (-4 *4 (-871)) (-5 *2 (-112))
+ (-5 *1 (-694 *4)))))
+(((*1 *2 *2 *2)
+ (-12
+ (-5 *2
+ (-666
+ (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-793)) (|:| |poli| *6)
+ (|:| |polj| *6))))
+ (-4 *4 (-815)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-466)) (-4 *5 (-871))
+ (-5 *1 (-463 *3 *4 *5 *6)))))
+(((*1 *2 *2)
+ (-12 (-5 *2 (-972 *3)) (-4 *3 (-13 (-376) (-1233) (-1033)))
+ (-5 *1 (-179 *3)))))
+(((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-1248)) (-5 *1 (-339 *3))))
+ ((*1 *1 *2)
+ (-12 (-5 *2 (-666 *3)) (-4 *3 (-1248)) (-5 *1 (-530 *3 *4))
+ (-14 *4 (-578)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-793)) (-5 *2 (-1 (-1188 (-981 *4)) (-1188 (-981 *4))))
+ (-5 *1 (-1306 *4)) (-4 *4 (-376)))))
+(((*1 *2 *1 *1 *3)
+ (-12 (-4 *4 (-1080)) (-4 *5 (-815)) (-4 *3 (-871))
+ (-5 *2 (-2 (|:| -1635 *1) (|:| |gap| (-793)) (|:| -3487 *1)))
+ (-4 *1 (-1096 *4 *5 *3))))
+ ((*1 *2 *1 *1)
+ (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871))
+ (-5 *2 (-2 (|:| -1635 *1) (|:| |gap| (-793)) (|:| -3487 *1)))
+ (-4 *1 (-1096 *3 *4 *5)))))
+(((*1 *1 *1) (-5 *1 (-1094))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-666 *8)) (-5 *4 (-138 *5 *6 *7)) (-14 *5 (-578))
(-14 *6 (-793)) (-4 *7 (-175)) (-4 *8 (-175))
@@ -3627,64 +6986,74 @@
(-4 *8 (-1080)) (-4 *2 (-978 *9 *7 *5))
(-5 *1 (-750 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-815))
(-4 *4 (-978 *8 *6 *5)))))
-(((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-955)))))
-(((*1 *2 *3)
- (-12 (-5 *2 (-1188 (-666 (-578)))) (-5 *1 (-908)) (-5 *3 (-578)))))
-(((*1 *2 *1 *3)
- (-12 (-5 *3 (-1 (-112) *7 (-666 *7))) (-4 *1 (-1241 *4 *5 *6 *7))
- (-4 *4 (-570)) (-4 *5 (-815)) (-4 *6 (-871))
- (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-112)))))
-(((*1 *2 *3)
- (-12 (-5 *3 (-972 *2)) (-5 *1 (-1013 *2)) (-4 *2 (-1080)))))
-(((*1 *2 *3 *3)
- (-12 (-5 *3 (-666 *4)) (-4 *4 (-376)) (-4 *2 (-1274 *4))
- (-5 *1 (-951 *4 *2)))))
-(((*1 *1 *1 *1)
- (-12 (-5 *1 (-138 *2 *3 *4)) (-14 *2 (-578)) (-14 *3 (-793))
- (-4 *4 (-175))))
- ((*1 *2 *2 *3)
- (-12 (-5 *3 (-1207)) (-4 *4 (-570)) (-5 *1 (-160 *4 *2))
- (-4 *2 (-444 *4))))
- ((*1 *2 *2 *3)
- (-12 (-5 *3 (-1123 *2)) (-4 *2 (-444 *4)) (-4 *4 (-570))
- (-5 *1 (-160 *4 *2))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1123 *1)) (-4 *1 (-162))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1207))))
- ((*1 *1 *1 *1)
- (-12 (-4 *1 (-479 *2 *3)) (-4 *2 (-175)) (-4 *3 (-23))))
- ((*1 *1 *1 *1 *2)
- (-12 (-5 *2 (-793)) (-5 *1 (-1318 *3 *4)) (-4 *3 (-871))
- (-4 *4 (-175)))))
-(((*1 *2 *1)
- (-12 (-5 *2 (-1283 *3 *4 *5)) (-5 *1 (-331 *3 *4 *5)) (-4 *3 (-376))
- (-14 *4 (-1207)) (-14 *5 *3)))
- ((*1 *2 *1) (-12 (-4 *1 (-418)) (-5 *2 (-578))))
- ((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-432 *3)) (-4 *3 (-570))))
- ((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-721))))
- ((*1 *2 *1)
- (-12 (-4 *2 (-1131)) (-5 *1 (-735 *3 *2 *4)) (-4 *3 (-871))
- (-14 *4
- (-1 (-112) (-2 (|:| -2085 *3) (|:| -3761 *2))
- (-2 (|:| -2085 *3) (|:| -3761 *2)))))))
-(((*1 *1) (-5 *1 (-623))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-1203 (-981 *6))) (-4 *6 (-570))
- (-4 *2 (-978 (-421 (-981 *6)) *5 *4)) (-5 *1 (-754 *5 *4 *6 *2))
- (-4 *5 (-815))
- (-4 *4 (-13 (-871) (-10 -8 (-15 -3342 ((-1207) $))))))))
-(((*1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-286)))))
-(((*1 *2) (-12 (-5 *2 (-666 *3)) (-5 *1 (-1115 *3)) (-4 *3 (-134)))))
+ (-12 (-5 *4 (-1207))
+ (-4 *5 (-13 (-570) (-1069 (-578)) (-660 (-578))))
+ (-5 *2
+ (-2 (|:| |func| *3) (|:| |kers| (-666 (-631 *3)))
+ (|:| |vals| (-666 *3))))
+ (-5 *1 (-288 *5 *3)) (-4 *3 (-13 (-27) (-1233) (-444 *5))))))
+(((*1 *2 *1 *3 *3 *3)
+ (-12 (-5 *3 (-392)) (-5 *2 (-1303)) (-5 *1 (-1300)))))
+(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-1182)))))
+(((*1 *2 *1)
+ (-12 (-4 *3 (-1080)) (-5 *2 (-666 *1)) (-4 *1 (-1165 *3)))))
+(((*1 *2 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-886)))))
+(((*1 *2 *1) (-12 (-4 *1 (-541)) (-5 *2 (-713 (-560))))))
+(((*1 *2) (-12 (-5 *2 (-950)) (-5 *1 (-1301))))
+ ((*1 *2 *2) (-12 (-5 *2 (-950)) (-5 *1 (-1301)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-666 (-2 (|:| -3528 *4) (|:| -2463 (-578)))))
+ (-4 *4 (-1131)) (-5 *2 (-1 *4)) (-5 *1 (-1048 *4)))))
+(((*1 *2)
+ (-12 (-5 *2 (-987 (-1151))) (-5 *1 (-356 *3 *4)) (-14 *3 (-950))
+ (-14 *4 (-950))))
+ ((*1 *2)
+ (-12 (-5 *2 (-987 (-1151))) (-5 *1 (-357 *3 *4)) (-4 *3 (-362))
+ (-14 *4 (-1203 *3))))
+ ((*1 *2)
+ (-12 (-5 *2 (-987 (-1151))) (-5 *1 (-358 *3 *4)) (-4 *3 (-362))
+ (-14 *4 (-950)))))
(((*1 *2 *1)
(-12 (-5 *2 (-666 *5)) (-5 *1 (-138 *3 *4 *5)) (-14 *3 (-578))
(-14 *4 (-793)) (-4 *5 (-175)))))
+(((*1 *2 *1)
+ (-12 (-4 *1 (-1241 *3 *4 *5 *6)) (-4 *3 (-570)) (-4 *4 (-815))
+ (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-666 *5)))))
+(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-256)))))
+(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3)
+ (-12 (-5 *3 (-578)) (-5 *4 (-112)) (-5 *5 (-711 (-229)))
+ (-5 *2 (-1066)) (-5 *1 (-777)))))
+(((*1 *2 *3 *3 *2)
+ (-12 (-5 *2 (-1066)) (-5 *3 (-1207)) (-5 *1 (-195)))))
+(((*1 *2 *3)
+ (-12
+ (-5 *3
+ (-666
+ (-2 (|:| -3062 (-793))
+ (|:| |eqns|
+ (-666
+ (-2 (|:| |det| *7) (|:| |rows| (-666 (-578)))
+ (|:| |cols| (-666 (-578))))))
+ (|:| |fgb| (-666 *7)))))
+ (-4 *7 (-978 *4 *6 *5)) (-4 *4 (-13 (-319) (-149)))
+ (-4 *5 (-13 (-871) (-633 (-1207)))) (-4 *6 (-815)) (-5 *2 (-793))
+ (-5 *1 (-953 *4 *5 *6 *7)))))
(((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-898)))))
-(((*1 *1) (-5 *1 (-482))))
-(((*1 *2) (-12 (-5 *2 (-666 (-950))) (-5 *1 (-1301))))
- ((*1 *2 *2) (-12 (-5 *2 (-666 (-950))) (-5 *1 (-1301)))))
-(((*1 *1 *1)
- (-12 (-5 *1 (-1195 *2 *3)) (-14 *2 (-950)) (-4 *3 (-1080)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-844)))))
-(((*1 *2 *3) (-12 (-5 *3 (-793)) (-5 *2 (-1303)) (-5 *1 (-392)))))
+(((*1 *2)
+ (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871))
+ (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303))
+ (-5 *1 (-1103 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6))))
+ ((*1 *2)
+ (-12 (-4 *3 (-466)) (-4 *4 (-815)) (-4 *5 (-871))
+ (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-1303))
+ (-5 *1 (-1139 *3 *4 *5 *6 *7)) (-4 *7 (-1102 *3 *4 *5 *6)))))
+(((*1 *2 *1 *3)
+ (-12 (-5 *3 (-578)) (-4 *1 (-335 *4 *2)) (-4 *4 (-1131))
+ (-4 *2 (-133)))))
+(((*1 *1 *1 *2 *3)
+ (-12 (-5 *2 (-666 (-1207))) (-5 *3 (-52)) (-5 *1 (-917 *4))
+ (-4 *4 (-1131)))))
(((*1 *1 *2 *2 *3)
(-12 (-5 *2 (-793)) (-4 *3 (-1248)) (-4 *1 (-57 *3 *4 *5))
(-4 *4 (-386 *3)) (-4 *5 (-386 *3))))
@@ -3702,591 +7071,850 @@
((*1 *1) (-12 (-5 *1 (-1195 *2 *3)) (-14 *2 (-950)) (-4 *3 (-1080))))
((*1 *1 *1) (-5 *1 (-1207))) ((*1 *1) (-5 *1 (-1207)))
((*1 *1) (-5 *1 (-1228))))
-(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-481))))
- ((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-481))))
- ((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-956)))))
-(((*1 *2 *3 *4 *2 *5)
- (-12 (-5 *3 (-666 *8)) (-5 *4 (-666 (-917 *6)))
- (-5 *5 (-1 (-914 *6 *8) *8 (-917 *6) (-914 *6 *8))) (-4 *6 (-1131))
- (-4 *8 (-13 (-1080) (-633 (-917 *6)) (-1069 *7)))
- (-5 *2 (-914 *6 *8)) (-4 *7 (-1080)) (-5 *1 (-970 *6 *7 *8)))))
+(((*1 *2 *2 *3)
+ (-12 (-5 *3 (-1207)) (-4 *4 (-466)) (-4 *4 (-1131))
+ (-5 *1 (-587 *4 *2)) (-4 *2 (-296)) (-4 *2 (-444 *4)))))
+(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-956)))))
+(((*1 *2 *3 *2)
+ (-12 (-5 *2 (-666 *3)) (-4 *3 (-319)) (-5 *1 (-182 *3)))))
+(((*1 *2 *3 *4 *3)
+ (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066))
+ (-5 *1 (-769)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-1203 *5)) (-4 *5 (-376)) (-5 *2 (-666 *6))
- (-5 *1 (-546 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-870))))))
-(((*1 *1 *1)
- (-12 (-4 *1 (-1315 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080))))
- ((*1 *1 *1)
- (-12 (-5 *1 (-1321 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-868)))))
-(((*1 *2)
- (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3))
- (-4 *5 (-1274 (-421 *4))) (-5 *2 (-711 (-421 *4))))))
-(((*1 *2 *1) (-12 (-5 *2 (-796)) (-5 *1 (-52)))))
-(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4)
- (-12 (-5 *3 (-1189)) (-5 *4 (-578)) (-5 *5 (-711 (-229)))
- (-5 *2 (-1066)) (-5 *1 (-776)))))
-(((*1 *2)
- (-12 (-4 *1 (-362))
- (-5 *2 (-666 (-2 (|:| -2798 (-578)) (|:| -3761 (-578))))))))
-(((*1 *1 *1 *2)
- (|partial| -12 (-4 *1 (-1241 *3 *4 *5 *2)) (-4 *3 (-570))
- (-4 *4 (-815)) (-4 *5 (-871)) (-4 *2 (-1096 *3 *4 *5)))))
+ (-12 (-5 *3 (-666 *8)) (-5 *4 (-666 *7)) (-4 *7 (-871))
+ (-4 *8 (-978 *5 *6 *7)) (-4 *5 (-570)) (-4 *6 (-815))
+ (-5 *2
+ (-2 (|:| |particular| (-3 (-1298 (-421 *8)) "failed"))
+ (|:| -1846 (-666 (-1298 (-421 *8))))))
+ (-5 *1 (-691 *5 *6 *7 *8)))))
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+ ((*1 *2 *2)
+ (-12 (-4 *3 (-570)) (-5 *1 (-649 *3 *2))
+ (-4 *2 (-13 (-444 *3) (-1033) (-1233))))))
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+(((*1 *2 *1 *3)
+ (-12 (-5 *3 (-578)) (-4 *1 (-335 *2 *4)) (-4 *4 (-133))
+ (-4 *2 (-1131))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-578)) (-5 *1 (-374 *2)) (-4 *2 (-1131))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-578)) (-4 *1 (-399 *2)) (-4 *2 (-1131))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-578)) (-5 *1 (-432 *2)) (-4 *2 (-570))))
+ ((*1 *2 *1 *3)
+ (-12 (-5 *3 (-578)) (-4 *2 (-1131)) (-5 *1 (-671 *2 *4 *5))
+ (-4 *4 (-23)) (-14 *5 *4))))
+(((*1 *1 *2 *3) (-12 (-5 *2 (-520)) (-5 *3 (-611)) (-5 *1 (-599)))))
(((*1 *1 *2 *1)
(-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1080))
(-4 *4 (-814))))
@@ -4477,9 +9359,9 @@
(-4 *6 (-376)) (-5 *2 (-600 *6)) (-5 *1 (-598 *5 *6))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-1 *6 *5))
- (-5 *4 (-3 (-2 (|:| -1786 *5) (|:| |coeff| *5)) "failed"))
+ (-5 *4 (-3 (-2 (|:| -2924 *5) (|:| |coeff| *5)) "failed"))
(-4 *5 (-376)) (-4 *6 (-376))
- (-5 *2 (-2 (|:| -1786 *6) (|:| |coeff| *6)))
+ (-5 *2 (-2 (|:| -2924 *6) (|:| |coeff| *6)))
(-5 *1 (-598 *5 *6))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed"))
@@ -4598,7 +9480,7 @@
(-4 *8 (-1080)) (-4 *6 (-815))
(-4 *2
(-13 (-1131)
- (-10 -8 (-15 -2471 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793))))))
+ (-10 -8 (-15 -2430 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-793))))))
(-5 *1 (-980 *6 *7 *8 *5 *2)) (-4 *5 (-978 *8 *6 *7))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-987 *5)) (-4 *5 (-1248))
@@ -4614,8 +9496,8 @@
(-4 *2 (-978 (-981 *4) *5 *6)) (-4 *5 (-815))
(-4 *6
(-13 (-871)
- (-10 -8 (-15 -3342 ((-1207) $))
- (-15 -3967 ((-3 $ "failed") (-1207))))))
+ (-10 -8 (-15 -1334 ((-1207) $))
+ (-15 -1518 ((-3 $ "failed") (-1207))))))
(-5 *1 (-1015 *4 *5 *6 *2))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-570)) (-4 *6 (-570))
@@ -4702,73 +9584,339 @@
((*1 *1 *2 *1)
(-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1080)) (-5 *1 (-1321 *3 *4))
(-4 *4 (-868)))))
-(((*1 *2 *3 *3)
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- (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-112))
- (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7))))
- ((*1 *2 *3 *3)
- (-12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871))
- (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-112))
- (-5 *1 (-1138 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7)))))
-(((*1 *2 *3)
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- (-5 *1 (-193)))))
-(((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-898))))
- ((*1 *2 *3)
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-(((*1 *2 *3 *4 *5)
- (-12 (-5 *4 (-1 *7 *7))
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- (-4 *6 (-376)) (-4 *7 (-1274 *6))
- (-5 *2 (-2 (|:| |answer| (-600 (-421 *7))) (|:| |a0| *6)))
- (-5 *1 (-588 *6 *7)) (-5 *3 (-421 *7)))))
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(((*1 *2 *1)
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+ ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
+ (-12 (-5 *3 (-328 (-578))) (-5 *4 (-1 (-229) (-229)))
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+ ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
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+ (-12 (|has| *1 (-6 -4508)) (-4 *1 (-251 *2)) (-4 *2 (-1248))))
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+ ((*1 *1 *1 *2) (-12 (-4 *1 (-294 *2)) (-4 *2 (-1248))))
+ ((*1 *1 *1 *2)
+ (-12 (|has| *1 (-6 -4508)) (-4 *1 (-1286 *2)) (-4 *2 (-1248))))
+ ((*1 *1 *1 *1)
+ (-12 (|has| *1 (-6 -4508)) (-4 *1 (-1286 *2)) (-4 *2 (-1248)))))
+(((*1 *1 *1 *2 *3)
+ (-12 (-5 *3 (-666 *6)) (-4 *6 (-871)) (-4 *4 (-376)) (-4 *5 (-815))
+ (-5 *1 (-518 *4 *5 *6 *2)) (-4 *2 (-978 *4 *5 *6))))
+ ((*1 *1 *1 *2)
+ (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871))
+ (-5 *1 (-518 *3 *4 *5 *2)) (-4 *2 (-978 *3 *4 *5)))))
+(((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-898)))))
+(((*1 *2 *1 *1)
+ (-12 (-4 *3 (-376)) (-4 *3 (-1080))
+ (-5 *2 (-2 (|:| -1351 *1) (|:| -3487 *1))) (-4 *1 (-876 *3))))
+ ((*1 *2 *3 *3 *4)
+ (-12 (-5 *4 (-99 *5)) (-4 *5 (-376)) (-4 *5 (-1080))
+ (-5 *2 (-2 (|:| -1351 *3) (|:| -3487 *3))) (-5 *1 (-877 *5 *3))
+ (-4 *3 (-876 *5)))))
(((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1248))))
((*1 *1 *2)
(-12 (-5 *2 (-981 (-392))) (-5 *1 (-352 *3 *4 *5))
@@ -5153,11 +10490,11 @@
(-3
(|:| |nia|
(-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229)))
- (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
+ (|:| -1868 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
(|:| |relerr| (-229))))
(|:| |mdnia|
(-2 (|:| |fn| (-328 (-229)))
- (|:| -1634 (-666 (-1125 (-865 (-229)))))
+ (|:| -1868 (-666 (-1125 (-865 (-229)))))
(|:| |abserr| (-229)) (|:| |relerr| (-229))))))
(-5 *1 (-791))))
((*1 *2 *1)
@@ -5173,13 +10510,13 @@
(-5 *2
(-3
(|:| |noa|
- (-2 (|:| |fn| (-328 (-229))) (|:| -2200 (-666 (-229)))
+ (-2 (|:| |fn| (-328 (-229))) (|:| -2911 (-666 (-229)))
(|:| |lb| (-666 (-865 (-229))))
(|:| |cf| (-666 (-328 (-229))))
(|:| |ub| (-666 (-865 (-229))))))
(|:| |lsa|
(-2 (|:| |lfn| (-666 (-328 (-229))))
- (|:| -2200 (-666 (-229)))))))
+ (|:| -2911 (-666 (-229)))))))
(-5 *1 (-863))))
((*1 *2 *1)
(-12
@@ -5198,26 +10535,26 @@
(-4 *4 (-815)) (-4 *5 (-871)) (-4 *1 (-1007 *3 *4 *5 *6))))
((*1 *2 *1) (-12 (-4 *1 (-1069 *2)) (-4 *2 (-1248))))
((*1 *1 *2)
- (-2230
+ (-2225
(-12 (-5 *2 (-981 *3))
- (-12 (-2309 (-4 *3 (-38 (-421 (-578)))))
- (-2309 (-4 *3 (-38 (-578)))) (-4 *5 (-633 (-1207))))
+ (-12 (-3523 (-4 *3 (-38 (-421 (-578)))))
+ (-3523 (-4 *3 (-38 (-578)))) (-4 *5 (-633 (-1207))))
(-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815))
(-4 *5 (-871)))
(-12 (-5 *2 (-981 *3))
- (-12 (-2309 (-4 *3 (-559))) (-2309 (-4 *3 (-38 (-421 (-578)))))
+ (-12 (-3523 (-4 *3 (-559))) (-3523 (-4 *3 (-38 (-421 (-578)))))
(-4 *3 (-38 (-578))) (-4 *5 (-633 (-1207))))
(-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815))
(-4 *5 (-871)))
(-12 (-5 *2 (-981 *3))
- (-12 (-2309 (-4 *3 (-1023 (-578)))) (-4 *3 (-38 (-421 (-578))))
+ (-12 (-3523 (-4 *3 (-1023 (-578)))) (-4 *3 (-38 (-421 (-578))))
(-4 *5 (-633 (-1207))))
(-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815))
(-4 *5 (-871)))))
((*1 *1 *2)
- (-2230
+ (-2225
(-12 (-5 *2 (-981 (-578))) (-4 *1 (-1096 *3 *4 *5))
- (-12 (-2309 (-4 *3 (-38 (-421 (-578))))) (-4 *3 (-38 (-578)))
+ (-12 (-3523 (-4 *3 (-38 (-421 (-578))))) (-4 *3 (-38 (-578)))
(-4 *5 (-633 (-1207))))
(-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)))
(-12 (-5 *2 (-981 (-578))) (-4 *1 (-1096 *3 *4 *5))
@@ -5228,6 +10565,210 @@
(-4 *3 (-38 (-421 (-578)))) (-4 *5 (-633 (-1207))) (-4 *3 (-1080))
(-4 *4 (-815)) (-4 *5 (-871)))))
(((*1 *2 *3)
+ (-12 (-4 *4 (-362))
+ (-5 *2 (-666 (-2 (|:| |deg| (-793)) (|:| -2540 *3))))
+ (-5 *1 (-220 *4 *3)) (-4 *3 (-1274 *4)))))
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+ (-12 (-4 *4 (-1131)) (-4 *2 (-927 *4)) (-5 *1 (-714 *4 *2 *5 *3))
+ (-4 *5 (-386 *2)) (-4 *3 (-13 (-386 *4) (-10 -7 (-6 -4507)))))))
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+ (-12 (-5 *2 (-666 (-578))) (-5 *3 (-711 (-578))) (-5 *1 (-1141)))))
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+ (-12 (-4 *1 (-1007 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-815))
+ (-4 *2 (-871)) (-4 *5 (-1096 *3 *4 *2)))))
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+ (-12 (-5 *2 (-793)) (-5 *1 (-1195 *3 *4)) (-14 *3 (-950))
+ (-4 *4 (-1080)))))
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+ ((*1 *1 *1 *1) (-12 (-4 *1 (-1129 *2)) (-4 *2 (-1131)))))
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+ (-12 (-5 *2 (-2 (|:| |preimage| (-666 *3)) (|:| |image| (-666 *3))))
+ (-5 *1 (-934 *3)) (-4 *3 (-1131)))))
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+ (|:| |extra| (-1066))))))
+ ((*1 *2 *3 *4)
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+ ((*1 *2 *3)
+ (-12 (-5 *3 (-830))
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+ (|:| |ub| (-666 (-865 (-229))))))
+ (-5 *2 (-2 (|:| -2558 (-392)) (|:| |explanations| (-1189))))))
+ ((*1 *2 *3)
+ (-12 (-5 *3 (-863))
+ (-5 *2
+ (-2 (|:| -2558 (-392)) (|:| -2178 (-1189))
+ (|:| |explanations| (-666 (-1189)))))
+ (-5 *1 (-862))))
+ ((*1 *2 *3 *4)
+ (-12 (-5 *3 (-863)) (-5 *4 (-1094))
+ (-5 *2
+ (-2 (|:| -2558 (-392)) (|:| -2178 (-1189))
+ (|:| |explanations| (-666 (-1189)))))
+ (-5 *1 (-862))))
+ ((*1 *2 *3 *4)
+ (-12 (-4 *1 (-922)) (-5 *3 (-1094))
+ (-5 *4
+ (-2 (|:| |pde| (-666 (-328 (-229))))
+ (|:| |constraints|
+ (-666
+ (-2 (|:| |start| (-229)) (|:| |finish| (-229))
+ (|:| |grid| (-793)) (|:| |boundaryType| (-578))
+ (|:| |dStart| (-711 (-229))) (|:| |dFinish| (-711 (-229))))))
+ (|:| |f| (-666 (-666 (-328 (-229))))) (|:| |st| (-1189))
+ (|:| |tol| (-229))))
+ (-5 *2 (-2 (|:| -2558 (-392)) (|:| |explanations| (-1189))))))
+ ((*1 *2 *3)
+ (-12 (-5 *3 (-925))
+ (-5 *2
+ (-2 (|:| -2558 (-392)) (|:| -2178 (-1189))
+ (|:| |explanations| (-666 (-1189)))))
+ (-5 *1 (-924))))
+ ((*1 *2 *3 *4)
+ (-12 (-5 *3 (-925)) (-5 *4 (-1094))
+ (-5 *2
+ (-2 (|:| -2558 (-392)) (|:| -2178 (-1189))
+ (|:| |explanations| (-666 (-1189)))))
+ (-5 *1 (-924)))))
+(((*1 *2 *1 *3 *3)
+ (-12 (|has| *1 (-6 -4508)) (-4 *1 (-618 *3 *4)) (-4 *3 (-1131))
+ (-4 *4 (-1248)) (-5 *2 (-1303)))))
+(((*1 *2 *3 *4)
+ (-12 (-5 *4 (-1207))
+ (-4 *5 (-13 (-466) (-149) (-1069 (-578)) (-660 (-578))))
+ (-5 *2 (-600 *3)) (-5 *1 (-571 *5 *3))
+ (-4 *3 (-13 (-27) (-1233) (-444 *5))))))
+(((*1 *1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-136)))))
+(((*1 *1 *2) (-12 (-5 *2 (-666 *3)) (-4 *3 (-871)) (-5 *1 (-498 *3)))))
+(((*1 *2 *3)
(-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175))
(-5 *2 (-666 (-981 *4)))))
((*1 *2)
@@ -5243,314 +10784,146 @@
(-12 (-5 *3 (-1298 (-467 *4 *5 *6 *7))) (-5 *2 (-666 (-981 *4)))
(-5 *1 (-467 *4 *5 *6 *7)) (-4 *4 (-570)) (-4 *4 (-175))
(-14 *5 (-950)) (-14 *6 (-666 (-1207))) (-14 *7 (-1298 (-711 *4))))))
-(((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-342))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-342)))))
(((*1 *2 *3)
- (-12 (-4 *4 (-570)) (-5 *2 (-793)) (-5 *1 (-43 *4 *3))
- (-4 *3 (-431 *4)))))
-(((*1 *2 *1)
- (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-666 (-972 *3)))))
- ((*1 *1 *2)
- (-12 (-5 *2 (-666 (-972 *3))) (-4 *3 (-1080)) (-4 *1 (-1165 *3))))
- ((*1 *1 *1 *2)
- (-12 (-5 *2 (-666 (-666 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080))))
- ((*1 *1 *1 *2)
- (-12 (-5 *2 (-666 (-972 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080)))))
-(((*1 *2 *1 *3)
- (-12 (-4 *1 (-932 *3)) (-4 *3 (-1131)) (-5 *2 (-1133 *3))))
- ((*1 *2 *1 *3)
- (-12 (-4 *4 (-1131)) (-5 *2 (-1133 (-666 *4))) (-5 *1 (-933 *4))
- (-5 *3 (-666 *4))))
- ((*1 *2 *1 *3)
- (-12 (-4 *4 (-1131)) (-5 *2 (-1133 (-1133 *4))) (-5 *1 (-933 *4))
- (-5 *3 (-1133 *4))))
- ((*1 *2 *1 *3)
- (-12 (-5 *2 (-1133 *3)) (-5 *1 (-933 *3)) (-4 *3 (-1131)))))
-(((*1 *2 *3 *4)
- (-12 (-5 *4 (-711 (-421 (-981 (-578)))))
- (-5 *2 (-666 (-711 (-328 (-578))))) (-5 *1 (-1062))
- (-5 *3 (-328 (-578))))))
-(((*1 *2 *2) (-12 (-5 *2 (-666 (-1189))) (-5 *1 (-411)))))
-(((*1 *1 *2)
- (-12 (-5 *2 (-1 (-972 (-229)) (-972 (-229)))) (-5 *1 (-272))))
- ((*1 *2 *3)
- (-12 (-5 *3 (-1298 *1)) (-4 *1 (-341 *4)) (-4 *4 (-376))
- (-5 *2 (-711 *4))))
- ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1298 *3))))
- ((*1 *2 *3 *3)
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- ((*1 *2 *1 *3)
- (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175))
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- ((*1 *2 *3 *3)
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@@ -5558,1214 +10931,1540 @@
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(((*1 *2 *2)
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@@ -6778,210 +12477,566 @@
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+ (-2
+ (|:| |endPointContinuity|
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+ (|:| |lowerSingular|
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+ (|:| |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")))
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+ (|:| |notEvaluated|
+ "Internal singularities not yet evaluated")))
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+ (-3 (|:| |finite| "The range is finite")
+ (|:| |lowerInfinite| "The bottom of range is infinite")
+ (|:| |upperInfinite| "The top of range is infinite")
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+ (|:| |notEvaluated| "Range not yet evaluated")))))
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-886))))
+ ((*1 *2 *1)
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(((*1 *1 *1 *2) (-12 (-5 *2 (-666 (-631 (-48)))) (-5 *1 (-48))))
((*1 *1 *1 *2) (-12 (-5 *2 (-631 (-48))) (-5 *1 (-48))))
((*1 *2 *2 *3)
@@ -7024,59 +13079,16 @@
((*1 *2 *1) (-12 (-4 *1 (-819 *2)) (-4 *2 (-175))))
((*1 *2 *1) (-12 (-4 *1 (-1028 *2)) (-4 *2 (-175))))
((*1 *1 *1) (-4 *1 (-1091))))
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- (-4 *3 (-1131)) (-4 *5 (-688 *4))))
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- (-12 (-5 *3 (-995 *4)) (-4 *4 (-1131)) (-5 *2 (-1133 *4))
- (-5 *1 (-996 *4)))))
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- (-12 (-5 *3 (-116)) (-4 *4 (-1080)) (-5 *1 (-736 *4 *2))
- (-4 *2 (-670 *4))))
- ((*1 *2 *3 *2) (-12 (-5 *3 (-116)) (-5 *1 (-858 *2)) (-4 *2 (-1080)))))
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-(((*1 *2 *3)
+(((*1 *2 *1 *1) (-12 (-4 *1 (-570)) (-5 *2 (-112)))))
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(-12
- (-5 *3
- (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229)))
- (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
- (|:| |relerr| (-229))))
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-(((*1 *2 *3 *4)
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+ (-5 *2
+ (-1018 (-421 (-578)) (-888 *3) (-247 *4 (-793))
+ (-255 *3 (-421 (-578)))))
+ (-14 *3 (-666 (-1207))) (-14 *4 (-793)) (-5 *1 (-1017 *3 *4)))))
(((*1 *2 *2)
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(-4 *2 (-13 (-444 *3) (-1033))))))
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(((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814))))
((*1 *1 *1)
(-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1080)) (-14 *3 (-666 (-1207)))))
@@ -7087,10 +13099,10 @@
(-12 (-4 *1 (-395 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-1131))))
((*1 *1 *1)
(-12 (-14 *2 (-666 (-1207))) (-4 *3 (-175))
- (-4 *5 (-245 (-3225 *2) (-793)))
+ (-4 *5 (-245 (-4415 *2) (-793)))
(-14 *6
- (-1 (-112) (-2 (|:| -2085 *4) (|:| -3761 *5))
- (-2 (|:| -2085 *4) (|:| -3761 *5))))
+ (-1 (-112) (-2 (|:| -2480 *4) (|:| -3945 *5))
+ (-2 (|:| -2480 *4) (|:| -3945 *5))))
(-5 *1 (-475 *2 *3 *4 *5 *6 *7)) (-4 *4 (-871))
(-4 *7 (-978 *3 *5 (-888 *2)))))
((*1 *1 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *2 (-102)) (-4 *3 (-874))))
@@ -7106,109 +13118,129 @@
(-4 *2 (-871))))
((*1 *1 *1)
(-12 (-5 *1 (-1321 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-868)))))
-(((*1 *2)
- (-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4))
- (-4 *3 (-380 *4))))
- ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-112)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-666 (-578))) (-5 *2 (-933 (-578))) (-5 *1 (-946))))
- ((*1 *2 *3)
- (-12 (-5 *3 (-1002)) (-5 *2 (-933 (-578))) (-5 *1 (-946)))))
-(((*1 *2 *2) (-12 (-5 *2 (-950)) (|has| *1 (-6 -4491)) (-4 *1 (-418))))
- ((*1 *2) (-12 (-4 *1 (-418)) (-5 *2 (-950))))
- ((*1 *2 *2) (-12 (-5 *2 (-950)) (-5 *1 (-721))))
- ((*1 *2) (-12 (-5 *2 (-950)) (-5 *1 (-721)))))
-(((*1 *2 *3 *4)
- (-12 (-5 *4 (-1207))
- (-4 *5 (-13 (-1069 (-578)) (-466) (-660 (-578))))
- (-5 *2 (-2 (|:| -2830 *3) (|:| |nconst| *3))) (-5 *1 (-581 *5 *3))
- (-4 *3 (-13 (-27) (-1233) (-444 *5))))))
-(((*1 *2)
- (-12 (-4 *3 (-570)) (-5 *2 (-666 *4)) (-5 *1 (-43 *3 *4))
- (-4 *4 (-431 *3)))))
-(((*1 *1 *2 *2) (-12 (-5 *1 (-902 *2)) (-4 *2 (-1248))))
- ((*1 *1 *2 *2 *2) (-12 (-5 *1 (-904 *2)) (-4 *2 (-1248))))
+ (-12 (-5 *3 (-1207)) (-5 *2 (-1 (-1203 (-981 *4)) (-981 *4)))
+ (-5 *1 (-1306 *4)) (-4 *4 (-376)))))
+(((*1 *2 *1 *3 *3 *4 *4)
+ (-12 (-5 *3 (-793)) (-5 *4 (-950)) (-5 *2 (-1303)) (-5 *1 (-1299))))
+ ((*1 *2 *1 *3 *3 *4 *4)
+ (-12 (-5 *3 (-793)) (-5 *4 (-950)) (-5 *2 (-1303)) (-5 *1 (-1300)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-666 *2)) (-4 *2 (-444 *4)) (-5 *1 (-160 *4 *2))
+ (-4 *4 (-570)))))
+(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-125))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-3 (|:| |fst| (-448)) (|:| -2205 "void")))
+ (-5 *2 (-1303)) (-5 *1 (-1210))))
+ ((*1 *2 *3 *4)
+ (-12 (-5 *3 (-1207))
+ (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2205 "void"))) (-5 *2 (-1303))
+ (-5 *1 (-1210))))
+ ((*1 *2 *3 *4 *1)
+ (-12 (-5 *3 (-1207))
+ (-5 *4 (-3 (|:| |fst| (-448)) (|:| -2205 "void"))) (-5 *2 (-1303))
+ (-5 *1 (-1210)))))
+(((*1 *1 *1) (-12 (-4 *1 (-121 *2)) (-4 *2 (-1248))))
+ ((*1 *1 *1) (-12 (-5 *1 (-694 *2)) (-4 *2 (-871))))
+ ((*1 *1 *1) (-12 (-5 *1 (-699 *2)) (-4 *2 (-871))))
+ ((*1 *1 *1) (-5 *1 (-886)))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-886))))
((*1 *2 *1)
- (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-666 (-972 *3)))))
- ((*1 *1 *2)
- (-12 (-5 *2 (-666 (-972 *3))) (-4 *3 (-1080)) (-4 *1 (-1165 *3))))
- ((*1 *1 *1 *2)
- (-12 (-5 *2 (-666 (-666 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080))))
- ((*1 *1 *1 *2)
- (-12 (-5 *2 (-666 (-972 *3))) (-4 *1 (-1165 *3)) (-4 *3 (-1080)))))
+ (-12 (-4 *2 (-13 (-870) (-376))) (-5 *1 (-1092 *2 *3))
+ (-4 *3 (-1274 *2)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-505)) (-5 *4 (-983)) (-5 *2 (-713 (-547)))
- (-5 *1 (-547))))
- ((*1 *2 *3 *4)
- (-12 (-5 *4 (-983)) (-4 *3 (-1131)) (-5 *2 (-713 *1))
- (-4 *1 (-789 *3)))))
-(((*1 *2 *2)
- (-12 (-5 *2 (-1188 *3)) (-4 *3 (-1080)) (-5 *1 (-1191 *3))))
- ((*1 *1 *1)
- (-12 (-5 *1 (-1290 *2 *3 *4)) (-4 *2 (-1080)) (-14 *3 (-1207))
- (-14 *4 *2))))
-(((*1 *1 *1 *1)
- (|partial| -12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7))
- (-4 *3 (-1274 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4))
- (-14 *6 (-1 (-3 *4 "failed") *4 *4))
- (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4))))
- ((*1 *1 *1 *1)
- (|partial| -12 (-5 *1 (-733 *2 *3 *4 *5 *6)) (-4 *2 (-175))
- (-4 *3 (-23)) (-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 *1 *1)
- (|partial| -12 (-5 *1 (-737 *2 *3 *4 *5 *6)) (-4 *2 (-175))
- (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3))
- (-14 *5 (-1 (-3 *3 "failed") *3 *3))
- (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))))
-(((*1 *2 *3 *4 *5)
- (|partial| -12 (-5 *5 (-1298 (-666 *3))) (-4 *4 (-319))
- (-5 *2 (-666 *3)) (-5 *1 (-469 *4 *3)) (-4 *3 (-1274 *4)))))
-(((*1 *2 *3 *4 *3)
- (-12 (-5 *3 (-578)) (-5 *4 (-711 (-229))) (-5 *2 (-1066))
- (-5 *1 (-769)))))
-(((*1 *2)
- (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1252)) (-4 *4 (-1274 *3))
- (-4 *5 (-1274 (-421 *4))) (-5 *2 (-711 (-421 *4))))))
+ (-12 (-5 *3 (-666 (-950))) (-5 *4 (-666 (-578)))
+ (-5 *2 (-711 (-578))) (-5 *1 (-1141)))))
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233)))))
+(((*1 *2 *2 *2 *2)
+ (-12 (-5 *2 (-711 *3)) (-4 *3 (-1080)) (-5 *1 (-712 *3)))))
+(((*1 *1 *1 *2)
+ (-12 (-5 *2 (-1189)) (-4 *1 (-377 *3 *4)) (-4 *3 (-1131))
+ (-4 *4 (-1131)))))
(((*1 *2 *1)
(-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-666 *1))
(-4 *1 (-978 *3 *4 *5)))))
-(((*1 *1 *2 *3)
- (-12 (-5 *3 (-374 (-116))) (-4 *2 (-1080)) (-5 *1 (-736 *2 *4))
- (-4 *4 (-670 *2))))
- ((*1 *1 *2 *3)
- (-12 (-5 *3 (-374 (-116))) (-5 *1 (-858 *2)) (-4 *2 (-1080)))))
-(((*1 *2 *3)
- (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-578))) (-5 *1 (-1078)))))
-(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-917 *3)) (-4 *3 (-1131)))))
-(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-392)) (-5 *1 (-97))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-392)) (-5 *1 (-97)))))
-(((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-956)))))
-(((*1 *2)
- (-12 (-5 *2 (-1303)) (-5 *1 (-1225 *3 *4)) (-4 *3 (-1131))
- (-4 *4 (-1131)))))
-(((*1 *2 *1) (-12 (-4 *1 (-523 *3 *2)) (-4 *3 (-102)) (-4 *2 (-874)))))
-(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-448)))))
(((*1 *2 *1)
- (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080))
- (-5 *2 (-666 (-666 (-666 (-972 *3))))))))
-(((*1 *2 *3)
- (-12
- (-5 *3
- (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
- (|:| |fn| (-1298 (-328 (-229)))) (|:| |yinit| (-666 (-229)))
- (|:| |intvals| (-666 (-229))) (|:| |g| (-328 (-229)))
- (|:| |abserr| (-229)) (|:| |relerr| (-229))))
- (-5 *2
- (-2 (|:| |stiffnessFactor| (-392)) (|:| |stabilityFactor| (-392))))
- (-5 *1 (-208)))))
-(((*1 *2 *3)
- (-12 (-5 *3 (-666 *2)) (-4 *2 (-1274 *4)) (-5 *1 (-553 *4 *2 *5 *6))
- (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-793))))))
+ (-12 (-4 *3 (-1248)) (-5 *2 (-666 *1)) (-4 *1 (-1041 *3)))))
+(((*1 *2 *2 *2)
+ (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3))))
+ ((*1 *1 *1 *1) (-12 (-4 *1 (-876 *2)) (-4 *2 (-1080)) (-4 *2 (-376)))))
+(((*1 *1) (-5 *1 (-146))))
+(((*1 *2 *1)
+ (-12 (-4 *1 (-1315 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080))
+ (-5 *2 (-112))))
+ ((*1 *2 *1)
+ (-12 (-5 *2 (-112)) (-5 *1 (-1321 *3 *4)) (-4 *3 (-1080))
+ (-4 *4 (-868)))))
+(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1066)))))
+(((*1 *2 *1)
+ (-12 (-4 *3 (-175)) (-4 *2 (-23)) (-5 *1 (-301 *3 *4 *2 *5 *6 *7))
+ (-4 *4 (-1274 *3)) (-14 *5 (-1 *4 *4 *2))
+ (-14 *6 (-1 (-3 *2 "failed") *2 *2))
+ (-14 *7 (-1 (-3 *4 "failed") *4 *4 *2))))
+ ((*1 *2 *1)
+ (-12 (-4 *2 (-23)) (-5 *1 (-733 *3 *2 *4 *5 *6)) (-4 *3 (-175))
+ (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2))
+ (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2))))
+ ((*1 *2)
+ (-12 (-4 *2 (-1274 *3)) (-5 *1 (-734 *3 *2)) (-4 *3 (-1080))))
+ ((*1 *2 *1)
+ (-12 (-4 *2 (-23)) (-5 *1 (-737 *3 *2 *4 *5 *6)) (-4 *3 (-175))
+ (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2))
+ (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2))))
+ ((*1 *2) (-12 (-4 *1 (-893 *3)) (-5 *2 (-578)))))
+(((*1 *2 *1 *3)
+ (-12 (-5 *3 (-666 *1)) (-4 *1 (-1096 *4 *5 *6)) (-4 *4 (-1080))
+ (-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-112))))
+ ((*1 *2 *1 *1)
+ (-12 (-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-815))
+ (-4 *5 (-871)) (-5 *2 (-112))))
+ ((*1 *2 *1)
+ (-12 (-4 *1 (-1241 *3 *4 *5 *6)) (-4 *3 (-570)) (-4 *4 (-815))
+ (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-112))))
+ ((*1 *2 *3 *1)
+ (-12 (-4 *1 (-1241 *4 *5 *6 *3)) (-4 *4 (-570)) (-4 *5 (-815))
+ (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-5 *2 (-112)))))
(((*1 *2 *2)
- (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2))
- (-4 *2 (-13 (-444 *3) (-1233))))))
+ (-12 (-4 *3 (-376)) (-4 *4 (-386 *3)) (-4 *5 (-386 *3))
+ (-5 *1 (-535 *3 *4 *5 *2)) (-4 *2 (-709 *3 *4 *5))))
+ ((*1 *2 *3)
+ (-12 (-4 *4 (-570)) (-4 *5 (-386 *4)) (-4 *6 (-386 *4))
+ (-4 *7 (-1023 *4)) (-4 *2 (-709 *7 *8 *9))
+ (-5 *1 (-536 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-709 *4 *5 *6))
+ (-4 *8 (-386 *7)) (-4 *9 (-386 *7))))
+ ((*1 *1 *1)
+ (-12 (-4 *1 (-709 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-386 *2))
+ (-4 *4 (-386 *2)) (-4 *2 (-319))))
+ ((*1 *2 *2)
+ (-12 (-4 *3 (-319)) (-4 *3 (-175)) (-4 *4 (-386 *3))
+ (-4 *5 (-386 *3)) (-5 *1 (-710 *3 *4 *5 *2))
+ (-4 *2 (-709 *3 *4 *5))))
+ ((*1 *2 *2 *3)
+ (-12 (-5 *2 (-711 *3)) (-4 *3 (-319)) (-5 *1 (-722 *3))))
+ ((*1 *1 *1)
+ (-12 (-4 *1 (-1084 *2 *3 *4 *5 *6)) (-4 *4 (-1080))
+ (-4 *5 (-245 *3 *4)) (-4 *6 (-245 *2 *4)) (-4 *4 (-319)))))
+(((*1 *2)
+ (-12 (-14 *4 (-793)) (-4 *5 (-1248)) (-5 *2 (-136))
+ (-5 *1 (-244 *3 *4 *5)) (-4 *3 (-245 *4 *5))))
+ ((*1 *2)
+ (-12 (-4 *4 (-376)) (-5 *2 (-136)) (-5 *1 (-340 *3 *4))
+ (-4 *3 (-341 *4))))
+ ((*1 *2)
+ (-12 (-5 *2 (-793)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2)
+ (-4 *5 (-175))))
+ ((*1 *2 *1)
+ (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-578))
+ (-5 *1 (-518 *3 *4 *5 *6)) (-4 *6 (-978 *3 *4 *5))))
+ ((*1 *2 *1 *3)
+ (-12 (-5 *3 (-666 *6)) (-4 *6 (-871)) (-4 *4 (-376)) (-4 *5 (-815))
+ (-5 *2 (-578)) (-5 *1 (-518 *4 *5 *6 *7)) (-4 *7 (-978 *4 *5 *6))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1011 *3)) (-4 *3 (-1080)) (-5 *2 (-950))))
+ ((*1 *2) (-12 (-4 *1 (-1305 *3)) (-4 *3 (-376)) (-5 *2 (-136)))))
+(((*1 *1 *1 *2 *2 *2 *2)
+ (-12 (-5 *2 (-578)) (-4 *1 (-709 *3 *4 *5)) (-4 *3 (-1080))
+ (-4 *4 (-386 *3)) (-4 *5 (-386 *3)))))
(((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1080))))
((*1 *2 *1)
(-12 (-4 *2 (-1080)) (-5 *1 (-50 *2 *3)) (-14 *3 (-666 (-1207)))))
@@ -7218,10 +13250,10 @@
((*1 *2 *1)
(-12 (-4 *1 (-395 *2 *3)) (-4 *3 (-1131)) (-4 *2 (-1080))))
((*1 *2 *1)
- (-12 (-14 *3 (-666 (-1207))) (-4 *5 (-245 (-3225 *3) (-793)))
+ (-12 (-14 *3 (-666 (-1207))) (-4 *5 (-245 (-4415 *3) (-793)))
(-14 *6
- (-1 (-112) (-2 (|:| -2085 *4) (|:| -3761 *5))
- (-2 (|:| -2085 *4) (|:| -3761 *5))))
+ (-1 (-112) (-2 (|:| -2480 *4) (|:| -3945 *5))
+ (-2 (|:| -2480 *4) (|:| -3945 *5))))
(-4 *2 (-175)) (-5 *1 (-475 *3 *2 *4 *5 *6 *7)) (-4 *4 (-871))
(-4 *7 (-978 *2 *5 (-888 *3)))))
((*1 *2 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *3 (-874)) (-4 *2 (-102))))
@@ -7238,46 +13270,51 @@
((*1 *1 *1 *2)
(-12 (-4 *1 (-1096 *3 *4 *2)) (-4 *3 (-1080)) (-4 *4 (-815))
(-4 *2 (-871)))))
-(((*1 *2 *2 *3)
- (-12 (-4 *3 (-319)) (-5 *1 (-469 *3 *2)) (-4 *2 (-1274 *3))))
- ((*1 *2 *2 *3)
- (-12 (-4 *3 (-319)) (-5 *1 (-474 *3 *2)) (-4 *2 (-1274 *3))))
- ((*1 *2 *2 *3)
- (-12 (-4 *3 (-319)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-793)))
- (-5 *1 (-553 *3 *2 *4 *5)) (-4 *2 (-1274 *3)))))
+(((*1 *2 *3 *3 *3 *4 *4 *5 *5 *5 *3 *5 *5 *3 *6 *3 *3 *3)
+ (-12 (-5 *5 (-711 (-229))) (-5 *6 (-711 (-578))) (-5 *3 (-578))
+ (-5 *4 (-229)) (-5 *2 (-1066)) (-5 *1 (-774)))))
+(((*1 *2 *1 *2) (-12 (-5 *2 (-666 (-1189))) (-5 *1 (-408))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-666 (-1189))) (-5 *1 (-1228)))))
+(((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-1207)))))
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233)))))
+(((*1 *2)
+ (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-544 *3)) (-4 *3 (-13 (-748) (-25))))))
(((*1 *2)
(-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4))
(-4 *3 (-380 *4))))
((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-112)))))
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-520)) (-5 *1 (-291)))))
-(((*1 *2 *3 *4)
- (-12 (-5 *3 (-666 (-711 *5))) (-5 *4 (-1298 *5)) (-4 *5 (-319))
- (-4 *5 (-1080)) (-5 *2 (-711 *5)) (-5 *1 (-1060 *5)))))
-(((*1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-1217)))))
-(((*1 *1 *1)
- (-12 (-5 *1 (-1172 *2 *3)) (-4 *2 (-13 (-1131) (-34)))
- (-4 *3 (-13 (-1131) (-34))))))
-(((*1 *1 *1) (-5 *1 (-1094))))
-(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
- (-12 (-5 *3 (-1 (-392) (-392))) (-5 *4 (-392))
+(((*1 *2 *3) (-12 (-5 *3 (-1207)) (-5 *2 (-1303)) (-5 *1 (-1210))))
+ ((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-1210)))))
+(((*1 *2)
+ (-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4))
+ (-4 *3 (-380 *4))))
+ ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-112)))))
+(((*1 *2 *3 *4 *5 *5 *4 *6)
+ (-12 (-5 *4 (-578)) (-5 *6 (-1 (-1303) (-1298 *5) (-1298 *5) (-392)))
+ (-5 *3 (-1298 (-392))) (-5 *5 (-392)) (-5 *2 (-1303))
+ (-5 *1 (-810)))))
+(((*1 *2 *3)
+ (-12
+ (-5 *3
+ (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229)))
+ (|:| -1868 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
+ (|:| |relerr| (-229))))
(-5 *2
- (-2 (|:| -4120 *4) (|:| -3396 *4) (|:| |totalpts| (-578))
- (|:| |success| (-112))))
- (-5 *1 (-811)) (-5 *5 (-578)))))
-(((*1 *2 *1)
- (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1248)) (-4 *2 (-1131))
- (-4 *2 (-871)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1212)) (-5 *1 (-291)))))
-(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-178)))))
+ (-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 (-195)))))
(((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814))))
((*1 *2 *1)
(-12 (-4 *1 (-395 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1131))))
((*1 *2 *1)
(-12 (-14 *3 (-666 (-1207))) (-4 *4 (-175))
- (-4 *6 (-245 (-3225 *3) (-793)))
+ (-4 *6 (-245 (-4415 *3) (-793)))
(-14 *7
- (-1 (-112) (-2 (|:| -2085 *5) (|:| -3761 *6))
- (-2 (|:| -2085 *5) (|:| -3761 *6))))
+ (-1 (-112) (-2 (|:| -2480 *5) (|:| -3945 *6))
+ (-2 (|:| -2480 *5) (|:| -3945 *6))))
(-5 *2 (-735 *5 *6 *7)) (-5 *1 (-475 *3 *4 *5 *6 *7 *8))
(-4 *5 (-871)) (-4 *8 (-978 *4 *6 (-888 *3)))))
((*1 *2 *1)
@@ -7286,205 +13323,247 @@
((*1 *1 *1)
(-12 (-4 *1 (-1004 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-814))
(-4 *4 (-871)))))
-(((*1 *2 *1)
- (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1248)) (-4 *2 (-1131))
- (-4 *2 (-871)))))
-(((*1 *2 *2 *3)
- (-12 (-5 *2 (-1298 *4)) (-5 *3 (-793)) (-4 *4 (-362))
- (-5 *1 (-542 *4)))))
-(((*1 *1 *1 *1) (-4 *1 (-314))) ((*1 *1 *1) (-4 *1 (-314))))
+(((*1 *2 *3 *4)
+ (-12 (-5 *4 (-1207))
+ (-4 *5 (-13 (-319) (-149) (-1069 (-578)) (-660 (-578))))
+ (-5 *2 (-600 *3)) (-5 *1 (-440 *5 *3))
+ (-4 *3 (-13 (-1233) (-29 *5))))))
(((*1 *2 *3)
- (-12 (-5 *2 (-1 (-972 *3) (-972 *3))) (-5 *1 (-179 *3))
- (-4 *3 (-13 (-376) (-1233) (-1033))))))
-(((*1 *2 *3 *3) (-12 (-5 *3 (-1151)) (-5 *2 (-1303)) (-5 *1 (-853)))))
-(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-52)) (-5 *1 (-1226)))))
-(((*1 *2 *2)
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- (-12
- (-5 *3
- (-2 (|:| |stiffness| (-392)) (|:| |stability| (-392))
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(((*1 *2 *3)
(-12 (-5 *3 (-1207))
(-4 *4 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *2 (-52))
@@ -7748,103 +13710,39 @@
((*1 *1 *2 *3)
(-12 (-5 *2 (-421 (-578))) (-4 *4 (-1080)) (-4 *1 (-1281 *4 *3))
(-4 *3 (-1258 *4)))))
+(((*1 *1 *1) (-4 *1 (-648)))
+ ((*1 *2 *2)
+ (-12 (-4 *3 (-570)) (-5 *1 (-649 *3 *2))
+ (-4 *2 (-13 (-444 *3) (-1033) (-1233))))))
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+ (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2))
+ (-4 *2 (-13 (-444 *3) (-1233))))))
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1125 (-229))) (-5 *1 (-956))))
+ ((*1 *2 *1 *3 *3 *3)
+ (-12 (-5 *3 (-392)) (-5 *2 (-1303)) (-5 *1 (-1300))))
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+ (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2))
+ (-4 *2 (-13 (-444 *3) (-1233))))))
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+ (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1248)) (-4 *2 (-1131))
+ (-4 *2 (-871)))))
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(((*1 *2 *3)
(-12 (-5 *3 (-1207))
(-4 *4 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *2 (-52))
@@ -7879,45 +13777,43 @@
(-4 *3 (-1289 *4))))
((*1 *2 *1)
(-12 (-4 *1 (-1281 *3 *2)) (-4 *3 (-1080)) (-4 *2 (-1258 *3)))))
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- ((*1 *1 *1) (|partial| -4 *1 (-744))))
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(((*1 *2 *1)
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+ (-4 *3 (-633 (-550)))))
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(((*1 *2 *3)
(-12 (-5 *3 (-1207))
(-4 *4 (-13 (-466) (-1069 (-578)) (-660 (-578)))) (-5 *2 (-52))
@@ -7960,221 +13856,226 @@
(-5 *1 (-473 *7 *3))))
((*1 *2 *1)
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+ (-5 *1 (-810))))
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+ (-12 (-5 *4 (-578)) (-5 *6 (-1 (-1303) (-1298 *5) (-1298 *5) (-392)))
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(((*1 *2 *3)
(-12
(-5 *3
- (-2 (|:| |lfn| (-666 (-328 (-229)))) (|:| -2200 (-666 (-229)))))
+ (-2 (|:| |lfn| (-666 (-328 (-229)))) (|:| -2911 (-666 (-229)))))
(-5 *2 (-666 (-1207))) (-5 *1 (-278))))
((*1 *2 *3)
(-12 (-5 *3 (-1203 *7)) (-4 *7 (-978 *6 *4 *5)) (-4 *4 (-815))
@@ -8196,7 +14097,7 @@
(-5 *1 (-979 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-376)
- (-10 -8 (-15 -2411 ($ *7)) (-15 -2518 (*7 $)) (-15 -2529 (*7 $)))))))
+ (-10 -8 (-15 -2863 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $)))))))
((*1 *2 *1)
(-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814))
(-4 *5 (-871)) (-5 *2 (-666 *5))))
@@ -8206,72 +14107,29 @@
((*1 *2 *3)
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(-5 *1 (-1074 *4)))))
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- (-4 *1 (-355 *4 *3 *5)) (-4 *5 (-1274 (-421 *3))))))
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- (-5 *1 (-777)))))
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+ (-12 (-4 *5 (-1131)) (-4 *3 (-927 *5)) (-5 *2 (-711 *3))
+ (-5 *1 (-714 *5 *3 *6 *4)) (-4 *6 (-386 *3))
+ (-4 *4 (-13 (-386 *5) (-10 -7 (-6 -4507)))))))
(((*1 *2 *3)
- (-12 (-4 *1 (-922))
- (-5 *3
- (-2 (|:| |pde| (-666 (-328 (-229))))
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- (-666
- (-2 (|:| |start| (-229)) (|:| |finish| (-229))
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- (-5 *2 (-2 (|:| -3458 *3) (|:| -2920 *3))) (-5 *1 (-877 *5 *3))
- (-4 *3 (-876 *5)))))
-(((*1 *2 *2 *3)
- (-12 (-4 *3 (-1080)) (-5 *1 (-458 *3 *2)) (-4 *2 (-1274 *3)))))
-(((*1 *1 *1) (-5 *1 (-1094))))
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- (-12 (-5 *2 (-711 *5)) (-4 *5 (-1080)) (-5 *1 (-1085 *3 *4 *5))
- (-14 *3 (-793)) (-14 *4 (-793)))))
+ (-12 (-5 *3 (-666 (-2 (|:| |den| (-578)) (|:| |gcdnum| (-578)))))
+ (-4 *4 (-1274 (-421 *2))) (-5 *2 (-578)) (-5 *1 (-942 *4 *5))
+ (-4 *5 (-1274 (-421 *4))))))
+(((*1 *2 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-950)) (-5 *1 (-808)))))
(((*1 *2 *3 *4 *2)
(-12 (-5 *3 (-1203 (-421 (-1203 *2)))) (-5 *4 (-631 *2))
(-4 *2 (-13 (-444 *5) (-27) (-1233)))
@@ -8288,30 +14146,65 @@
(-4 *6 (-1080))
(-4 *2
(-13 (-376)
- (-10 -8 (-15 -2411 ($ *7)) (-15 -2518 (*7 $)) (-15 -2529 (*7 $)))))
+ (-10 -8 (-15 -2863 ($ *7)) (-15 -1467 (*7 $)) (-15 -1482 (*7 $)))))
(-5 *1 (-979 *5 *4 *6 *7 *2)) (-4 *7 (-978 *6 *5 *4))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-421 (-1203 (-421 (-981 *5))))) (-5 *4 (-1207))
(-5 *2 (-421 (-981 *5))) (-5 *1 (-1074 *5)) (-4 *5 (-570)))))
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- (-12 (-4 *1 (-1154 *3 *4 *2 *5)) (-4 *4 (-1080)) (-4 *5 (-245 *3 *4))
- (-4 *2 (-245 *3 *4)))))
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- (-5 *1 (-1008 *4 *5 *6 *3)) (-4 *3 (-1096 *4 *5 *6)))))
(((*1 *2 *3)
- (|partial| -12 (-4 *4 (-1252)) (-4 *5 (-1274 *4))
- (-5 *2 (-2 (|:| |radicand| (-421 *5)) (|:| |deg| (-793))))
- (-5 *1 (-150 *4 *5 *3)) (-4 *3 (-1274 (-421 *5))))))
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-(((*1 *1 *1 *1)
- (-12 (|has| *1 (-6 -4501)) (-4 *1 (-121 *2)) (-4 *2 (-1248)))))
+ (-12
+ (-5 *3
+ (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
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+ (|:| |intvals| (-666 (-229))) (|:| |g| (-328 (-229)))
+ (|:| |abserr| (-229)) (|:| |relerr| (-229))))
+ (-5 *2 (-392)) (-5 *1 (-208)))))
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+ (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2))
+ (-4 *2 (-13 (-444 *3) (-1233))))))
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+ (-12 (-5 *3 (-666 (-865 (-229)))) (-5 *4 (-229)) (-5 *2 (-666 *4))
+ (-5 *1 (-278)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-711 (-421 (-981 *4)))) (-4 *4 (-466))
- (-5 *2 (-666 (-3 (-421 (-981 *4)) (-1196 (-1207) (-981 *4)))))
- (-5 *1 (-304 *4)))))
-(((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-266)))))
+ (-12 (-4 *4 (-386 *2)) (-4 *5 (-386 *2)) (-4 *2 (-376))
+ (-5 *1 (-535 *2 *4 *5 *3)) (-4 *3 (-709 *2 *4 *5))))
+ ((*1 *2 *1)
+ (-12 (-4 *1 (-709 *2 *3 *4)) (-4 *3 (-386 *2)) (-4 *4 (-386 *2))
+ (|has| *2 (-6 (-4509 "*"))) (-4 *2 (-1080))))
+ ((*1 *2 *3)
+ (-12 (-4 *4 (-386 *2)) (-4 *5 (-386 *2)) (-4 *2 (-175))
+ (-5 *1 (-710 *2 *4 *5 *3)) (-4 *3 (-709 *2 *4 *5))))
+ ((*1 *2 *1)
+ (-12 (-4 *1 (-1154 *3 *2 *4 *5)) (-4 *4 (-245 *3 *2))
+ (-4 *5 (-245 *3 *2)) (|has| *2 (-6 (-4509 "*"))) (-4 *2 (-1080)))))
(((*1 *1 *2 *3)
(-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814))))
((*1 *1 *2 *3)
@@ -8319,10 +14212,10 @@
(-4 *2 (-376)) (-14 *5 (-1024 *4 *2))))
((*1 *1 *2 *3)
(-12 (-5 *3 (-735 *5 *6 *7)) (-4 *5 (-871))
- (-4 *6 (-245 (-3225 *4) (-793)))
+ (-4 *6 (-245 (-4415 *4) (-793)))
(-14 *7
- (-1 (-112) (-2 (|:| -2085 *5) (|:| -3761 *6))
- (-2 (|:| -2085 *5) (|:| -3761 *6))))
+ (-1 (-112) (-2 (|:| -2480 *5) (|:| -3945 *6))
+ (-2 (|:| -2480 *5) (|:| -3945 *6))))
(-14 *4 (-666 (-1207))) (-4 *2 (-175))
(-5 *1 (-475 *4 *2 *5 *6 *7 *8)) (-4 *8 (-978 *2 *6 (-888 *4)))))
((*1 *1 *2 *3)
@@ -8352,469 +14245,313 @@
((*1 *1 *1 *2 *3)
(-12 (-4 *1 (-1004 *4 *3 *2)) (-4 *4 (-1080)) (-4 *3 (-814))
(-4 *2 (-871)))))
-(((*1 *2 *2) (-12 (-5 *2 (-793)) (-5 *1 (-459 *3)) (-4 *3 (-1080))))
- ((*1 *2) (-12 (-5 *2 (-793)) (-5 *1 (-459 *3)) (-4 *3 (-1080)))))
-(((*1 *2 *1 *2) (-12 (-5 *1 (-1057 *2)) (-4 *2 (-1248)))))
-(((*1 *1 *1 *1) (-12 (-5 *1 (-804 *2)) (-4 *2 (-1080)))))
-(((*1 *1 *2 *3) (-12 (-5 *3 (-578)) (-5 *1 (-432 *2)) (-4 *2 (-570)))))
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- (-12 (-4 *1 (-1007 *4 *5 *6 *3)) (-4 *4 (-1080)) (-4 *5 (-815))
- (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-4 *4 (-570))
- (-5 *2 (-2 (|:| |rnum| *4) (|:| |polnum| *3) (|:| |den| *4))))))
-(((*1 *1 *1) (-12 (-4 *1 (-439 *2)) (-4 *2 (-1131)) (-4 *2 (-381)))))
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- (|partial| -12 (-4 *3 (-376)) (-4 *4 (-386 *3)) (-4 *5 (-386 *3))
- (-5 *1 (-535 *3 *4 *5 *2)) (-4 *2 (-709 *3 *4 *5))))
- ((*1 *2 *3)
- (|partial| -12 (-4 *4 (-570)) (-4 *5 (-386 *4)) (-4 *6 (-386 *4))
- (-4 *7 (-1023 *4)) (-4 *2 (-709 *7 *8 *9))
- (-5 *1 (-536 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-709 *4 *5 *6))
- (-4 *8 (-386 *7)) (-4 *9 (-386 *7))))
- ((*1 *1 *1)
- (|partial| -12 (-4 *1 (-709 *2 *3 *4)) (-4 *2 (-1080))
- (-4 *3 (-386 *2)) (-4 *4 (-386 *2)) (-4 *2 (-376))))
- ((*1 *2 *2)
- (|partial| -12 (-4 *3 (-376)) (-4 *3 (-175)) (-4 *4 (-386 *3))
- (-4 *5 (-386 *3)) (-5 *1 (-710 *3 *4 *5 *2))
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- ((*1 *1 *1)
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- (-4 *2 (-871)) (-4 *5 (-1096 *3 *4 *2)))))
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((*1 *2 *3)
(-12 (-4 *4 (-13 (-570) (-1069 (-578)))) (-5 *2 (-328 *4))
@@ -8822,36 +14559,41 @@
((*1 *2 *2)
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- (-4 *6 (-678 *5)))))
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((*1 *2 *3)
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@@ -8861,157 +14603,48 @@
((*1 *2 *2)
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+ ((*1 *1 *1 *1)
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+ ((*1 *1 *1 *2)
+ (-12 (-5 *2 (-841 *3)) (-4 *1 (-1315 *3 *4)) (-4 *3 (-871))
+ (-4 *4 (-1080))))
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+ (-12 (-4 *1 (-1315 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080)))))
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+ (|partial| -12 (-5 *4 (-1 (-3 (-578) "failed") *5)) (-4 *5 (-1080))
+ (-5 *2 (-578)) (-5 *1 (-557 *5 *3)) (-4 *3 (-1274 *5))))
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+ (|partial| -12 (-5 *5 (-1 (-3 (-578) "failed") *4)) (-4 *4 (-1080))
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+ (|partial| -12 (-5 *5 (-1 (-3 (-578) "failed") *4)) (-4 *4 (-1080))
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(((*1 *1 *1)
(-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-666 (-1207)))
(-14 *3 (-666 (-1207))) (-4 *4 (-401))))
@@ -9021,42 +14654,35 @@
((*1 *1 *2) (-12 (-5 *2 (-421 (-578))) (-4 *1 (-1043))))
((*1 *1 *1 *2) (-12 (-4 *1 (-1043)) (-5 *2 (-950))))
((*1 *1 *1) (-4 *1 (-1043))))
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- ((*1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-1300)))))
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+ (-4 *4 (-277 *3)) (-4 *5 (-815)))))
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+ (-5 *1 (-727 *3 *4)) (-4 *3 (-1248)) (-4 *4 (-1248)))))
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+ (-12 (-4 *1 (-1007 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-815))
+ (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-570))
+ (-5 *2 (-112)))))
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+ (-12 (-5 *2 (-1 (-1157 *4 *3 *5))) (-4 *4 (-38 (-421 (-578))))
+ (-4 *4 (-1080)) (-4 *3 (-871)) (-5 *1 (-1157 *4 *3 *5))
+ (-4 *5 (-978 *4 (-545 *3) *3))))
+ ((*1 *1 *2 *3 *4)
+ (-12 (-5 *2 (-1 (-1242 *4))) (-5 *3 (-1207)) (-5 *1 (-1242 *4))
+ (-4 *4 (-38 (-421 (-578)))) (-4 *4 (-1080)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-666 (-48))) (-5 *2 (-432 *3)) (-5 *1 (-39 *3))
(-4 *3 (-1274 (-48)))))
@@ -9105,8 +14731,8 @@
(-12
(-4 *4
(-13 (-871)
- (-10 -8 (-15 -3342 ((-1207) $))
- (-15 -3967 ((-3 $ "failed") (-1207))))))
+ (-10 -8 (-15 -1334 ((-1207) $))
+ (-15 -1518 ((-3 $ "failed") (-1207))))))
(-4 *5 (-815)) (-4 *7 (-570)) (-5 *2 (-432 *3))
(-5 *1 (-470 *4 *5 *6 *7 *3)) (-4 *6 (-570))
(-4 *3 (-978 *7 *5 *4))))
@@ -9155,13 +14781,13 @@
(-12 (-4 *4 (-815))
(-4 *5
(-13 (-871)
- (-10 -8 (-15 -3342 ((-1207) $))
- (-15 -3967 ((-3 $ "failed") (-1207))))))
+ (-10 -8 (-15 -1334 ((-1207) $))
+ (-15 -1518 ((-3 $ "failed") (-1207))))))
(-4 *6 (-319)) (-5 *2 (-432 *3)) (-5 *1 (-752 *4 *5 *6 *3))
(-4 *3 (-978 (-981 *6) *4 *5))))
((*1 *2 *3)
(-12 (-4 *4 (-815))
- (-4 *5 (-13 (-871) (-10 -8 (-15 -3342 ((-1207) $))))) (-4 *6 (-570))
+ (-4 *5 (-13 (-871) (-10 -8 (-15 -1334 ((-1207) $))))) (-4 *6 (-570))
(-5 *2 (-432 *3)) (-5 *1 (-754 *4 *5 *6 *3))
(-4 *3 (-978 (-421 (-981 *6)) *4 *5))))
((*1 *2 *3)
@@ -9197,237 +14823,301 @@
((*1 *2 *1) (-12 (-5 *2 (-432 *1)) (-4 *1 (-1252))))
((*1 *2 *3)
(-12 (-5 *2 (-432 *3)) (-5 *1 (-1263 *3)) (-4 *3 (-1274 (-578))))))
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- (-4 *2 (-871)) (-4 *3 (-175))))
- ((*1 *2 *3 *3)
- (-12 (-4 *2 (-570)) (-5 *1 (-1000 *2 *3)) (-4 *3 (-1274 *2))))
- ((*1 *1 *1 *1)
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- (-4 *4 (-871)) (-4 *2 (-570))))
- ((*1 *2 *1 *1)
- (-12 (-4 *1 (-1274 *2)) (-4 *2 (-1080)) (-4 *2 (-175)))))
+ (-4 *4 (-871)) (-4 *2 (-466)))))
+(((*1 *1) (-4 *1 (-998))))
+(((*1 *1 *1 *1) (-12 (-4 *1 (-678 *2)) (-4 *2 (-1080)) (-4 *2 (-376))))
+ ((*1 *2 *2 *2 *3)
+ (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-376)) (-5 *1 (-681 *4 *2))
+ (-4 *2 (-678 *4)))))
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+ (-4 *2 (-13 (-444 *3) (-1233))))))
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+ (-4 *6 (-1274 (-421 *5)))
+ (-5 *2
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+ (|:| |gd| *5)))
+ (-4 *1 (-355 *4 *5 *6)))))
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(((*1 *2 *3 *3)
(-12 (-5 *3 (-666 *7)) (-4 *7 (-1096 *4 *5 *6)) (-4 *4 (-466))
(-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-112))
@@ -9436,456 +15126,268 @@
(-12 (-5 *3 (-666 *7)) (-4 *7 (-1096 *4 *5 *6)) (-4 *4 (-466))
(-4 *5 (-815)) (-4 *6 (-871)) (-5 *2 (-112))
(-5 *1 (-1138 *4 *5 *6 *7 *8)) (-4 *8 (-1102 *4 *5 *6 *7)))))
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- (|:| |endPointContinuity|
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- (|:| |upperSingular|
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@@ -9896,49 +15398,45 @@
(-4 *2 (-1080))))
((*1 *2 *1 *3)
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@@ -9992,187 +15490,234 @@
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- (-12
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- (-2
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- (|:| |upperSingular|
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- (|:| |bothSingular|
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- (|:| |notEvaluated|
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- (-5 *2
- (-2
- (|:| |endPointContinuity|
- (-3 (|:| |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|
- (-3 (|:| |str| (-1188 (-229)))
- (|:| |notEvaluated|
- "Internal singularities not yet evaluated")))
- (|:| -1634
- (-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 (-573)))))
-(((*1 *1 *2 *2)
- (-12
- (-5 *2
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- (-5 *1 (-1206)))))
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-(((*1 *2) (-12 (-5 *2 (-933 (-578))) (-5 *1 (-946)))))
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- (-12 (-5 *2 (-1203 (-421 (-578)))) (-5 *1 (-971)) (-5 *3 (-578)))))
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- ((*1 *1 *1 *2) (-12 (-5 *1 (-740 *2)) (-4 *2 (-376))))
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- ((*1 *2 *1 *3 *4 *4)
- (-12 (-5 *3 (-950)) (-5 *4 (-392)) (-5 *2 (-1303)) (-5 *1 (-1299)))))
-(((*1 *2 *2) (-12 (-5 *2 (-392)) (-5 *1 (-1300))))
- ((*1 *2) (-12 (-5 *2 (-392)) (-5 *1 (-1300)))))
-(((*1 *2 *3)
- (-12 (-4 *4 (-570))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -1769 *4)))
- (-5 *1 (-1000 *4 *3)) (-4 *3 (-1274 *4)))))
+ (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1248)) (-5 *1 (-1188 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1248)) (-5 *1 (-1188 *3)))))
(((*1 *2)
(-12 (-14 *4 *2) (-4 *5 (-1248)) (-5 *2 (-793))
(-5 *1 (-244 *3 *4 *5)) (-4 *3 (-245 *4 *5))))
@@ -12977,1380 +15863,100 @@
((*1 *2 *1)
(-12 (-4 *2 (-13 (-870) (-376))) (-5 *1 (-1092 *2 *3))
(-4 *3 (-1274 *2)))))
-(((*1 *1 *1 *2)
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- (-4 *2 (-13 (-444 *3) (-1033))))))
-(((*1 *1 *1) (-5 *1 (-1206)))
- ((*1 *1 *2)
- (-12
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- (-3 (|:| I (-328 (-578))) (|:| -2155 (-328 (-392)))
- (|:| CF (-328 (-172 (-392)))) (|:| |switch| (-1206))))
- (-5 *1 (-1206)))))
-(((*1 *2 *3)
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- (-4 *3
- (-13 (-376) (-314)
- (-10 -8 (-15 -2518 ((-1156 *4 (-631 $)) $))
- (-15 -2529 ((-1156 *4 (-631 $)) $))
- (-15 -2411 ($ (-1156 *4 (-631 $))))))))))
-(((*1 *2 *2) (-12 (-5 *2 (-578)) (-5 *1 (-955)))))
-(((*1 *2 *3) (-12 (-5 *3 (-1298 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175))))
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- (-4 *6 (-815)) (-5 *2 (-421 (-981 *4))) (-5 *1 (-953 *4 *5 *6 *3))
- (-4 *3 (-978 *4 *6 *5))))
- ((*1 *2 *3)
- (-12 (-5 *3 (-711 *7)) (-4 *7 (-978 *4 *6 *5))
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- (-5 *1 (-953 *4 *5 *6 *7))))
- ((*1 *2 *3)
- (-12 (-5 *3 (-666 *7)) (-4 *7 (-978 *4 *6 *5))
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-(((*1 *2 *1)
- (-12 (-5 *2 (-2 (|:| |var| (-666 (-1207))) (|:| |pred| (-52))))
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- ((*1 *2 *3 *3)
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-(((*1 *1 *2 *2 *2 *2) (-12 (-4 *1 (-1028 *2)) (-4 *2 (-175)))))
-(((*1 *1 *1) (-4 *1 (-648)))
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- ((*1 *1 *1) (-5 *1 (-886))))
-(((*1 *2 *3)
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-(((*1 *1 *1 *1)
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- (-12 (-5 *4 (-578)) (-5 *5 (-711 (-229)))
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-(((*1 *2)
- (-12 (-4 *4 (-175)) (-5 *2 (-112)) (-5 *1 (-379 *3 *4))
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- (-12 (-5 *3 (-229)) (-5 *4 (-578)) (-5 *2 (-1066)) (-5 *1 (-780)))))
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- (-12 (-4 *1 (-1296 *2)) (-4 *2 (-1248)) (-4 *2 (-1080)))))
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- (-12 (-5 *2 (-578)) (-4 *1 (-294 *3)) (-4 *3 (-1248))))
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- (-12 (-5 *3 (-578)) (-4 *1 (-294 *2)) (-4 *2 (-1248))))
- ((*1 *1 *2)
- (-12
- (-5 *2
- (-2
- (|:| -3172
- (-2 (|:| |var| (-1207)) (|:| |fn| (-328 (-229)))
- (|:| -1634 (-1125 (-865 (-229)))) (|:| |abserr| (-229))
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- (|:| -2754
- (-2
- (|:| |endPointContinuity|
- (-3 (|:| |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|
- (-3 (|:| |str| (-1188 (-229)))
- (|:| |notEvaluated|
- "Internal singularities not yet evaluated")))
- (|:| -1634
- (-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 (-573))))
- ((*1 *1 *2 *1 *3)
- (-12 (-5 *3 (-793)) (-4 *1 (-717 *2)) (-4 *2 (-1131))))
- ((*1 *1 *2)
- (-12
- (-5 *2
- (-2
- (|:| -3172
- (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
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- (|:| |intvals| (-666 (-229))) (|:| |g| (-328 (-229)))
- (|:| |abserr| (-229)) (|:| |relerr| (-229))))
- (|:| -2754
- (-2 (|:| |stiffness| (-392)) (|:| |stability| (-392))
- (|:| |expense| (-392)) (|:| |accuracy| (-392))
- (|:| |intermediateResults| (-392))))))
- (-5 *1 (-825))))
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- (-12 (-5 *2 (-1303)) (-5 *1 (-1225 *3 *4)) (-4 *3 (-1131))
- (-4 *4 (-1131)))))
-(((*1 *2 *2) (-12 (-5 *2 (-666 (-328 (-229)))) (-5 *1 (-278)))))
-(((*1 *2 *1 *1)
- (-12 (-4 *3 (-570)) (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871))
- (-5 *2 (-666 *1)) (-4 *1 (-1096 *3 *4 *5)))))
-(((*1 *1 *2 *3)
- (-12 (-5 *2 (-520)) (-5 *3 (-666 (-994))) (-5 *1 (-109)))))
-(((*1 *1 *1) (-5 *1 (-886)))
- ((*1 *2 *1)
- (-12 (-4 *1 (-1134 *2 *3 *4 *5 *6)) (-4 *3 (-1131)) (-4 *4 (-1131))
- (-4 *5 (-1131)) (-4 *6 (-1131)) (-4 *2 (-1131))))
- ((*1 *1 *2) (-12 (-5 *2 (-229)) (-5 *1 (-1189))))
- ((*1 *1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-1189))))
- ((*1 *2 *1) (-12 (-5 *2 (-1189)) (-5 *1 (-1207)))))
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- (-12 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1289 *4))
- (-4 *4 (-38 (-421 (-578))))
- (-5 *2 (-1 (-1188 *4) (-1188 *4) (-1188 *4))) (-5 *1 (-1291 *4 *5)))))
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- (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815))
- (-4 *4 (-871)))))
-(((*1 *2 *1) (-12 (-5 *2 (-666 (-109))) (-5 *1 (-178)))))
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- (-12 (-5 *3 (-116)) (-5 *4 (-793))
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- (-5 *1 (-41 *5 *2)) (-4 *2 (-444 *5))
- (-4 *2
- (-13 (-376) (-314)
- (-10 -8 (-15 -2518 ((-1156 *5 (-631 $)) $))
- (-15 -2529 ((-1156 *5 (-631 $)) $))
- (-15 -2411 ($ (-1156 *5 (-631 $))))))))))
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- (-12 (-4 *3 (-1131)) (-4 *4 (-13 (-1080) (-911 *3) (-633 (-917 *3))))
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- (-12 (-5 *3 (-711 (-172 (-421 (-578))))) (-5 *2 (-666 (-172 *4)))
- (-5 *1 (-786 *4)) (-4 *4 (-13 (-376) (-870))))))
-(((*1 *2) (-12 (-5 *2 (-1303)) (-5 *1 (-573)))))
+ (-12 (-4 *4 (-1080))
+ (-4 *2 (-13 (-418) (-1069 *4) (-376) (-1233) (-296)))
+ (-5 *1 (-457 *4 *3 *2)) (-4 *3 (-1274 *4))))
+ ((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-631 *3)) (-4 *3 (-1131))))
+ ((*1 *2) (-12 (-5 *2 (-578)) (-5 *1 (-886))))
+ ((*1 *2 *1) (-12 (-5 *2 (-578)) (-5 *1 (-886)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-666 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *6 (-633 (-1207)))
- (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-871))
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- (-5 *1 (-518 *4 *5 *6 *7)))))
-(((*1 *1) (-5 *1 (-451))))
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- (-12 (-5 *5 (-1125 *3)) (-4 *3 (-978 *7 *6 *4)) (-4 *6 (-815))
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- (-5 *1 (-608 *6 *4 *7 *3))))
- ((*1 *2 *3 *4)
- (-12 (-4 *5 (-815)) (-4 *4 (-871)) (-4 *6 (-570))
- (-5 *2 (-2 (|:| |num| *3) (|:| |den| (-578))))
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- ((*1 *2 *2 *3)
- (-12 (-5 *3 (-1207))
- (-4 *4 (-13 (-570) (-1069 (-578)) (-660 (-578))))
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- (-12 (-5 *4 (-1207)) (-4 *5 (-13 (-570) (-1069 (-578))))
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- ((*1 *2 *3 *4)
- (-12 (-5 *4 (-1207)) (-4 *5 (-13 (-570) (-1069 (-578))))
- (-5 *2 (-3 (-421 (-981 *5)) (-328 *5))) (-5 *1 (-1200 *5))
- (-5 *3 (-421 (-981 *5)))))
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- (-12 (-5 *4 (-1123 (-981 *5))) (-5 *3 (-981 *5))
- (-4 *5 (-13 (-570) (-1069 (-578)))) (-5 *2 (-421 *3))
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- ((*1 *2 *3 *4)
- (-12 (-5 *4 (-1123 (-421 (-981 *5)))) (-5 *3 (-421 (-981 *5)))
- (-4 *5 (-13 (-570) (-1069 (-578)))) (-5 *2 (-3 *3 (-328 *5)))
- (-5 *1 (-1200 *5)))))
-(((*1 *2 *3 *4)
- (-12 (-5 *3 (-666 (-711 *5))) (-5 *4 (-578)) (-4 *5 (-376))
- (-4 *5 (-1080)) (-5 *2 (-112)) (-5 *1 (-1060 *5))))
+ (-12 (-5 *3 (-793)) (-5 *2 (-1303)) (-5 *1 (-890 *4 *5 *6 *7))
+ (-4 *4 (-1080)) (-14 *5 (-666 (-1207))) (-14 *6 (-666 *3))
+ (-14 *7 *3)))
((*1 *2 *3)
- (-12 (-5 *3 (-666 (-711 *4))) (-4 *4 (-376)) (-4 *4 (-1080))
- (-5 *2 (-112)) (-5 *1 (-1060 *4)))))
-(((*1 *1) (-5 *1 (-159)))
- ((*1 *2 *1) (-12 (-4 *1 (-1075 *2)) (-4 *2 (-23)))))
-(((*1 *2 *1)
- (-12 (-4 *1 (-377 *3 *4)) (-4 *3 (-1131)) (-4 *4 (-1131))
- (-5 *2 (-1189)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1002)) (-5 *1 (-934 *3)) (-4 *3 (-1131)))))
+ (-12 (-5 *3 (-793)) (-4 *4 (-1080)) (-4 *5 (-871)) (-4 *6 (-815))
+ (-14 *8 (-666 *5)) (-5 *2 (-1303))
+ (-5 *1 (-1310 *4 *5 *6 *7 *8 *9 *10)) (-4 *7 (-978 *4 *6 *5))
+ (-14 *9 (-666 *3)) (-14 *10 *3))))
(((*1 *2 *1)
- (-12 (-4 *4 (-1131)) (-5 *2 (-914 *3 *5)) (-5 *1 (-910 *3 *4 *5))
- (-4 *3 (-1131)) (-4 *5 (-688 *4)))))
-(((*1 *1 *1 *1 *2)
- (|partial| -12 (-5 *2 (-112)) (-5 *1 (-609 *3)) (-4 *3 (-1080)))))
-(((*1 *2 *3)
- (|partial| -12 (-4 *4 (-13 (-570) (-149)))
- (-5 *2 (-2 (|:| -3855 *3) (|:| -3868 *3))) (-5 *1 (-1268 *4 *3))
- (-4 *3 (-1274 *4)))))
-(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4)
- (-12 (-5 *3 (-1189)) (-5 *4 (-578)) (-5 *5 (-711 (-229)))
- (-5 *6 (-229)) (-5 *2 (-1066)) (-5 *1 (-774)))))
-(((*1 *2 *2)
- (-12 (-5 *2 (-666 *3)) (-4 *3 (-1274 (-578))) (-5 *1 (-500 *3)))))
-(((*1 *2 *3 *2) (-12 (-5 *2 (-1189)) (-5 *3 (-578)) (-5 *1 (-248)))))
-(((*1 *2 *2 *3 *4)
- (-12 (-5 *3 (-666 (-631 *6))) (-5 *4 (-1207)) (-5 *2 (-631 *6))
- (-4 *6 (-444 *5)) (-4 *5 (-1131)) (-5 *1 (-587 *5 *6)))))
-(((*1 *1 *1 *2)
- (|partial| -12 (-5 *2 (-950)) (-5 *1 (-1132 *3 *4)) (-14 *3 *2)
- (-14 *4 *2))))
-(((*1 *2 *1 *3 *3)
- (-12 (-5 *3 (-578)) (-5 *2 (-1303)) (-5 *1 (-933 *4))
- (-4 *4 (-1131))))
- ((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-933 *3)) (-4 *3 (-1131)))))
-(((*1 *1 *2 *2 *2)
- (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1233)))))
- ((*1 *2 *1 *3 *4 *4)
- (-12 (-5 *3 (-950)) (-5 *4 (-392)) (-5 *2 (-1303)) (-5 *1 (-1299))))
- ((*1 *2 *1 *3 *3)
- (-12 (-5 *3 (-392)) (-5 *2 (-1303)) (-5 *1 (-1300)))))
-(((*1 *2 *2 *3 *3)
- (-12 (-5 *2 (-666 *7)) (-5 *3 (-578)) (-4 *7 (-978 *4 *5 *6))
- (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871))
- (-5 *1 (-463 *4 *5 *6 *7)))))
+ (-12 (-4 *1 (-338 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1080))
+ (-4 *2 (-466))))
+ ((*1 *2 *3)
+ (-12 (-5 *3 (-666 *4)) (-4 *4 (-1274 (-578))) (-5 *2 (-666 (-578)))
+ (-5 *1 (-500 *4))))
+ ((*1 *2 *1) (-12 (-4 *1 (-876 *2)) (-4 *2 (-1080)) (-4 *2 (-466))))
+ ((*1 *1 *1 *2)
+ (-12 (-4 *1 (-978 *3 *4 *2)) (-4 *3 (-1080)) (-4 *4 (-815))
+ (-4 *2 (-871)) (-4 *3 (-466)))))
+(((*1 *2 *3 *1)
+ (-12 (-5 *3 (-934 *4)) (-4 *4 (-1131)) (-5 *2 (-666 (-793)))
+ (-5 *1 (-933 *4)))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-666 (-421 (-981 (-578)))))
(-5 *2 (-666 (-666 (-306 (-981 *4))))) (-5 *1 (-393 *4))
@@ -14370,7 +15976,7 @@
(|partial| -12 (-5 *5 (-1207))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-4 *4 (-13 (-29 *6) (-1233) (-988)))
- (-5 *2 (-2 (|:| |particular| *4) (|:| -3819 (-666 *4))))
+ (-5 *2 (-2 (|:| |particular| *4) (|:| -1846 (-666 *4))))
(-5 *1 (-674 *6 *4 *3)) (-4 *3 (-678 *4))))
((*1 *2 *3 *2 *4 *2 *5)
(|partial| -12 (-5 *4 (-1207)) (-5 *5 (-666 *2))
@@ -14381,40 +15987,40 @@
(-12 (-5 *3 (-711 *5)) (-4 *5 (-376))
(-5 *2
(-2 (|:| |particular| (-3 (-1298 *5) "failed"))
- (|:| -3819 (-666 (-1298 *5)))))
+ (|:| -1846 (-666 (-1298 *5)))))
(-5 *1 (-689 *5)) (-5 *4 (-1298 *5))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-666 (-666 *5))) (-4 *5 (-376))
(-5 *2
(-2 (|:| |particular| (-3 (-1298 *5) "failed"))
- (|:| -3819 (-666 (-1298 *5)))))
+ (|:| -1846 (-666 (-1298 *5)))))
(-5 *1 (-689 *5)) (-5 *4 (-1298 *5))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-711 *5)) (-4 *5 (-376))
(-5 *2
(-666
(-2 (|:| |particular| (-3 (-1298 *5) "failed"))
- (|:| -3819 (-666 (-1298 *5))))))
+ (|:| -1846 (-666 (-1298 *5))))))
(-5 *1 (-689 *5)) (-5 *4 (-666 (-1298 *5)))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-666 (-666 *5))) (-4 *5 (-376))
(-5 *2
(-666
(-2 (|:| |particular| (-3 (-1298 *5) "failed"))
- (|:| -3819 (-666 (-1298 *5))))))
+ (|:| -1846 (-666 (-1298 *5))))))
(-5 *1 (-689 *5)) (-5 *4 (-666 (-1298 *5)))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-376)) (-4 *6 (-13 (-386 *5) (-10 -7 (-6 -4501))))
- (-4 *4 (-13 (-386 *5) (-10 -7 (-6 -4501))))
+ (-12 (-4 *5 (-376)) (-4 *6 (-13 (-386 *5) (-10 -7 (-6 -4508))))
+ (-4 *4 (-13 (-386 *5) (-10 -7 (-6 -4508))))
(-5 *2
- (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3819 (-666 *4))))
+ (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1846 (-666 *4))))
(-5 *1 (-690 *5 *6 *4 *3)) (-4 *3 (-709 *5 *6 *4))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-376)) (-4 *6 (-13 (-386 *5) (-10 -7 (-6 -4501))))
- (-4 *7 (-13 (-386 *5) (-10 -7 (-6 -4501))))
+ (-12 (-4 *5 (-376)) (-4 *6 (-13 (-386 *5) (-10 -7 (-6 -4508))))
+ (-4 *7 (-13 (-386 *5) (-10 -7 (-6 -4508))))
(-5 *2
(-666
- (-2 (|:| |particular| (-3 *7 "failed")) (|:| -3819 (-666 *7)))))
+ (-2 (|:| |particular| (-3 *7 "failed")) (|:| -1846 (-666 *7)))))
(-5 *1 (-690 *5 *6 *7 *3)) (-5 *4 (-666 *7))
(-4 *3 (-709 *5 *6 *7))))
((*1 *2 *3 *4)
@@ -14432,7 +16038,7 @@
(-4 *7 (-13 (-29 *6) (-1233) (-988)))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-5 *2
- (-2 (|:| |particular| (-1298 *7)) (|:| -3819 (-666 (-1298 *7)))))
+ (-2 (|:| |particular| (-1298 *7)) (|:| -1846 (-666 (-1298 *7)))))
(-5 *1 (-824 *6 *7)) (-5 *4 (-1298 *7))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-711 *6)) (-5 *4 (-1207))
@@ -14444,27 +16050,27 @@
(-5 *5 (-1207)) (-4 *7 (-13 (-29 *6) (-1233) (-988)))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-5 *2
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(-5 *1 (-824 *6 *7))))
((*1 *2 *3 *4 *5)
(|partial| -12 (-5 *3 (-666 *7)) (-5 *4 (-666 (-116)))
(-5 *5 (-1207)) (-4 *7 (-13 (-29 *6) (-1233) (-988)))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-5 *2
- (-2 (|:| |particular| (-1298 *7)) (|:| -3819 (-666 (-1298 *7)))))
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(-5 *1 (-824 *6 *7))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-306 *7)) (-5 *4 (-116)) (-5 *5 (-1207))
(-4 *7 (-13 (-29 *6) (-1233) (-988)))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-5 *2
- (-3 (-2 (|:| |particular| *7) (|:| -3819 (-666 *7))) *7 "failed"))
+ (-3 (-2 (|:| |particular| *7) (|:| -1846 (-666 *7))) *7 "failed"))
(-5 *1 (-824 *6 *7))))
((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-116)) (-5 *5 (-1207))
(-4 *6 (-13 (-319) (-1069 (-578)) (-660 (-578)) (-149)))
(-5 *2
- (-3 (-2 (|:| |particular| *3) (|:| -3819 (-666 *3))) *3 "failed"))
+ (-3 (-2 (|:| |particular| *3) (|:| -1846 (-666 *3))) *3 "failed"))
(-5 *1 (-824 *6 *3)) (-4 *3 (-13 (-29 *6) (-1233) (-988)))))
((*1 *2 *3 *4 *3 *5)
(|partial| -12 (-5 *3 (-306 *2)) (-5 *4 (-116)) (-5 *5 (-666 *2))
@@ -14500,10 +16106,10 @@
(|partial| -12
(-5 *5
(-1
- (-3 (-2 (|:| |particular| *6) (|:| -3819 (-666 *6))) "failed")
+ (-3 (-2 (|:| |particular| *6) (|:| -1846 (-666 *6))) "failed")
*7 *6))
(-4 *6 (-376)) (-4 *7 (-678 *6))
- (-5 *2 (-2 (|:| |particular| (-1298 *6)) (|:| -3819 (-711 *6))))
+ (-5 *2 (-2 (|:| |particular| (-1298 *6)) (|:| -1846 (-711 *6))))
(-5 *1 (-835 *6 *7)) (-5 *3 (-711 *6)) (-5 *4 (-1298 *6))))
((*1 *2 *3) (-12 (-5 *3 (-925)) (-5 *2 (-1066)) (-5 *1 (-924))))
((*1 *2 *3 *4)
@@ -14576,406 +16182,114 @@
((*1 *2 *3)
(-12 (-4 *4 (-570)) (-5 *2 (-666 (-306 (-421 (-981 *4)))))
(-5 *1 (-1216 *4)) (-5 *3 (-306 (-421 (-981 *4)))))))
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- (-5 *2
- (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3)))
- (-5 *1 (-1000 *4 *3)) (-4 *3 (-1274 *4)))))
+(((*1 *2 *3 *4 *4)
+ (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1289 *4)) (-5 *1 (-1291 *4 *2))
+ (-4 *4 (-38 (-421 (-578)))))))
(((*1 *2 *3)
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- (-5 *1 (-614 *4 *3 *2)) (-4 *3 (-13 (-444 *4) (-1033) (-1233))))))
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(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233)))))
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(((*1 *2 *3)
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((*1 *2 *3 *4)
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